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textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.03%3A_Build_a_Transformer.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Steel flat bar, 4 pieces • Miscellaneous bolts, nuts, washers • 28 gauge “magnet” wire • Low-voltage AC power supply “Magnet wire” is small-gauge wire insulated with a thin enamel coating. It is intended to be used to make electromagnets, because many “turns” of wire may be wrapped in a relatively small-diameter coil. Any gauge of wire will work, but 28 gauge is recommended so as to make a coil with as many turns as possible in a small diameter. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 9: “Transformers” LEARNING OBJECTIVES • Effects of electromagnetism. • Effects of electromagnetic induction. • Effects of magnetic coupling on voltage regulation. • Effects of a winding turn on “step” ratio. SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Wrap two, equal-length bars of steel with a thin layer of electrically-insulating tape. Wrap several hundred turns of magnet wire around these two bars. You may make these windings with an equal or unequal number of turns, depending on whether or not you want the transformer to be able to “step” voltage up or down. I recommend equal turns, to begin with, then experiment later with coils of unequal turn count. Join those bars together in a rectangle with two other, shorter, bars of steel. Use bolts to secure the bars together (it is recommended that you drill bolt holes through the bars before you wrap the wire around them). Check for shorted windings (ohmmeter reading between wire ends and steel bar) after you’re finished wrapping the windings. There should be no continuity (infinite resistance) between the winding and the steel bar. Check for continuity between winding ends to ensure that the wire isn’t broken open somewhere within the coil. If either resistance measurements indicate a problem, the winding must be re-made. Power your transformer with the low-voltage output of the “power supply” described at the beginning of this chapter. Do not power your transformer directly from wall-socket voltage (120 volts), as your home-made windings really aren’t rated for any significant voltage! Measure the output voltage (secondary winding) of your transformer with an AC voltmeter. Connect a load of some kind (light bulbs are good!) to the secondary winding and re-measure voltage. Note the degree of voltage “sag” at the secondary winding as the load current is increased. Loosen or remove the connecting bolts from one of the short bar pieces, thus increasing the reluctance(analogous to resistance) of the magnetic “circuit” coupling the two windings together. Note the effect on the output voltage and voltage “sag” under load. If you’ve made your transformer with unequal-turn windings. try it in step-up versus step-down mode, powering different AC loads. 4.04: Variable Inductor PARTS AND MATERIALS • Paper tube, from a toilet-paper roll • Bar of iron or steel, large enough to almost fill diameter of paper tube • 28 gauge “magnet” wire • Low-voltage AC power supply • Incandescent lamp, rated for power supply voltage CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 14: “Magnetism and Electromagnetism” Lessons In Electric Circuits, Volume 1, chapter 15: “Inductors” Lessons In Electric Circuits, Volume 2, chapter 3: “Reactance and Impedance—Inductive” LEARNING OBJECTIVES • Effects of magnetic permeability on inductance. • How inductive reactance can control current in an AC circuit. SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Wrap hundreds of turns of magnet wire around the paper tube. Connect this home-made inductor in series with an AC power supply and lamp to form a circuit. When the tube is empty, the lamp should glow brightly. When the steel bar is inserted in the tube, the lamp dims from increased inductance (L) and consequently increased inductive reactance (XL). Try using bars of different materials, such as copper and stainless steel, if available. Not all metals have the same effect, due to differences in magnetic permeability.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.05%3A_Sensitive_Audio_Detector.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • High-quality “closed-cup” audio headphones • Headphone jack: female receptacle for headphone plug (Radio Shack catalog # 274-312) • Small step-down power transformer (Radio Shack catalog # 273-1365 or equivalent, using the 6-volt secondary winding tap) • Two 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • 1 kΩ resistor • 100 kΩ potentiometer (Radio Shack catalog # 271-092) • Two “banana” jack style binding posts, or other terminal hardware, for connection to potentiometer circuit (Radio Shack catalog # 274-662 or equivalent) • Plastic or metal mounting box Regarding the headphones, the higher the “sensitivity” rating in decibels (dB), the better, but listening is believing: if you’re serious about building a detector with maximum sensitivity for small electrical signals, you should try a few different headphone models at a high-quality audio store and “listen” for which ones produce an audible sound for the lowest volume setting on a radio or CD player. Beware, as you could spend hundreds of dollars on a pair of headphones to get the absolute best sensitivity! Take heart, though: I’ve used an old pair of Radio Shack “Realistic” brand headphones with perfectly adequate results, so you don’t need to buy the best. Normally, the transformer used in this type of application (audio speaker impedance matching) is called an “audio transformer,” with its primary and secondary windings represented by impedance values (1000 Ω: 8 Ω) instead of voltages. An audio transformer will work, but I’ve found small step-down power transformers of 120/6 volt ratio to be perfectly adequate for the task, cheaper (especially when taken from an old thrift-store alarm clock radio), and far more rugged.Ω: 8 Ω) instead of voltages. An audio transformer will work, but I’ve found small step-down power transformers of 120/6 volt ratio to be perfectly adequate for the task, cheaper (especially when taken from an old thrift-store alarm clock radio), and far more rugged. The tolerance (precision) rating for the 1 kΩ resistor is irrelevant. The 100 kΩ potentiometer is a recommended option for incorporation into this project, as it gives the user control over the loudness for any given signal. Even though an audio-taper potentiometer would be appropriate for this application, it is not necessary. A linear-taper potentiometer works quite well. CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 8: “DC Metering Circuits” Lessons In Electric Circuits, Volume 2, chapter 9: “Transformers” Lessons In Electric Circuits, Volume 2, chapter 12: “AC Metering Circuits” LEARNING OBJECTIVES • Soldering practice • Use of a transformer for impedance matching • Detection of extremely small electrical signals • Using diodes to “clip” voltage at some maximum level SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This experiment is identical in construction to the “Sensitive Voltage Detector” described in the DC experiments chapter. If you’ve already built this detector, you may skip this experiment. The headphones, most likely being stereo units (separate left and right speakers) will have a three-contact plug. You will be connecting to only two of those three contact points. If you only have a “mono” headphone set with a two-contact plug, just connect to those two contact points. You may either connect the two stereo speakers in series or in parallel. I’ve found the series connection to work best, that is, to produce the most sound from a small signal: Solder all wire connections well. This detector system is extremely sensitive, and any loose wire connections in the circuit will add unwanted noise to the sounds produced by the measured voltage signal. The two diodes connected in parallel with the transformer’s primary winding, along with the series-connected 1 kΩ resistor, work together to “clip” the input voltage to a maximum of about 0.7 volts. This does one thing and one thing only: limit the amount of sound the headphones can produce. The system will work without the diodes and resistor in place, but there will be no limit to sound volume in the circuit, and the resulting sound caused by accidentally connecting the test leads across a substantial voltage source (like a battery) can be deafening! Binding posts provide points of connection for a pair of test probes with banana-style plugs, once the detector components are mounted inside a box. You may use ordinary multimeter probes, or make your own probes with alligator clips at the ends for secure connection to a circuit. Detectors are intended to be used for balancing bridge measurement circuits, potentiometric (null-balance) voltmeter circuits, and detect extremely low-amplitude AC (“alternating current”) signals in the audio frequency range. It is a valuable piece of test equipment, especially for the low-budget experimenter without an oscilloscope. It is also valuable in that it allows you to use a different bodily sense in interpreting the behavior of a circuit. For connection across any non-trivial source of voltage (1 volt and greater), the detector’s extremely high sensitivity should be attenuated. This may be accomplished by connecting a voltage divider to the “front” of the circuit: SCHEMATIC DIAGRAM ILLUSTRATION Adjust the 100 kΩ voltage divider potentiometer to about mid-range when initially sensing a voltage signal of unknown magnitude. If the sound is too loud, turn the potentiometer down and try again. If too soft, turn it up and try again. This detector even senses DC and radio-frequency signals (frequencies below and above the audio range, respectively), a “click” is heard whenever the test leads make or break contact with the source under test. With my cheap headphones, I’ve been able to detect currents of less than 1/10 of a microamp ( < 0.1 µA) DC, and similarly low-magnitude RF signals up to 2 MHz. A good demonstration of the detector’s sensitivity is to touch both tests leads to the end of your tongue, with the sensitivity adjustment set to maximum. The voltage produced by metal-to-electrolyte contact (called galvanic voltage) is very small, but enough to produce soft “clicking” sounds every time the leads make and break contact on the wet skin of your tongue. Try unplugging the headphone plug from the jack (receptacle) and similarly touching it to the end of your tongue. You should still hear soft clicking sounds, but they will be much smaller in amplitude. Headphone speakers are “low impedance” devices: they require low voltage and “high” current to deliver substantial sound power. Impedance is a measure of opposition to any and all forms of electric current, including alternating current (AC). Resistance, by comparison, is a strict measure of opposition to direct current (DC). Like resistance, impedance is measured in the unit of the Ohm (Ω), but it is symbolized in equations by the capital letter “Z” rather than the capital letter “R”. We use the term “impedance” to describe the headphone’s opposition to current because it is primarily AC signals that headphones are normally subjected to, not DC. Most small signal sources have high internal impedances, some much higher than the nominal 8 Ω of the headphone speakers. This is a technical way of saying that they are incapable of supplying substantial amounts of current. As the Maximum Power Transfer Theorem predicts, maximum sound power will be delivered by the headphone speakers when their impedance is “matched” to the impedance of the voltage source. The transformer does this. The transformer also helps aid the detection of small DC signals by producing inductive “kickback” every time the test lead circuit is broken, thus “amplifying” the signal by magnetically storing up electrical energy and suddenly releasing it to the headphone speakers. As with the low-voltage AC power supply experiment, I recommend building this detector in a permanent fashion (mounting all components inside of a box and providing nice test lead wires) so it can be easily used in the future. Constructed as such, it might look something like this:
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.06%3A_Sensing_AC_Magnetic_Fields.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Audio detector with headphones • Electromagnet coil from relay or solenoid What is needed for an electromagnet coil is a coil with many turns of wire, so as to produce the most voltage possible from induction with stray magnetic fields? The coil taken from an old relay or solenoid works well for this purpose. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 7: “Mixed-Frequency AC Signals” LEARNING OBJECTIVES • Effects of electromagnetic induction. • Electromagnetic shielding techniques. SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Using the audio detector circuit explained earlier to detect AC voltage in the audio frequencies, a coil of wire may serve as a sensor of AC magnetic fields. The voltages produced by the coil will be quite small, so it is advisable to adjust the detector’s sensitivity control to “maximum.” There are many sources of AC magnetic fields to be found in the average home. Try, for instance, holding the coil close to a television screen or circuit-breaker box. The coil’s orientation is every bit as important as its proximity to the source, as you will soon discover on your own! If you want to listen to more interesting tones, try holding the coil close to the motherboard of an operating computer (be careful not to “short” any connections together on the computer’s circuit board with any exposed metal parts on the sensing coil!), or to its hard drive while a read/write operation is taking place. One very strong source of AC magnetic fields is the home-made transformer project described earlier. Try experimenting with various degrees of “coupling” between the coils (the steel bars tightly fastened together, versus loosely fastened, versus dismantled). Another source is the variable inductor and lamp circuit described in another section of this chapter. Note that physical contact with a magnetic field source is unnecessary: magnetic fields extend through space quite easily. You may also want to try “shielding” the coil from a strong source using various materials. Try aluminum foil, paper, sheet steel, plastic, or whatever other materials you can think of. What materials work best? Why? What angles (orientations) of coil position minimize magnetic coupling (result in a minimum of detected signal)? What does this tell us regarding inductor positioning if inter-circuit interference from other inductors is a bad thing? Whether or not stray magnetic fields like these pose any health hazard to the human body is a hotly debated subject. One thing is clear: in today’s modern society, low-level magnetic fields of all frequencies are easy to find! 4.07: Sensing AC Electric Fields PARTS AND MATERIALS • Audio detector with headphones CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 7: “Mixed-Frequency AC Signals” LEARNING OBJECTIVES • Effects of electrostatic (capacitive) coupling. • Electrostatic shielding techniques. SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS “Ground” one lead of the detector to a metal object in contact with the earth (dirt). Most any water pipe or faucet in a house will suffice. Take the other lead and hold it close to an electrical appliance or lamp fixture. Do not try to make contact with the appliance or with any conductors within! Any AC electric fields produced by the appliance will be heard in the headphones as a buzzing tone. Try holding the wire in different positions next to a good, strong source of electric fields. Try using a piece of aluminum foil clipped to the wire’s end to maximize capacitance (and therefore its ability to intercept an electric field). Try using different types of material to “shield” the wire from an electric field source. What material(s) work best? How does this compare with the AC magnetic field experiment? As with magnetic fields, there is controversy whether or not stray electric fields like these pose any health hazard to the human body.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.08%3A_Automotive_Alternator.txt	princeton-nlp/TextbookChapters	Project Parts and Materials • Automotive alternator (one required, but two recommended) Old alternators may be obtained for low prices at automobile wrecking yards. Many yards have alternators already removed from the automobile, for your convenience. I do not recommend paying full price for a new alternator, as used units cost far less money and function just as well for the purposes of this experiment. I highly recommend using a Delco-Remy brand of the alternator. This is the type used on General Motors (GMC, Chevrolet, Cadillac, Buick, Oldsmobile) vehicles. One particular model has been produced by Delco-Remy since the early 1960’s with little design change. It is a very common unit to locate in a wrecking yard, and very easy to work with. If you obtain two alternators, you may use one as a generator and the other as a motor. The steps needed to prepare an alternator as a three-phase generator and as a three-phase motor are the same. Learning Objectives • Effects of electromagnetism • Effects of electromagnetic induction • Construction of real electromagnetic machines • Construction and application of three-phase windings Automotive Alternator Schematic Diagram An automotive alternator is a three-phase generator with a built-in rectifier circuit consisting of six diodes. As the sheave (most people call it a “pulley”) is rotated by a belt connected to the automobile engine’s crankshaft, a magnet is spun past a stationary set of three-phase windings (called the stator), usually connected in a Y configuration. The spinning magnet is actually an electromagnet, not a permanent magnet. Alternators are designed this way so that the magnetic field strength can be controlled, in order that output voltage may be controlled independently of rotor speed. This rotor magnet coil (called the field coil, or simply field) is energized by battery power so that it takes a small amount of electrical power input to the alternator to get it to generate a lot of output power. Electrical power is conducted to the rotating field coil through a pair of copper “slip rings” mounted concentrically on the shaft, contacted by stationary carbon “brushes.” The brushes are held in firm contact with the slip rings by spring pressure. Many modern alternators are equipped with built-in “regulator” circuits that automatically switch battery power on and off to the rotor coil to regulate output voltage. This circuit, if present in the alternator you choose for the experiment, is unnecessary and will only impede your study if left in place. Feel free to “surgically remove” it, just make sure you leave access to the brush terminals so that you can power the field coil with the alternator fully assembled. Experiment Instructions First, consult an automotive repair manual on the specific details of your alternator. The documentation provided in the book you’re reading now is as general as possible to accommodate different brands of alternators. You may need more specific information, and a service manual is the best place to obtain it. For this experiment, you’ll be connecting wires to the coils inside the alternator and extending them outside the alternator case, for easy connection to test equipment and circuits. Unfortunately, the connection terminals provided by the manufacturer won’t suit our needs here, so you need to make your own connections. Disassemble the unit and locate terminals for connecting to the two carbon brushes. Solder a pair of wires to these terminals (at least 20 gauge in size) and extend these wires through vent holes in the alternator case, making sure they won’t get snagged on the spinning rotor when the alternator is re-assembled and used. Locate the three-phase line connections coming from the stator windings and connect wires to them as well, extending these wires outside the alternator case through some vent holes. Use the largest gauge wire that is convenient to work with for these wires, as they may be carrying substantial current. As with the field wires, route them in such a way that the rotor will turn freely with the alternator reassembled. The stator winding line terminals are easy to locate: the three of them connect to three terminals on the diode assembly, usually with “ring-lug” terminals soldered to the ends of the wires. I recommend that you solder ring-lug terminals to your wires, and attach them underneath the terminal nuts along with the stator wire ends so that each diode block terminal is securing two ring lugs. Re-assemble the alternator, taking care to secure the carbon brushes in a retracted position so that the rotor doesn’t damage them upon re-insertion. On Delco-Remy alternators, a small hole is provided on the back case half, and also at the front of the brush holder assembly, through which a paper clip or thin-gauge wire may be inserted to hold the brushes back against their spring pressure. Consult the service manual for more details on alternator assembly. When the alternator has been assembled, try spinning the shaft and listen for any sounds indicative of colliding parts or snagged wires. If there is any such trouble, take it apart again and correct whatever is wrong. If and when it spins freely as it should, connect the two “field” wires to a 6-volt battery. Connect a voltmeter to any two of the three-phase line connections: With the multimeter set to the “DC volts” function, slowly rotate the alternator shaft. The voltmeter reading should alternate between positive and negative as the shaft it turned: a demonstration of very slow alternating voltage (AC voltage) being generated. If this test is successful, switch the multimeter to the “AC volts” setting and try again. Try spinning the shaft slow and fast, comparing voltmeter readings between the two conditions. Short-circuit any two of the three-phase line wires and try spinning the alternator. What you should notice is that the alternator shaft becomes more difficult to spin. The heavy electrical load you’ve created via the short circuit causes a heavy mechanical load on the alternator, as mechanical energy is converted into electrical energy. Now, try connecting 12 volts DC to the field wires. Repeat the DC voltmeter, AC voltmeter, and short-circuit tests described above. What difference(s) do you notice? Find some sort of polarity-insensitive 6 or 12 volts loads, such as small incandescent lamps, and connect them to the three-phase line wires. Wrap a thin rope or heavy string around the groove of the sheave (“pulley”) and spin the alternator rapidly, and the loads should function. If you have a second alternator, modify it as you modified the first one, connecting five of your own wires to the field brushes and stator line terminals, respectively. You can then use it as a three-phase motor, powered by the first alternator. Connect each of the three-phase line wires of the first alternator to the respective wires of the second alternator. Connect the field wires of one alternator to a 6-volt battery. This alternator will be the generator. Wrap rope around the sheave in preparation to spin it. Take the two field wires of the second alternator and short them together. This alternator will be the motor: Spin the generator shaft while watching the motor shaft’s rotation. Try reversing any two of the three-phase line connections between the two units and spin the generator again. What is different this time? Connect the field wires of the motor unit to the 6-volt battery (you may parallel-connect this field with the field of the generator unit, across the same battery terminals, if the battery is strong enough to deliver the several amps of current both coils will draw together). This will magnetize the rotor of the motor. Try spinning the generator again and note any differences in operation. In the first motor setup, where the field wires were simple shorted together, the motor was functioning as an induction motor. In the second setup, where the motor’s rotor was magnetized, it functioned as a synchronous motor. Take your Modified Alternator to the Next Level If you are feeling particularly ambitious and are skilled in metal fabrication techniques, you may make your own high-power generator platform by connecting the modified alternator to a bicycle. I’ve built an arrangement that looks like this: The rear wheel drives the generator sheave with a long v-belt. This belt also supports the rear of the bicycle, maintaining a constant tension when a rider is pedaling the bicycle. The generator hangs from a steel support structure (I used welded 2-inch square tubing, but a frame could be made out of lumber). Not only is this machine practical, but it is reliable enough to be used as an exercise machine, and it is inexpensive to make: You can see a bank of three 12-volt “RV” light bulbs behind the bicycle unit (in the lower-left corner of the photograph), which I use for a load when riding the bicycle as an exercise machine. A set of three switches is mounted at the front of the bicycle, where I can turn loads on and off while riding. By rectifying the three-phase AC power produced, it is possible to have the alternator power its own field coil with DC voltage, eliminating the need for a battery. However, some independent source of DC voltage will still be necessary for start-up, as the field coil must be energized before any AC power can be produced.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.09%3A_Induction_Motor.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • AC power source: 120VAC • Capacitor, 3.3 µF (or 2.2 µF) 120VAC or 350VDC, non-polarized • 15 to 25 watt incandescent lamp or 820Ω 25 watt resistors • #32 AWG magnet wire • wooden board approx. 5 in. square. • AC line cord with plug • 1.75 inch dia. cardboard tubing (toilet paper roll) • lamp socket • AC power source: 220VAC • Capacitor, 1.5 µF 240VAC or 680VDC, non-polarized • 25 to 40 watt incandescent lamp or 820Ω 25 watt resistors • #32 AWG magnet wire • wooden board approx. 15 cm. square. • AC line cord with plug • 4.5 to 5 cm. dia. cardboard tubing. • lamp socket CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 13: “AC motors”, “Single Phase induction motors”,“Permanent split-capacitor motor”. LEARNING OBJECTIVES • To build an AC permanent capacitor split-phase induction motor. • To illustrate the simplicity of the AC induction motor. SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS There are two parts lists to choose from depending upon the availability of 120VAC or 220VAC. Choose the one for your location. This set of instructions is for the 120VAC version. This is a simplified version of a “permanent capacitor split-phase induction motor”. By simplifying, we mean the coils only requires a few hundred turns of wire instead of a few thousand. This is easier to wind. Though, the larger few thousand turns model is impressive. There are two stator coils as shown in the illustration above. Approximately 440 turns of #32 AWG (American wire gauge) enameled magnet wire are wound over a one-inch length of a slightly longer section of 1.75-inch diameter toilet paper tube. To avoid counting the turns, close-wind four layers of magnet wire over a one-inch width of the tube. See (b) above. Leave a few inches of magnet wire for the leads. Tape the beginning lead near the end of the tube so that the windings will cover and anchor the tape. Do not cut the final width of the cardboard tube until the winding is finished. Close wind a single layer. Tape or cement the first layer to prevent unwinding before proceeding to the second layer. Though it is possible to wind additional layers directly over existing layers, consider applying tape or paper between the layers as shown in schematic (b). After four layers are wound, glue the windings in place. If close winding four layers of magnet wire it too difficult, scramble wind 440 turns of the magnet wire over the end of the cardboard tube. However, the close-wound style coil mounts more easily to the baseboard. Keep the windings within a one-inch length. Cut the finished winding from the end of the cardboard tube with a razor knife allowing the form to extend a little beyond the winding. Strip the enamel from an inch off the ends of the pair of lead wires with sandpaper. Splice the bare ends to heavier gauge insulated hook-up wire. Solder the splice. Insulate with tape or heat-shrink tubing. Secure the splice to the coil body. Then proceed with a second identical coil. Refer to both the schematic diagram and the illustration for assembly. Note that the coils are mounted at right angles. They may be cemented to an insulating baseboard like wood. The 25-watt lamp is wired in series with one coil. This limits the current flowing through the coil. The lamp is a substitute for an 820 Ω power resistor. The capacitor is wired in series with the other coil. It also limits the current through the coil. In addition, it provides a leading phase shift of the current with respect to voltage. The schematic and illustration show no power switch or fuse. Add these if desired. The rotor must be made of a ferromagnetic material like a steel can lid or bottle cap. The illustration below shows how to make the rotor. Select a circular rotor either smaller than the coil forms or a little larger. Use geometry to locate and mark the center. The center needs to be dimpled. Select an eighth-inch diameter (a few mm) nail (a) and file or grind the point round as shown at (b). Place the rotor atop a piece of softwood (c) and hammer the rounded point into the center (d). Practice on a piece of similar scrap metal. Take care not to pierce the rotor. A dished rotor (f) or a lid (g) balance better than the flat rotor (e). The pivot point (e) may be a straight pin driven through a movable wooden pedestal, or through the main board. The tip of a ball-point pen also works. If the rotor does not balance atop the pivot, remove metal from the heavy side. Double check the wiring. Check that any bare wire has been insulated. The circuit may be powered-up without the rotor. The lamp should light. Both coils will warm within a few minutes. The excessive heating means that a lower wattage (higher resistance) lamp and a lower value capacitor should be substituted in series with the respective coils. Place the rotor atop the pivot and move it between both coils. It should spin. The closer it is, the faster it should spin. Both coils should be warm, indicating power. Try different size and style rotors. Try a small rotor on the opposite side of the coils compared to the illustration. For lack of #32 AWG magnet wire try 440 turns of slightly a larger diameter (lesser AWG number) wire. This will require more than 4 layers for the required turns. A night-light fixture might be less expensive than the full-size lamp socket illustrated. Though night-light bulbs are too low a wattage at 3 or 7 watts, 15-watt bulbs fit the socket.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.10%3A_Induction_Motor%2C_Large.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • AC power source: 120VAC • Capacitor, 3.3 µF 120VAC or 350VDC, non-polarized • #33 AWG magnet wire, 2 pounds • wooden board approx. 6 to 12 in. square. • AC line cord with plug • 5.1-inch dia. plastic 3-liter soda bottle • discarded ballpoint pen • misc. small wood blocks CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 13: “AC motors”, “Single Phase induction motors”,“Permanent split-capacitor motor”. LEARNING OBJECTIVES • To build a large exhibit size AC permanent split-capacitor induction motor. • To illustrate the simplicity of the AC induction motor. SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This is a larger version of a “permanent capacitor split-phase induction motor”. There are two different stator coils. The 1.0 inch wide 3200 turn L2 winding is shown in the illustration above (b), wound over a section of 5.1-inch diameter plastic 3-liter soda bottle. L1 is approximately 3800 turns of #33 AWG (American wire gauge) enameled magnet wire wound over a 1.25 width of a section of a soda bottle, wider than shown at (b). Mark a 1.25-inch wide cylinder with 0.25-inch margins on each end. The wire will be wound on the 1.25-inch zone. The form is cut from the bottle on the outside edges of the margin. Cuts of 0.25 inch from the margin to the winding zone are spaced at 1-inch intervals around the circumference of both ends so that the margin may be bent up at 90o to hold the wire on the form. To avoid counting the 3800 turns, scramble wind a 1/8 inch thickness of magnet wire over the one-inch width of the form. Else, count the turns. Scrape the enamel from 1-inch on the free end, and scrape only a small section from the lead to the spool. Do NOT cut the lead to the spool. Measure the resistance, and estimate how much more wire to wind to achieve 894 Ω. Apply enamel, nail polish, tape, or other insulation to the bare spot on the spool lead. Continue winding, and recheck the resistance. Once the approximate 894 Ω is achieved, leave a few inches of magnet wire for the lead. Cut the lead from the spool. Secure the windings to the form with lacing twine or other means. The L1 winding of 3200 turns is approximately 744 Ω and is wound on a 1.0-inch wide form as shown at (b) in a manner similar to the previous L2 winding. Strip the enamel off 1-inch of the ends of magnet wire leads if not already done. Splice the bare ends to heavier gauge insulated hook-up wire. Solder the splice. Insulate with tape or heat-shrink tubing. Secure the splice to the coil body. Then proceed with the second coil. The coils may be mounted in one corner of the wooden base. Alternatively, for more flexibility in use, they may be mounted to movable pallets. Refer to both the schematic diagram and the illustration for assembly. Note that the coils are mounted at right angles. L2, the smaller coil is wired to both sides of the 120 Vac line. The capacitor is wired in series with the wider coil L1. The capacitor provides a leading phase shift of the current with respect to voltage. The schematic and illustration show no power switch or fuse. Add these additions are recommended. If this device is intended for use by non-technicians as an unsupervised exhibit, all exposed bare terminations like the capacitor must be made finger safe by covering with shields. The switch and fuse mentioned above are necessary. Finally, the enamel on the coils only provides a single layer of insulation. For safety, a second layer such as an insulating wrapping, Plexiglas box, or other means is called for. Replace all wooden components with Plexiglas for superior fire safety in an unsupervised exhibit. The rotor must be made of a ferromagnetic material like a steel vegetable can, fruitcake can, etc. A too long vegetable can may be cut in half. The illustration for the previous small induction motor shows rotor dimpled bearing and pivot details. The rotor may be smaller than the coil forms as in the case of a cut down the vegetable can. It can even be as small as the can lid rotor used with the previous small motor. It is also possible to drive a rotor larger than the coils, which is the case with the fruitcake can. Locate and mark the center of the rotor. The center needs to be dimpled. Select an eighth-inch diameter (a few mm) nail (a) and file or grind the point round. Use this and a block of wood to dimple the rotor as shown in the previous small motor A fairly long can balances better than a flat rotor due to the lower center of gravity. The tip of a ballpoint pen works well as a pivot for larger rotors. Mount the pivot to a movable wooden pedestal. Double check the wiring. Check that any bare wire has been insulated. The circuit may be powered-up without the rotor. Excessive heating in L2 indicates that more turns are required. Excessive heat in L1 calls for a reduction in the capacitance of C1. No heat at all indicates an open circuit to the affected coil. Place the rotor atop the pivot and move it between both energized coils. It should spin. The closer it is, the faster it should spin. Both coils should be warm, indicating power. Try different size and style rotors. Try a small rotor on the opposite side of the coils compared to the illustration. Three models of this motor have been built using #33 AWG magnet wire because a large spool was on hand. AWG #32 magnet wire is probably easier to get. It should work. Although the current will be higher due to the lower resistance of the larger diameter #32 wire. If a 3.3µF capacitor is not available, use something close as long as it has an adequate voltage rating. A discarded AC motor run capacitor (bathtub shaped) was used by the author. Do no use a motor start capacitor (black cylinder). These are only usable for a few seconds of motor starting and may explode if used longer than that. Try this: It is possible to simultaneously spin more than one rotor. For example, in addition to the main rotor inside the right angle formed by the coils, place a second smaller rotor (can or bottle lid) near the pair of coils outside the right angle at the vertex. It is possible to reverse the direction of rotation by reversing one of the coils. If the coils are mounted to movable pallets, rotate one coil 180o. Another method, especially useful with fixed coils, is to wire one of the coils to a DPDT polarity reversing switch. For example, disconnect L2 and wire it to the wipers (center contacts) of the DPDT switch. The top contacts go to the 120 Vac. The top contacts also go to the bottom contacts in an X-crossover pattern.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.11%3A_Phase_Shift.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Low-voltage AC power supply • Two capacitors, 0.1 µF each, non-polarized (Radio Shack catalog # 272-135) • Two 27 kΩ resistors I recommend ceramic disk capacitors because they are insensitive to polarity (non-polarized), inexpensive, and durable. Avoid capacitors with any kind of polarity marking, as these will be destroyed when powered by AC! CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 1: “Basic AC Theory” Lessons In Electric Circuits, Volume 2, chapter 4: “Reactance and Impedance—Capacitive” LEARNING OBJECTIVES • How out-of-phase AC voltages do not add algebraically, but according to vector (phasor) arithmetic SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Build the circuit and measure voltage drops across each component with an AC voltmeter. Measure total (supply) voltage with the same voltmeter. You will discover that the voltage drops do not add up to equal the total voltage. This is due to phase shifts in the circuit: voltage dropped across the capacitors is out-of-phase with voltage dropped across the resistors, and thus the voltage drop figures do not add up as one might expect. Taking phase angle into consideration, they do add up to equal the total, but a voltmeter doesn’t provide phase angle measurements, only amplitude. Try measuring voltage dropped across both resistors at once. This voltage drop will equal the sum of the voltage drops measured across each resistor separately. This tells you that both the resistors’ voltage drop waveforms are in-phase with each other since they add simply and directly. Measure voltage dropped across both capacitors at once. This voltage drop, like the drop measured across the two resistors, will equal the sum of the voltage drops measured across each capacitor separately. Likewise, this tells you that both the capacitors’ voltage drop waveforms are in-phase with each other. Given that the power supply frequency is 60 Hz (household power frequency in the United States), calculate impedances for all components and determine all voltage drops using Ohm’s Law (E=IZ ; I=E/Z ; Z=E/I). The polar magnitudes of the results should closely agree with your voltmeter readings. COMPUTER SIMULATION Schematic with SPICE node numbers: The two large-value resistors Rbogus1 and Rbogus1 are connected across the capacitors to provide a DC path to ground in order that SPICE will work. This is a “fix” for one of SPICE’s quirks, to avoid it from seeing the capacitors as open circuits in its analysis. These two resistors are entirely unnecessary in the real circuit. Netlist (make a text file containing the following text, verbatim): 4.12: Sound Cancellation PARTS AND MATERIALS • Low-voltage AC power supply • Two audio speakers • Two 220 Ω resistors Large, low-frequency (“woofer”) speakers are most appropriate for this experiment. For optimum results, the speakers should be identical and mounted in enclosures. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 1: “Basic AC Theory” LEARNING OBJECTIVES • How phase shift can cause waves to either reinforce or interfere with each other • The importance of speaker “phasing” in stereo systems SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Connect each speaker to the low-voltage AC power supply through a 220 Ω resistor. The resistor limits the amount of power delivered to each speaker by the power supply. A low-pitched, 60-Hertz tone should be heard from the speakers. If the tone sounds too loud, use higher-value resistors. With both speakers connected and producing sound, position them so that they are only a foot or two away, facing toward each other. Listen to the volume of the 60-Hertz tone. Now, reverse the connections (the “polarity”) of just one of the speakers and note the volume again. Try switching the polarity of one speaker back and forth from original to reversed, comparing volume levels each way. What do you notice? By reversing wire connections to one speaker, you are reversing the phase of that speaker’s sound wave in reference to the other speaker. In one mode, the sound waves will reinforce one another for a strong volume. In the other mode, the sound waves will destructively interfere, resulting in diminished volume. This phenomenon is common to all wave events: sound waves, electrical signals (voltage “waves”), waves in water, and even light waves! Multiple speakers in a stereo sound system must be properly “phased” so that their respective sound waves don’t cancel each other, leaving less total sound level for the listener(s) to hear. So, even in an AC system where there really is no such thing as constant “polarity,” the sequence of wire connections may make a significant difference in system performance. This principle of volume reduction by destructive interference may be exploited for noise cancellation. Such systems sample the waveform of the ambient noise, then produce an identical sound signal 180o out of phase with the noise. When the two sound signals meet, they cancel each other out, ideally eliminating all the noise. As one might guess, this is much easier accomplished with noise sources of steady frequency and amplitude. Cancellation of random, broad-spectrum noise is very difficult, as some sort of signal-processing circuit must sample the noise and generate precisely the right amount of cancellation sound at just the right time in order to be effective.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.13%3A_Musical_Keyboard_as_a_Signal_Generator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Electronic “keyboard” (musical) • “Mono” (not stereo) headphone-type plug • Impedance matching transformer (1k Ω to 8 Ω ratio; Radio Shack catalog # 273-1380) • 10 kΩ resistor In this experiment, you’ll learn how to use an electronic musical keyboard as a source of variable-frequency AC voltage signals. You need not purchase an expensive keyboard for this—but one with at least a few dozen “voice” selections (piano, flute, harp, etc.) would be good. The “mono” plug will be plugged into the headphone jack of the musical keyboard, so get a plug that’s the correct size for the keyboard. The “impedance matching transformer” is a small-size transformer easily obtained from an electronics supply store. One may be scavenged from a small, junk radio: it connects between the speaker and the circuit board (amplifier), so is easily identifiable by location. The primary winding is rated in ohms of impedance (1000 Ω), and is usually center-tapped. The secondary winding is 8 Ω and not center-tapped. These impedance figures are not the same as DC resistance, so don’t expect to read 1000 Ω and 8 Ω with your ohmmeter—however, the 1000 Ω winding will read more resistance than the 8 Ω winding, because it has more turns. If such a transformer cannot be obtained for the experiment, a regular 120V/6V step-down power transformer works fairly well, too. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 1: “Basic AC Theory” Lessons In Electric Circuits, Volume 2, chapter 7: “Mixed-Frequency AC Signals” LEARNING OBJECTIVES • Difference between amplitude and frequency • Measuring AC voltage, current with a meter • Transformer operation, step-up SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Normally, a student of electronics in a school would have access to a device called a signal generator, or function generator used to make variable-frequency voltage waveforms to power AC circuits. An inexpensive electronic keyboard is a cheaper alternative to a regular signal generator and provides features that most signal generators cannot match, such as producing mixed-frequency waves. To “tap in” to the AC voltage produced by the keyboard, you’ll need to insert a plug into the headphone jack (sometimes just labeled “phone” on the keyboard) complete with two wires for connection to circuits of your own design. When you insert the plug into the jack, the normal speaker built into the keyboard will be disconnected (assuming the keyboard is equipped with one), and the signal that used to power that speaker will be available at the plug wires. In this particular experiment, I recommend using the keyboard to power the 8 Ω side of an audio “output” transformer to step up voltage to a higher level. If using a power transformer instead of an audio output transformer, connect the keyboard to the low-voltage winding so that it operates as a step-up device. Keyboards produce very low voltage signals, so there is no shock hazard in this experiment. Using an inexpensive Yamaha keyboard, I have found that the “panflute” voice setting produces the truest sine-wave waveform. This waveform, or something close to it (flute, for example), is recommended to start experimenting with since it is relatively free of harmonics (many waveforms mixed together, of integer-multiple frequency). Being composed of just one frequency, it is a less complex waveform for your multimeter to measure. Make sure the keyboard is set to a mode where the note will be sustained as any key is held down—otherwise, the amplitude (voltage) of the waveform will be constantly changing (high when the key is first pressed, then decaying rapidly to zero). Using an AC voltmeter, read the voltage direct from the headphone plug. Then, read the voltage as stepped up by the transformer, noting the step ratio. If your multimeter has a “frequency” function, use it to measure the frequency of the waveform produced by the keyboard. Try different notes on the keyboard and record their frequencies. Do you notice a pattern in frequency as you activate different notes, especially keys that are similar to each other (notice the 12-key black-and-white pattern repeated on the keyboard from left to right)? If you don’t mind making marks on your keyboard, write the frequencies in Hertz in black ink on the white keys, near the tops where fingers are less likely to rub the numbers off. Ideally, there should be no change in signal amplitude (voltage) as different frequencies (notes on the keyboard) are tried. If you adjust the volume up and down, you should discover that changes in amplitude should have little or no impact on frequency measurement. Amplitude and frequency are two completely independent aspects of an AC signal. Try connecting the keyboard output to a 10 kΩ load resistance (through the headphone plug), and measure AC current with your multimeter. If your multimeter has a frequency function, you can measure the frequency of this current as well. It should be the same as for the voltage for any given note (keyboard key).
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.14%3A_PC_Oscilloscope.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • IBM-compatible personal computer with sound card, running Windows 3.1 or better • Winscope software, downloaded free from internet • Electronic “keyboard” (musical) • “Mono” (not stereo) headphone-type plug for keyboard • “Mono” (not stereo) headphone-type plug for computer sound card microphone input • 10 kΩ potentiometer The Winscope program I’ve used was written by Dr. Constantin Zeldovich, for free personal and academic use. It plots waveforms on the computer screen in response to AC voltage signals interpreted by the sound card microphone input. A similar program, called Oscope, is made for the Linux operating system. If you don’t have access to either software, you may use the “sound recorder” utility that comes stock with most versions of Microsoft Windows to display crude waveshapes. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 7: “Mixed-Frequency AC Signals” Lessons In Electric Circuits, Volume 2, chapter 12: “AC Metering Circuits” LEARNING OBJECTIVES • Computer use • Basic oscilloscope function SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS The oscilloscope is an indispensable test instrument for the electronics student and professional. No serious electronics lab should be without one (or two!). Unfortunately, commercial oscilloscopes tend to be expensive, and it is almost impossible to design and build your own without another oscilloscope to troubleshoot it! However, the sound card of a personal computer is capable of “digitizing” low-voltage AC signals from a range of a few hundred Hertz to several thousand Hertz with respectable resolution, and free software is available for displaying these signals in oscilloscope form on the computer screen. Since most people either have a personal computer or can obtain one for less cost than an oscilloscope, this becomes a viable alternative for the experimenter on a budget. One word of caution: you can cause significant hardware damage to your computer if signals of excessive voltage are connected to the sound card’s microphone input! The AC voltages produced by a musical keyboard are too low to cause damage to your computer through the sound card, but other voltage sources might be hazardous to your computer’s health. Use this “oscilloscope” at your own risk! Using the keyboard and plug arrangement described in the previous experiment, connect the keyboard output to the outer terminals of a 10 kΩ potentiometer. Solder two wires to the connection points on the sound card microphone input plug, so that you have a set of “test leads” for the “oscilloscope.” Connect these test leads to the potentiometer: between the middle terminal (the wiper) and either of the outer terminals. Start the Winscope program and click on the “arrow” icon in the upper-left corner (it looks like the “play” arrow seen on tape player and CD player control buttons). If you press a key on the musical keyboard, you should see some kind of waveform displayed on the screen. Choose the “panflute” or some other flute-like voice on the musical keyboard for the best sine-wave shape. If the computer displays a waveform that looks kind of like a square wave, you need to adjust the potentiometer for a lower-amplitude signal. Almost any waveshape will be “clipped” to look like a square wave if it exceeds the amplitude limit of the sound card. Test different instrument “voices” on the musical keyboard and note the different waveshapes. Note how complex some of the waveshapes are, compared to the panflute voice. Experiment with the different controls in the Winscope window, noting how they change the appearance of the waveform. As a test instrument, this “oscilloscope” is quite poor. It has almost no capability to make precision measurements of voltage, although its frequency precision is surprisingly good. It is very limited in the range of voltage and frequency it can display, relegating it to the analysis of low- and mid-range audio tones. I have had very little success getting the “oscilloscope” to display good square waves, presumably because of its limited frequency response. Also, the coupling capacitor found in sound card microphone input circuits prevents it from measuring DC voltage: it is as though the “AC coupling” feature of a normal oscilloscope were stuck “on.” Despite these shortcomings, it is useful as a demonstration tool, and for initial explorations into waveform analysis for the beginning student of electronics. For those who are interested, there are several professional-quality oscilloscope adapter devices manufactured for personal computers whose performance is far beyond that of a sound card, and they are typically sold at less cost than a complete stand-alone oscilloscope (around \$400, the year 2002). Radio Shack sells one made by Velleman, catalog # 910-3914. Having a computer serve as the display medium brings many advantages, not the least of which is the ability to easily store waveform pictures as digital files.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.15%3A_Waveform_Analysis.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • IBM-compatible personal computer with sound card, running Windows 3.1 or better • Winscope software, downloaded free from internet • Electronic “keyboard” (musical) • “Mono” (not stereo) headphone-type plug for keyboard • “Mono” (not stereo) headphone-type plug for computer sound card microphone input, with wires for connecting to voltage sources • 10 kΩ potentiometer Parts and equipment for this experiment are identical to those required for the “PC oscilloscope” experiment. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 7: “Mixed-Frequency AC Signals” LEARNING OBJECTIVES • Understand the difference between time-domain and frequency-domain plots • Develop a qualitative sense of Fourier analysis SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS The Winscope program comes with another feature other than the typical “time-domain” oscilloscope display: “frequency-domain” display, which plots amplitude (vertical) over frequency (horizontal). An oscilloscope’s “time-domain” display plots amplitude (vertical) over time (horizontal), which is fine for displaying waveshape. However, when it is desirable to see the harmonic constituency of a complex wave, a frequency-domain plot is the best tool. If using Winscope, click on the “rainbow” icon to switch to frequency-domain mode. Generate a sine-wave signal using the musical keyboard (panflute or flute voice), and you should see a single “spike” on the display, corresponding to the amplitude of the single-frequency signal. Moving the mouse cursor beneath the peak should result in the frequency being displayed numerically at the bottom of the screen. If two notes are activated on the musical keyboard, the plot should show two distinct peaks, each one corresponding to a particular note (frequency). Basic chords (three notes) produce three spikes on the frequency-domain plot, and so on. Contrast this with a normal oscilloscope (time-domain) plot by clicking once again on the “rainbow” icon. A musical chord displayed in time-domain format is a very complex waveform but is quite simple to resolve into constituent notes (frequencies) on a frequency-domain display. Experiment with different instrument “voices” on the musical keyboard, correlating the time-domain plot with the frequency-domain plot. Waveforms that are symmetrical above and below their centerlines contain only odd-numbered harmonics (odd-integer multiples of the base, or fundamental frequency), while non symmetrical waveforms contain even-numbered harmonics as well. Use the cursor to locate the specific frequency of each peak on the plot, and a calculator to determine whether each peak is even- or odd-numbered. 4.16: Inductor-Capacitor “tank” Circuit PARTS AND MATERIALS • Oscilloscope • Assortment of non-polarized capacitors (0.1 µF to 10 µF) • Step-down power transformer (120V / 6 V) • 10 kΩ resistors • Six-volt battery The power transformer is used simply as an inductor, with only one winding connected. The unused winding should be left open. A simple iron core, single-winding inductor (sometimes known as a choke) may also be used, but such inductors are more difficult to obtain than power transformers. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 6: “Resonance” LEARNING OBJECTIVES • How to build a resonant circuit • Effects of capacitor size on resonant frequency • How to produce antiresonance SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS If an inductor and a capacitor are connected in parallel with each other, and then briefly energized by connection to a DC voltage source, oscillations will ensue as energy is exchanged from the capacitor to inductor and vice versa. These oscillations may be viewed with an oscilloscope connected in parallel with the inductor/capacitor circuit. Parallel inductor/capacitor circuits are commonly known as tank circuits. Important note: I recommend against using a PC/sound card as an oscilloscope for this experiment because very high voltages can be generated by the inductor when the battery is disconnected (inductive “kickback”). These high voltages will surely damage the sound card’s input, and perhaps other portions of the computer as well. A tank circuit’s natural frequency, called the resonant frequency, is determined by the size of the inductor and the size of the capacitor, according to the following equation: Many small power transformers have primary (120 volts) winding inductance of approximately 1 H. Use this figure as a rough estimate of inductance for your circuit to calculate expected oscillation frequency. Ideally, the oscillations produced by a tank circuit continue indefinitely. Realistically, oscillations will decay in amplitude over the course of several cycles due to the resistive and magnetic losses of the inductor. Inductors with a high “Q” rating will, of course, produce longer-lasting oscillations than low-Q inductors. Try changing capacitor values and noting the effect on oscillation frequency. You might notice changes in the duration of oscillations as well, due to capacitor size. Since you know how to calculate resonant frequency from inductance and capacitance, can you figure out a way to calculate inductor inductance from known values of circuit capacitance (as measured by a capacitance meter) and resonant frequency (as measured by an oscilloscope)? Resistance may be intentionally added to the circuit—either in series or parallel—for the express purpose of dampening oscillations. This effect of resistance dampening tank circuit oscillation is known as antiresonance. It is analogous to the action of a shock absorber in dampening the bouncing of a car after striking a bump in the road. COMPUTER SIMULATION Schematic with SPICE node numbers: Rstray is placed in the circuit to dampen oscillations and produce a more realistic simulation. A lower Rstrayvalue causes longer-lived oscillations because less energy is dissipated. Eliminating this resistor from the circuit results in endless oscillation. Netlist (make a text file containing the following text, verbatim):
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/04%3A_AC_Circuits/4.17%3A_Signal_Coupling.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • 6 volt battery • One capacitor, 0.22 µF (Radio Shack catalog # 272-1070 or equivalent) • One capacitor, 0.047 µF (Radio Shack catalog # 272-134 or equivalent) • Small “hobby” motor, permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) • Audio detector with headphones • Length of telephone cable, several feet long (Radio Shack catalog # 278-872) Telephone cable is also available from hardware stores. Any unshielded multiconductor cable will suffice for this experiment. Cables with thin conductors (telephone cable is typically 24-gauge) produce a more pronounced effect. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 7: “Mixed-Frequency AC Signals” Lessons In Electric Circuits, Volume 2, chapter 8: “Filters” LEARNING OBJECTIVES • How to “couple” AC signals and block DC signals to a measuring instrument • How stray coupling happens in cables • Techniques to minimize inter-cable coupling SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Connect the motor to the battery using two of the telephone cable’s four conductors. The motor should run, as expected. Now, connect the audio signal detector across the motor terminals, with the 0.047 µF capacitor in series, like this: You should be able to hear a “buzz” or “whine” in the headphones, representing the AC “noise” voltage produced by the motor as the brushes make and break contact with the rotating commutator bars. The purpose of the series capacitor is to act as a high-pass filter so that the detector only receives the AC voltage across the motor’s terminals, not any DC voltage. This is precisely how oscilloscopes provide an “AC coupling” feature for measuring the AC content of a signal without any DC bias voltage: a capacitor is connected in series with one test probe. Ideally, one would expect nothing but pure DC voltage at the motor’s terminals, because the motor is connected directly in parallel with the battery. Since the motor’s terminals are electrically common with the respective terminals of the battery, and the battery’s nature is to maintain a constant DC voltage, nothing but DC voltage should appear at the motor terminals, right? Well, because of resistance internal to the battery and along the conductor lengths, current pulses drawn by the motor produce oscillating voltage “dips” at the motor terminals, causing the AC “noise” heard by the detector: Use the audio detector to measure “noise” voltage directly across the battery. Since the AC noise is produced in this circuit by pulsating voltage drops along stray resistances, the less resistance we measure across, the less noise voltage we should detect: You may also measure noise voltage dropped along either of the telephone cable conductors supplying power to the motor, by connecting the audio detector between both ends of a single cable conductor. The noise detected here originates from current pulses through the resistance of the wire: Now that we have established how AC noise is created and distributed in this circuit, let’s explore how it is coupled to adjacent wires in the cable. Use the audio detector to measure voltage between one of the motor terminals and one of the unused wires in the telephone cable. The 0.047 µF capacitor is not needed in this exercise, because there is no DC voltage between these points for the detector to detect anyway: The noise voltage detected here is due to stray capacitance between adjacent cable conductors creating an AC current “path” between the wires. Remember that no current actually goes through a capacitance, but the alternate charging and discharging action of a capacitance, whether it be intentional or unintentional, provides alternating current a pathway of sorts. If we were to try and conduct a voltage signal between one of the unused wires and a point common with the motor, that signal would become tainted with noise voltage from the motor. This could be quite detrimental, depending on how much noise was coupled between the two circuits and how sensitive one circuit was to the other’s noise. Since the primary coupling phenomenon in this circuit is capacitive in nature, higher-frequency noise voltages are more strongly coupled than lower-frequency noise voltages. If the additional signal was a DC signal, with no AC expected in it, we could mitigate the problem of coupled noise by “decoupling” the AC noise with a relatively large capacitor connected across the DC signal’s conductors. Use the 0.22 µF capacitor for this purpose, as shown: The decoupling capacitor acts as a practical short-circuit to any AC noise voltage, while not affecting DC voltage signals between those two points at all. So long as the decoupling capacitor value is significantly larger than the stray “coupling” capacitance between the cable’s conductors, the AC noise voltage will be held to a minimum. Another way of minimizing coupled noise in a cable is to avoid having two circuits share a common conductor. To illustrate, connect the audio detector between the two unused wires and listen for a noise signal: There should be far less noise detected between any two of the unused conductors than between one unused conductor and one used in the motor circuit. The reason for this drastic reduction in noise is that stray capacitance between cable conductors tends to couple the same noise voltage to both of the unused conductors in approximately equal proportions. Thus, when measuring voltage between those two conductors, the detector only “sees” the difference between two approximately identical noise signals.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.01%3A_Introduction_to_Discrete_Semiconductor_Circuits.txt	princeton-nlp/TextbookChapters	A semiconductor device is one made of silicon or any number of other specially prepared materials designed to exploit the unique properties of electrons in a crystal lattice, where electrons are not as free to move as in a conductor but are far more mobile than in an insulator. A discrete device is one contained in its own package, not built on a common semiconductor substrate with other components, as is the case with ICs, or integrated circuits. Thus, “discrete semiconductor circuits” are circuits built out of individual semiconductor components, connected together on some kind of circuit board or terminal strip. These circuits employ all the components and concepts explored in the previous chapters, so a firm comprehension of DC and AC electricity is essential before embarking on these experiments. Just for fun, one circuit is included in this section using a vacuum tube for amplification instead of a semiconductor transistor. Before the advent of transistors, “vacuum tubes” were the workhorses of the electronics industry: used to make rectifiers, amplifiers, oscillators, and many other circuits. Though now considered obsolete for most purposes, there are still some applications for vacuum tubes, and it can be fun building and operating circuits using these devices. 5.02: Commutating Diode PARTS AND MATERIALS • 6 volt battery • Power transformer, 120VAC step-down to 12VAC (Radio Shack catalog # 273-1365, 273-1352, or 273-1511). • One 1N4001 rectifying diode (Radio Shack catalog # 276-1101) • One neon lamp (Radio Shack catalog # 272-1102) • Two toggle switches, SPST (“Single-Pole, Single-Throw”) A power transformer is specified, but any iron-core inductor will suffice, even the home-made inductor or transformer from the AC experiments chapter! The diode need not be an exact model 1N4001. Any of the “1N400X” series of rectifying diodes are suitable for the task, and they are quite easy to obtain. I recommend household light switches for their low cost and durability. CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 16: “RC and L/R Time Constants” Lessons In Electric Circuits, Volume 3, chapter 3: “Diodes and Rectifiers” LEARNING OBJECTIVES • Review inductive “kickback” • Learn how to suppress “kickback” using a diode SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS When assembling the circuit, be very careful of the diode’s orientation. The cathode end of the diode (the end marked with a single band) must face the positive (+) side of the battery. The diode should be reverse-biased and nonconducting with switch #1 in the “on” position. Use the high-voltage (120 V) winding of the transformer for the inductor coil. The primary winding of a step-down transformer has more inductance than the secondary winding and will give a greater lamp-flashing effect. Set switch #2 to the “off” position. This disconnects the diode from the circuit so that it has no effect. Quickly close and open (turn “on” and then “off”) switch #1. When that switch is opened, the neon bulb will flash from the effect of inductive “kickback.” Rapid current decrease caused by the switch’s opening causes the inductor to create a large voltage drop as it attempts to keep current at the same magnitude and going in the same direction. Inductive kickback is detrimental to switch contacts, as it causes excessive arcing whenever they are opened. In this circuit, the neon lamp actually diminishes the effect by providing an alternate current path for the inductor’s current when the switch opens, dissipating the inductor’s stored energy harmlessly in the form of light and heat. However, there is still a fairly high voltage dropped across the opening contacts of switch #1, causing undue arcing and shortened switch life. If switch #2 is closed (turned “on”), the diode will now be a part of the circuit. Quickly close and open switch #1 again, noting the difference in circuit behavior. This time, the neon lamp does not flash. Connect a voltmeter across the inductor to verify that the inductor is still receiving full battery voltage with switch #1 closed. If the voltmeter registers only a small voltage with switch #1 “on,” the diode is probably connected backward, creating a short-circuit.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.03%3A_Half-wave_Rectifier.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Low-voltage AC power supply (6-volt output) • 6-volt battery • One 1N4001 rectifying diode (Radio Shack catalog # 276-1101) • Small “hobby” motor, permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) • Audio detector with headphones • 0.1 µF capacitor (Radio Shack catalog # 272-135 or equivalent) The diode need not be an exact model 1N4001. Any of the “1N400X” series of rectifying diodes are suitable for the task, and they are quite easy to obtain. See the AC experiments chapter for detailed instructions on building the “audio detector” listed here. If you haven’t built one already, you’re missing a simple and valuable tool for experimentation. A 0.1 µF capacitor is specified for “coupling” the audio detector to the circuit so that only AC reaches the detector circuit. This capacitor’s value is not critical. I’ve used capacitors ranging from 0.27 µF to 0.015 µF with success. Lower capacitor values attenuate low-frequency signals to a greater degree, resulting in less sound intensity from the headphones, so use a greater-value capacitor value if you experience difficulty hearing the tone(s). CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 3: “Diodes and Rectifiers” LEARNING OBJECTIVES • Function of a diode as a rectifier • Permanent-magnet motor operation on AC versus DC power • Measuring “ripple” voltage with a voltmeter SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Connect the motor to the low-voltage AC power supply through the rectifying diode as shown. The diode only allows current to pass through during one half-cycle of a full positive-and-negative cycle of power supply voltage, eliminating one half-cycle from ever reaching the motor. As a result, the motor only “sees” current in one direction, albeit a pulsating current, allowing it to spin in one direction. Take a jumper wire and short past the diode momentarily, noting the effect on the motor’s operation: As you can see, permanent-magnet “DC” motors do not function well on alternating current. Remove the temporary jumper wire and reverse the diode’s orientation in the circuit. Note the effect on the motor. Measure DC voltage across the motor like this: Then, measure AC voltage across the motor as well: Most digital multimeters do a good job of discriminating AC from DC voltage, and these two measurements show the DC average and AC “ripple” voltages, respectively of the power “seen” by the motor. Ripple voltage is the varying portion of the voltage, interpreted as an AC quantity by measurement equipment although the voltage waveform never actually reverses polarity. Ripple may be envisioned as an AC signal superimposed on a steady DC “bias” or “offset” signal. Compare these measurements of DC and AC with voltage measurements taken across the motor while powered by a battery: Batteries give very “pure” DC power, and as a result, there should be very little AC voltage measured across the motor in this circuit. Whatever AC voltage is measured across the motor is due to the motor’s pulsating current draw as the brushes make and break contact with the rotating commutator bars. This pulsating current causes pulsating voltages to be dropped across any stray resistances in the circuit, resulting in pulsating voltage “dips” at the motor terminals. A qualitative assessment of ripple voltage may be obtained by using the sensitive audio detector described in the AC experiments chapter (the same device described as a “sensitive voltage detector” in the DC experiments chapter). Turn the detector’s sensitivity down for low volume, and connect it across the motor terminals through a small (0.1 µF) capacitor, like this: The capacitor acts as a high-pass filter, blocking DC voltage from reaching the detector and allowing easier “listening” of the remaining AC voltage. This is the exact same technique used in oscilloscope circuitry for “AC coupling,” where DC signals are blocked from viewing by a series-connected capacitor. With a battery powering the motor, the ripple should sound like a high-pitched “buzz” or “whine.” Try replacing the battery with the AC power supply and rectifying diode, “listening” with the detector to the low-pitched “buzz” of the half-wave rectified power: COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): This simulation plots the input voltage as a sine wave and the output voltage as a series of “humps” corresponding to the positive half-cycles of the AC source voltage. The dynamics of a DC motor are far too complex to be simulated using SPICE, unfortunately. AC source voltage is specified as 8.485 instead of 6 volts because SPICE understands AC voltage in terms of peak value only. A 6 volt RMS sine-wave voltage is actually 8.485 volts peak. In simulations where the distinction between RMS and peak value isn’t relevant, I will not bother with a RMS-to-peak conversion like this. To be truthful, the distinction is not terribly important in this simulation, but I discuss it here for your edification.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.04%3A_Full-wave_Bridge_Rectifier.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Low-voltage AC power supply (6 volt output) • Four 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • Small “hobby” motor, permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 3: “Diodes and Rectifiers” LEARNING OBJECTIVES • Design of a bridge rectifier circuit • Advantages and disadvantages of the bridge rectifier circuit, compared to the center-tap circuit SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This circuit provides full-wave rectification without the necessity of a center-tapped transformer. In applications where a center-tapped, or split-phase, source is unavailable, this is the only practical method of full-wave rectification. In addition to requiring more diodes than the center-tap circuit, the full-wave bridge suffers a slight performance disadvantage as well: the additional voltage drop caused by current having to go through two diodes in each half-cycle rather than through only one. With a low-voltage source such as the one you’re using (6 volts RMS), this disadvantage is easily measured. Compare the DC voltage reading across the motor terminals with the reading obtained from the last experiment, given the same AC power supply and the same motor. COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): 5.05: Full-wave Center-tap Rectifier PARTS AND MATERIALS • Low-voltage AC power supply (6-volt output) • Two 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • Small “hobby” motor, permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) • Audio detector with headphones • 0.1 µF capacitor • One toggle switch, SPST (“Single-Pole, Single-Throw”) It is essential for this experiment that the low-voltage AC power supply is equipped with a center tap. A transformer with a non-tapped secondary winding simply will not work for this circuit. The diodes need not be exact model 1N4001 units. Any of the “1N400X” series of rectifying diodes are suitable for the task, and they are quite easy to obtain. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 3: “Diodes and Rectifiers” LEARNING OBJECTIVES • Design of a center-tap rectifier circuit • Measuring “ripple” voltage with a voltmeter SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This rectifier circuit is called full-wave because it makes use of the entire waveform, both positive and negative half-cycles, of the AC source voltage in powering the DC load. As a result, there is less “ripple” voltage seen at the load. The RMS (Root-Mean-Square) value of the rectifier’s output is also greater for this circuit than for the half-wave rectifier. Use a voltmeter to measure both the DC and AC voltage delivered to the motor. You should notice the advantages of the full-wave rectifier immediately by the greater DC and lower AC indications as compared to the last experiment. An experimental advantage of this circuit is the ease of which it may be “de-converted” to a half-wave rectifier: simply disconnect the short jumper wire connecting the two diodes’ cathode ends together on the terminal strip. Better yet, for a quick comparison between half and full-wave rectification, you may add a switch in the circuit to open and close this connection at will: With the ability to quickly switch between half- and full-wave rectification, you may easily perform qualitative comparisons between the two different operating modes. Use the audio signal detector to “listen” to the ripple voltage present between the motor terminals for half-wave and full-wave rectification modes, noting both the intensity and the quality of the tone. Remember to use a coupling capacitor in series with the detector so that it only receives the AC “ripple” voltage and not DC voltage: COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim):
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.06%3A_Rectifier/Filter_Circuit.txt	princeton-nlp/TextbookChapters	This page was auto-generated because a user created a sub-page to this page. 5.06: Rectifier PARTS AND MATERIALS • Low-voltage AC power supply • Bridge rectifier pack (Radio Shack catalog # 276-1185 or equivalent) • Electrolytic capacitor, 1000 µF, at least 25 WVDC (Radio Shack catalog # 272-1047 or equivalent) • Four “banana” jack style binding posts, or other terminal hardware, for connection to potentiometer circuit (Radio Shack catalog # 274-662 or equivalent) • Metal box • 12-volt light bulb, 25 watt • Lamp Socket A bridge rectifier “pack” is highly recommended over constructing a bridge rectifier circuit from individual diodes, because such “packs” are made to bolt onto a metal heat sink. A metal box is recommended over a plastic box for its ability to function as a heat sink for the rectifier. A larger capacitor value is fine to use in this experiment, so long as its working voltage is high enough. To be safe, choose a capacitor with a working voltage rating at least twice the RMS AC voltage output of the low-voltage AC power supply. High-wattage 12-volt lamps may be purchased from a recreational vehicle (RV) and boating supply store. Common sizes are 25 watts and 50 watts. This lamp will be used as a “heavy” load for the power supply. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 8: “Filters” LEARNING OBJECTIVES • Capacitive filter function in an AC/DC power supply • Importance of heat sinks for power semiconductors SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This experiment involves constructing a rectifier and filter circuit for attachment to the low-voltage AC power supply constructed earlier. With this device, you will have a source of low-voltage, DC power suitable as a replacement for a battery in battery-powered experiments. If you would like to make this device its own, self-contained 120VAC/DC power supply, you may add all the componentry of the low-voltage AC supply to the “AC in” side of this circuit: a transformer, power cord, and plug. Even if you don’t choose to do this, I recommend using a metal box larger than necessary to provide room for additional voltage regulation circuitry you might choose to add to this project later. The bridge rectifier unit should be rated for a current at least as high as the transformer’s secondary winding is rated for, and for a voltage at least twice as high as the RMS voltage of the transformer’s output (this allows for peak voltage, plus an additional safety margin). The Radio Shack rectifier specified in the parts list is rated for 25 amps and 50 volts, more than enough for the output of the low-voltage AC power supply specified in the AC experiments chapter. Rectifier units of this size are often equipped with “quick-disconnect” terminals. Complimentary “quick-disconnect” lugs are sold that crimp onto the bare ends of a wire. This is the preferred method of terminal connection. You may solder wires directly to the lugs of the rectifier, but I recommend against direct soldering to any semiconductor component for two reasons: possible heat damage during soldering, and difficulty of replacing the component in the event of failure. Semiconductor devices are more prone to failure than most of the components covered in these experiments thus far, and so if you have any intention of making a circuit permanent, you should build it to be maintained. “Maintainable construction” involves, among other things, making all delicate components replaceable. It also means making “test points” accessible to meter probes throughout the circuit, so that troubleshooting may be executed with a minimum of inconvenience. Terminal strips inherently provide test points for taking voltage measurements, and they also allow for easy disconnection of wires without sacrificing connection durability. Bolt the rectifier unit to the inside of the metal box. The box’s surface area will act as a radiator, keeping the rectifier unit cool as it passes high currents. Any metal radiator surface designed to lower the operating temperature of an electronic component is called a heat sink. Semiconductor devices, in general, are prone to damage from overheating, so providing a path for heat transfer from the device(s) to the ambient air is very important when the circuit in question may handle large amounts of power. A capacitor is included in the circuit to act as a filter to reduce ripple voltage. Make sure that you connect the capacitor properly across the DC output terminals of the rectifier so that the polarities match. Being an electrolytic capacitor, it is sensitive to damage by polarity reversal. In this circuit especially, where the internal resistance of the transformer and rectifier are low and the short-circuit current consequently is high, the potential for damage is great. Warning: a failed capacitor in this circuit will likely explode with alarming force! After the rectifier/filter circuit is built, connect it to the low-voltage AC power supply like this: Measure the AC voltage output by the low-voltage power supply. Your meter should indicate approximately 6 volts if the circuit is connected as shown. This voltage measurement is the RMS voltage of the AC power supply. Now, switch your multimeter to the DC voltage function and measure the DC voltage output by the rectifier/filter circuit. It should read substantially higher than the RMS voltage of the AC input measured before. The filtering action of the capacitor provides a DC output voltage equal to the peak AC voltage, hence the greater voltage indication: Measure the AC ripple voltage magnitude with a digital voltmeter set to AC volts (or AC millivolts). You should notice a much smaller ripple voltage in this circuit than what was measured in any of the unfiltered rectifier circuits previously built. Feel free to use your audio detector to “listen” to the AC ripple voltage output by the rectifier/filter unit. As usual, connect a small “coupling” capacitor in series with the detector so that it does not respond to the DC voltage, but only the AC ripple. Very little sound should be heard. After taking unloaded AC ripple voltage measurements, connect the 25 watt light bulb to the output of the rectifier/filter circuit like this: Re-measure the ripple voltage present between the rectifier/filter unit’s “DC out” terminals. With a heavy load, the filter capacitor becomes discharged between rectified voltage peaks, resulting in greater ripple than before: If less ripple is desired under heavy-load conditions, a larger capacitor may be used, or a more complex filter circuit may be built using two capacitors and an inductor: If you choose to build such a filter circuit, be sure to use an iron-core inductor for maximum inductance, and one with thick enough wire to safely handle the full rated current of power supply. Inductors used for the purpose of filtering are sometimes referred to as chokes because they “choke” AC ripple voltage from getting to the load. If a suitable choke cannot be obtained, the secondary winding of a step-down power transformer like the type used to step 120 volts AC down to 12 or 6 volts AC in the low-voltage power supply may be used. Leave the primary (120 volts) winding open: COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): You may decrease the value of Rload in the simulation from 10 kΩ to some lower value to explore the effects of loading on ripple voltage. As it is with a 10 kΩ load resistor, the ripple is undetectable on the waveform plotted by SPICE.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.07%3A_Voltage_Regulator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Four 6 volt batteries • Zener diode, 12 volt—type 1N4742 (Radio Shack catalog # 276-563 or equivalent) • One 10 kΩ resistor Any low-voltage zener diode is appropriate for this experiment. The 1N4742 model listed here (zener voltage = 12 volts) is but one suggestion. Whatever diode model you choose, I highly recommend one with a zener voltage rating greater than the voltage of a single battery, for a maximum learning experience. It is important that you see how a zener diode functions when exposed to a voltage less than its breakdown rating. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 3: “Diodes and Rectifiers” LEARNING OBJECTIVES • Zener diode function SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Build this simple circuit, being sure to connect the diode in “reverse-bias” fashion (cathode positive and anode negative), and measure the voltage across the diode with one battery as a power source. Record this voltage drop for future reference. Also, measure and record the voltage drop across the 10 kΩ resistors. Modify the circuit by connecting two 6-volt batteries in series, for 12 volts total power source voltage. Re-measure the diode’s voltage drop, as well as the resistor’s voltage drop, with a voltmeter: Connect three, then four 6-volt batteries together in series, forming an 18 volt and 24-volt power source, respectively. Measure and record the diode’s and resistor’s voltage drops for each new power supply voltage. What do you notice about the diode’s voltage drop for these four different source voltages? Do you see how the diode voltage never exceeds a level of 12 volts? What do you notice about the resistor’s voltage drop for these four different source voltage levels? Zener diodes are frequently used as voltage regulating devices because they act to clamp the voltage drop across themselves at a predetermined level. Whatever excess voltage is supplied by the power source becomes dropped across the series resistor. However, it is important to note that a zener diode cannot make up for a deficiency in source voltage. For instance, this 12-volt zener diode does not drop 12 volts when the power source is only 6 volts strong. It is helpful to think of a zener diode as a voltage limiter: establishing a maximum voltage drop, but not a minimum voltage drop. COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): A zener diode may be simulated in SPICE with a normal diode, the reverse breakdown parameter (bv=12) set to the desired zener breakdown voltage. 5.08: Transistor as a Switch PARTS AND MATERIALS • Two 6-volt batteries • One NPN transistor—models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • One 100 kΩ resistor • One 560 Ω resistor • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) Resistor values are not critical for this experiment. Neither is the particular light emitting diode (LED) selected. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” LEARNING OBJECTIVES • Current amplification of a bipolar junction transistor SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS The red wire shown in the diagram (the one terminating in an arrowhead, connected to one end of the 100 kΩ resistor) is intended to remain loose, so that you may touch it momentarily to other points in the circuit.resistor) is intended to remain loose, so that you may touch it momentarily to other points in the circuit. If you touch the end of the loose wire to any point in the circuit more positive than it, such as the positive side of the DC power source, the LED should light up. It takes 20 mA to fully illuminate a standard LED, so this behavior should strike you as interesting because the 100 kΩ resistor to which the loose wire is attached restricts current through it to a far lesser value than 20 mA. At most, a total voltage of 12 volts across a 100 kΩ resistance yields a current of only 0.12 mA, or 120 µA! The connection made by your touching the wire to a positive point in the circuit conducts far less current than 1 mA, yet through the amplifying action of the transistor, is able to control a much greater current through the LED. Try using an ammeter to connect the loose wire to the positive side of the power source, like this: You may have to select the most sensitive current range on the meter to measure this small flow. After measuring this controlling current, try measuring the LED’s current (the controlled current) and compare magnitudes. Don’t be surprised if you find a ratio in excess of 200 (the controlled current 200 times as great as the controlling current)! As you can see, the transistor is acting as a kind of electrically-controlled switch, switching current on and off to the LED at the command of a much smaller current signal conducted through its base terminal. To further illustrate just how minuscule the controlling current is, remove the loose wire from the circuit and try “bridging” the unconnected end of the 100 kΩ resistor to the power source’s positive pole with two fingers of one hand. You may need to wet the ends of those fingers to maximize conductivity: Try varying the contact pressure of your fingers with these two points in the circuit to vary the amount of resistance in the controlling current’s path. Can you vary the brightness of the LED by doing so? What does this indicate about the transistor’s ability to act as more than just a switch; i.e. as a variable COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): In this simulation, the voltage drop across the 560 Ω resistor v(1,3) turns out to be 10.26 volts, indicating a LED current of 18.32 mA by Ohm’s Law (I=E/R). R1‘s voltage drop (voltage between nodes 1 and 2) ends up being 11.15 volts, which across 100 kΩ gives a current of only 111.5 µA. Obviously, a very small current is exerting control over a much larger current in this circuit. In case you were wondering, the is=1e-28 parameter in the diode’s .model line is there to make the diode act more like an LED with a higher forward voltage drop.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.09%3A_Static_Electricity_Sensor.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • One N-channel junction field-effect transistor, models 2N3819 or J309 recommended (Radio Shack catalog # 276-2035 is the model 2N3819) • One 6 volt battery • One 100 kΩ resistor • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • Plastic Comb The particular junction field-effect transistor, or JFET, model used in this experiment is not critical. P-channel JFETs are also okay to use but are not as popular as N-channel transistors. Beware that not all transistors share the same terminal designations, or pinouts, even if they share the same physical appearance. This will dictate how you connect the transistors together and to other components, so be sure to check the manufacturer’s specifications (component datasheet), easily obtained from the manufacturer’s website. Beware that it is possible for the transistor’s package and even the manufacturer’s datasheet to show incorrect terminal identification diagrams! Double-checking pin identities with your multimeter’s “diode check” function is highly recommended. For details on how to identify junction field-effect transistor terminals using a multimeter, consult chapter 5 of the Semiconductor volume (volume III) of this book series. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 5: “Junction Field-Effect Transistors” LEARNING OBJECTIVES • How the JFET is used as an on/off switch • How JFET current gain differs from a bipolar transistor SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This experiment is very similar to the previous experiment using a bipolar junction transistor (BJT) as a switching device to control current through an LED. In this experiment, a junction field-effect transistor is used instead, giving dramatically improved sensitivity. Build this circuit and touch the loose wire end (the wire shown in red on the schematic diagram and in the illustration, connected to the 100 kΩ resistor) with your hand. Simply touching this wire will likely have an effect on the LED’s status. This circuit makes a fine sensor of static electricity! Try scuffing your feet on a carpet and then touching the wire end if no effect on the light is seen yet. For a more controlled test, touch the wire with one hand and alternately touch the positive (+) and negative (-) terminals of the battery with one finger of your other hand. Your body acts as a conductor (albeit a poor one), connecting the gate terminal of the JFET to either terminal of the battery as you touch them. Make a note which terminal makes the LED turn on and which makes the LED turn off. Try to relate this behavior with what you’ve read about JFETs in chapter 5 of the Semiconductor volume. The fact that a JFET is turned on and off so easily (requiring so little control current), as evidenced by full on-and-off control simply by conduction of a control current through your body, demonstrates how great of a current gain it has. With the BJT “switch” experiment, a much more “solid” connection between the transistor’s gate terminal and a source of voltage was needed to turn it on. Not so with the JFET. In fact, the mere presence of static electricity can turn it on and off at a distance. To further experiment with the effects of static electricity on this circuit, brush your hair with the plastic comb and then wave the comb near the transistor, watching the effect on the LED. The action of combing your hair with a plastic object creates a high static voltage between the comb and your body. The strong electric field produced between these two objects should be detectable by this circuit from a significant distance! In case you’re wondering why there is no 560 Ω “dropping” resistor to limit current through the LED, many small-signal JFETs tend to self-limit their controlled current to a level acceptable by LEDs. The model 2N3819, for example, has a typical saturated drain current (IDSS) of 10 mA and a maximum of 20 mA. Since most LEDs are rated at a forward current of 20 mA, there is no need for a dropping resistor to limit circuit current: the JFET does it intrinsically. 5.10: Pulsed-light Sensor PARTS AND MATERIALS • Two 6-volt batteries • One NPN transistor—models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • Audio detector with headphones If you don’t have an audio detector already constructed, you can use a nice set of audio headphones (closed-cup style, that completely covers your ears) and a 120V/6V step-down transformer to build a sensitive audio detector without volume control or overvoltage protection, just for this experiment. Connect these portions of the headphone stereo plug to the transformer’s secondary (6 volts) winding: Try both the series and the parallel connection schemes for the loudest sound. If you haven’t made an audio detector as outlined in both the DC and AC experiments chapters, you really should—it is a valuable piece of test equipment for your collection. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” LEARNING OBJECTIVES • How to use a transistor as a crude common-emitter amplifier • How to use an LED as a light sensor SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This circuit detects pulses of light striking the LED and converts them into relatively strong audio signals to be heard through the headphones. Forrest Mims teaches that LEDs have the ability to produce current when exposed to light, in a manner not unlike a semiconductor solar cell. [MIM] By itself, the LED does not produce enough electrical power to drive the audio detector circuit, so a transistor is used to amplify the LED’s signals. If the LED is exposed to a pulsing source of light, a tone will be heard in the headphones. Sources of light suitable for this experiment include fluorescent and neon lamps, which blink rapidly with the 60 Hz AC power energizing them. You may also try using bright sunlight for a steady light source, then waving your fingers in front of the LED. The rapidly passing shadows will cause the LED to generate pulses of voltage, creating a brief “buzzing” sound in the headphones. LEDs serving as photo-detectors are narrow-band devices, responding to a narrow band of wavelengths close, but not identical, to that normally emitted. Infrared remote controls are a good illumination source for near-infrared LEDs employed as photo-sensors, producing a receiver sound. [MIM3] With a little imagination, it is not difficult to grasp the concept of transmitting audio information—such as music or speech—over a beam of pulsing light. Given a suitable “transmitter” circuit to pulse an LED on and off with the positive and negative crests of an audio waveform from a microphone, the “receiver” circuit shown here would convert those light pulses back into audio signals. [MIM2]
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.11%3A_Voltage_Follower.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • One NPN transistor—models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 6-volt batteries • Two 1 kΩ resistors • One 10 kΩ potentiometer, single-turn, linear taper (Radio Shack catalog # 271-1715) Beware that not all transistors share the same terminal designations, or pinouts, even if they share the same physical appearance. This will dictate how you connect the transistors together and to other components, so be sure to check the manufacturer’s specifications (component datasheet), easily obtained from the manufacturer’s website. Beware that it is possible for the transistor’s package and even the manufacturer’s datasheet to show incorrect terminal identification diagrams! Double-checking pin identities with your multimeter’s “diode check” function is highly recommended. For details on how to identify bipolar transistor terminals using a multimeter, consult chapter 4 of the Semiconductor volume (volume III) of this book series. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” LEARNING OBJECTIVES • Purpose of circuit “ground” when there is no actual connection to earth ground • Using a shunt resistor to measure current with a voltmeter • Measure amplifier voltage gain • Measure amplifier current gain • Amplifier impedance transformation SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Again, beware that the transistor you select for this experiment may not have the same terminal designations shown here, and so the breadboard layout shown in the illustration may not be correct for you. In my illustrations, I show all TO-92 package transistors with terminals labeled “CBE”: Collector, Base, and Emitter, from left to right. This is correct for the model 2N2222 transistor and some others, but not for all; not even for all NPN-type transistors! As usual, check with the manufacturer for details on the particular component(s) you choose for a project. With bipolar junction transistors, it is easy enough to verify terminal assignments with a multimeter. The voltage follower is the safest and easiest transistor amplifier circuit to build. Its purpose is to provide approximately the same voltage to a load as what is input to the amplifier but at a much greater current. In other words, it has no voltage gain, but it does have current gain. Note that the negative (-) side of the power supply is shown in the schematic diagram to be connected to ground, as indicated by the symbol in the lower-left corner of the diagram. This does not necessarily represent a connection to the actual earth. What it means is that this point in the circuit—and all points electrically common to it—constitute the default reference point for all voltage measurements in the circuit. Since voltage is by necessity a quantity relative between two points, a “common” point of reference designated in a circuit gives us the ability to speak meaningfully of voltage at particular, single points in that circuit. For example, if I were to speak of voltage at the base of the transistor (VB), I would mean the voltage measured between the transistor’s base terminal and the negative side of the power supply (ground), with the red probe touching the base terminal and the black probe touching ground. Normally, it is nonsense to speak of voltage at a single point, but having an implicit reference point for voltage measurements makes such statements meaningful: Build this circuit, and measure output voltage versus input voltage for several different potentiometer settings. Input voltage is the voltage at the potentiometer’s wiper (voltage between the wiper and circuit ground), while output voltage is the load resistor voltage (voltage across the load resistor, or emitter voltage: between the emitter and circuit ground). You should see a close correlation between these two voltages: one is just a little bit greater than the other (about 0.6 volts or so?), but a change in the input voltage gives almost equal change in the output voltage. Because the relationship between input change and output change is almost 1:1, we say that the AC voltage gain of this amplifier is nearly 1. Not very impressive, is it? Now measure current through the base of the transistor (input current) versus current through the load resistor (output current). Before you break the circuit and insert your ammeter to take these measurements, consider an alternative method: measure voltage across the base and load resistors, whose resistance values are known. Using Ohm’s Law, current through each resistor may be easily calculated: divide the measured voltage by the known resistance (I=E/R). This calculation is particularly easy with resistors of 1 kΩ value: there will be 1 milliamp of current for every volt of drop across them. For best precision, you may measure the resistance of each resistor rather than assume an exact value of 1 kΩ, but it really doesn’t matter much for the purposes of this experiment. When resistors are used to take current measurements by “translating” a current into a corresponding voltage, they are often referred to as shunt resistors. You should expect to find huge differences between input and output currents for this amplifier circuit. In fact, it is not uncommon to experience current gains well in excess of 200 for a small-signal transistor operating at low current levels. This is the primary purpose of a voltage follower circuit: to boost the current capacity of a “weak” signal without altering its voltage. Another way of thinking of this circuit’s function is in terms of impedance. The input side of this amplifier accepts a voltage signal without drawing much current. The output side of this amplifier delivers the same voltage, but at a current limited only by load resistance and the current-handling ability of the transistor. Cast in terms of impedance, we could say that this amplifier has a high input impedance (voltage dropped with very little current drawn) and a low output impedance (voltage dropped with almost unlimited current-sourcing capacity). COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): When this simulation is run through the SPICE program, it shows an input voltage of 5.937 volts and an output voltage of 5.095 volts, with an input current of 25.35 µA (2.535E-02 volts dropped across the 1 kΩ Rbase resistor). Output current is, of course, 5.095 mA, inferred from the output voltage of 5.095 volts dropped across a load resistance of exactly 1 kΩ. You may change the “potentiometer” setting in this circuit by adjusting the values of Rpot1 and Rpot2, always keeping their sum at 10 kΩ.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.12%3A_Common-Emitter_Amplifier.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • One NPN transistor—model 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 6-volt batteries • One 10 kΩ potentiometer, single-turn, linear taper (Radio Shack catalog # 271-1715) • One 1 MΩ resistor • One 100 kΩ resistor • One 10 kΩ resistor • One 1.5 kΩ resistor CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” LEARNING OBJECTIVES • Design of a simple common-emitter amplifier circuit • How to measure amplifier voltage gain • The difference between an inverting and a noninverting amplifier • Ways to introduce negative feedback in an amplifier circuit SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Build this circuit and measure output voltage (voltage measured between the transistor’s collector terminal and ground) and input voltage (voltage measured between the potentiometer’s wiper terminal and ground) for several position settings of the potentiometer. I recommend determining the output voltage range as the potentiometer is adjusted through its entire range of motion, then choosing several voltages spanning that output range to take measurements at. For example, if full rotation on the potentiometer drives the amplifier circuit’s output voltage from 0.1 volts (low) to 11.7 volts (high), choose several voltage levels between those limits (1 volt, 3 volts, 5 volts, 7 volts, 9 volts, and 11 volts). Measuring the output voltage with a meter, adjust the potentiometer to obtain each of these predetermined voltages at the output, noting the exact figure for later reference. Then, measure the exact input voltage producing that output voltage, and record that voltage figure as well. In the end, you should have a table of numbers representing several different output voltages along with their corresponding input voltages. Take any two pairs of voltage figures and calculate voltage gain by dividing the difference in output voltages by the difference in input voltages. For example, if an input voltage of 1.5 volts gives me an output voltage of 7.0 volts and an input voltage of 1.66 volts gives me an output voltage of 1.0 volt, the amplifier’s voltage gain is (7.0 - 1.0)/(1.66 - 1.5), or 6 divided by 0.16: a gain ratio of 37.50. You should immediately notice two characteristics while taking these voltage measurements: first, that the input-to-output effect is “reversed;” that is, an increasing input voltage results in a decreasing output voltage. This effect is known as signal inversion, and this kind of amplifier as an inverting amplifier. Secondly, this amplifier exhibits a very strong voltage gain: a small change in input voltage results in a large change in output voltage. This should stand in stark contrast to the “voltage follower” amplifier circuit discussed earlier, which had a voltage gain of about 1. Common-emitter amplifiers are widely used due to their high voltage gain, but they are rarely used in as crude a form as this. Although this amplifier circuit works to demonstrate the basic concept, it is very susceptible to changes in temperature. Try leaving the potentiometer in one position and heating the transistor by grasping it firmly with your hand or heating it with some other source of heat such as an electric hair dryer (WARNING: be careful not to get it so hot that your plastic breadboard melts!). You may also explore temperature effects by cooling the transistor: touch an ice cube to its surface and note the change in output voltage. When the transistor’s temperature changes, its base-emitter diode characteristics change, resulting in different amounts of base current for the same input voltage. This, in turn, alters the controlled current through the collector terminal, thus affecting output voltage. Such changes may be minimized through the use of signal feedback, whereby a portion of the output voltage is “fed back” to the amplifier’s input so as to have a negative, or canceling, effect on voltage gain. Stability is improved at the expense of voltage gain, a compromise solution, but practical nonetheless. Perhaps the simplest way to add negative feedback to a common-emitter amplifier is to add some resistance between the emitter terminal and ground so that the input voltage becomes divided between the base-emitter PN junction and the voltage drop across the new resistance: Repeat the same voltage measurement and recording exercise with the 1.5 kΩ resistor installed, calculating the new (reduced) voltage gain. Try altering the transistor’s temperature again and noting the output voltage for a steady input voltage. Does it change more or less than without the 1.5 kΩ resistor? Another method of introducing negative feedback to this amplifier circuit is to “couple” the output to the input through a high-value resistor. Connecting a 1 MΩ resistor between the transistor’s collector and base terminals works well: Although this different method of feedback accomplishes the same goal of increased stability by diminishing gain, the two feedback circuits will not behave identically. Note the range of possible output voltages with each feedback scheme (the low and high voltage values obtained with a full sweep of the input voltage potentiometer), and how this differs between the two circuits. COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): This SPICE simulation sets up a circuit with a variable DC voltage source (vin) as the input signal and measures the corresponding output voltage between nodes 2 and 0. The input voltage is varied, or “swept,” from 0 to 2 volts in 0.05-volt increments. Results are shown on a plot, with the input voltage appearing as a straight line and the output voltage as a “step” figure where the voltage begins and ends level, with a steep change in the middle where the transistor is in its active mode of operation.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.13%3A_Multi-Stage_Amplifier.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Three NPN transistors—model 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 6-volt batteries • One 10 kΩ potentiometer, single-turn, linear taper (Radio Shack catalog # 271-1715) • One 1 MΩ resistor • Three 100 kΩ resistors • Three 10 kΩ resistors CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” LEARNING OBJECTIVES • Design of a multi-stage, direct-coupled common-emitter amplifier circuit • Effect of negative feedback in an amplifier circuit SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS By connecting three common-emitter amplifier circuit together—the collector terminal of the previous transistor to the base (resistor) of the next transistor—the voltage gains of each stage compound to give a very high overall voltage gain. I recommend building this circuit without the 1 MΩ feedback resistor, to begin with, to see for yourself just how high the unrestricted voltage gain is. You may find it impossible to adjust the potentiometer for a stable output voltage (that isn’t saturated at full supply voltage or zero), the gain is so high. Even if you can’t adjust the input voltage fine enough to stabilize the output voltage in the active range of the last transistor, you should be able to tell that the output-to-input relationship is inverting; that is, the output tends to drive to a high voltage when the input goes low, and vice versa. Since any one of the common-emitter “stages” is inverting in itself, an even number of staged common-emitter amplifiers gives noninverting response, while an odd number of stages gives inverting. You may experience these relationships by measuring the collector-to-ground voltage at each transistor while adjusting the input voltage potentiometer, noting whether or not the output voltage increases or decreases with an increase in input voltage. Connect the 1 MΩ feedback resistor into the circuit, coupling the collector of the last transistor to the base of the first. Since the overall response of this three-stage amplifier is inverting, the feedback signal provided through the 1 MΩ resistor from the output of the last transistor to the input of the first should be negative in nature. As such, it will act to stabilize the amplifier’s response and minimize the voltage gain. You should notice the reduction in gain immediately by the decreased sensitivity of the output signal on input signal changes (changes in potentiometer position). Simply put, the amplifier isn’t nearly as “touchy” as it was without the feedback resistor in place. As with the simple common-emitter amplifier discussed in an earlier experiment, it is a good idea here to make a table of input versus output voltage figures with which you may calculate voltage gain. Experiment with different values of feedback resistance. What effect do you think a decrease in feedback resistance has on voltage gain? What about an increase in feedback resistance? Try it and find out! An advantage of using negative feedback to “tame” a high-gain amplifier circuit is that the resulting voltage gain becomes more dependent upon the resistor values and less dependent upon the characteristics of the constituent transistors. This is good because it is far easier to manufacture consistent resistors than consistent transistors. Thus, it is easier to design an amplifier with predictable gain by building a staged network of transistors with an arbitrarily high voltage gain, then mitigate that gain precisely through negative feedback. It is this same principle that is used to make operational amplifier circuits behave so predictably. This amplifier circuit is a bit simplified from what you will normally encounter in practical multi-stage circuits. Rarely is a pure common-emitter configuration (i.e. with no emitter-to-ground resistor) used, and if the amplifier’s service is for AC signals, the inter-stage coupling is often capacitive with voltage divider networks connected to each transistor base for proper biasing of each stage. Radio-frequency amplifier circuits are often transformer-coupled, with capacitors connected in parallel with the transformer windings for resonant tuning. COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): This simulation plots output voltage against input voltage and allows comparison between those variables in numerical form: a list of voltage figures printed to the left of the plot. You may calculate voltage gain by taking any two analysis points and dividing the difference in output voltages by the difference in input voltages, just like you do for the real circuit. Experiment with different feedback resistance values (rf) and see the impact on overall voltage gain. Do you notice a pattern? Here’s a hint: the overall voltage gain may be closely approximated by using the resistance figures of r1 and rf, without reference to any other circuit component!
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.14%3A_How_to_Build_a_Current_Mirror_Circuit.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two NPN transistors—models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 6-volt batteries • One 10 kΩ potentiometer, single-turn, linear taper (Radio Shack catalog # 271-1715) • Two 10 kΩ resistors • Four 1.5 kΩ resistors Small signal transistors are recommended so as to be able to experience “thermal runaway” in the latter portion of the experiment. Larger “power” transistors may not exhibit the same behavior at these low current levels. However, any pair of identical NPN transistors may be used to build a current mirror. Beware that not all transistors share the same terminal designations, or pinouts, even if they share the same physical appearance. This will dictate how you connect the transistors together and to other components, so be sure to check the manufacturer’s specifications (component datasheet), easily obtained from the manufacturer’s website. Beware that it is possible for the transistor’s package and even the manufacturer’s datasheet to show incorrect terminal identification diagrams! Double-checking pin identities with your multimeter’s “diode check” function is highly recommended. For details on how to identify bipolar transistor terminals using a multimeter, consult chapter 4 of the Semiconductor volume (volume III) of this book series. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” LEARNING OBJECTIVES • How to build a current mirror circuit • Current limitations of a current mirror circuit • Temperature dependence of BJTs • Experience a controlled “thermal runaway” situation SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS A current mirror may be thought of as an adjustable current regulator, the current limit being easily set by a single resistance. It is a rather crude current regulator circuit, but one that finds wide use due to its simplicity. In this experiment, you will get the opportunity to build one of these circuits, explore its current-regulating properties, and also experience some of its practical limitations firsthand. Build the circuit as shown in the schematic and illustration. You will have one extra 1.5 kΩ fixed-value resistor from the parts specified in the parts list. You will be using it in the last part of this experiment. The potentiometer sets the amount of current through transistor Q1. This transistor is connected to act as a simple diode: just a PN junction. Why use a transistor instead of a regular diode? Because it is important to match the junction characteristics of these two transistors when using them in a current mirror circuit. Voltage dropped across the base-emitter junction of Q1 is impressed across the base-emitter junction of the other transistor, Q2, causing it to turn “on” and likewise conduct current. Since voltage across the two transistors’ base-emitter junctions is the same—the two junction pairs being connected in parallel with each other—so should the current be through their base terminals, assuming identical junction characteristics and identical junction temperatures. Matched transistors should have the same β ratios, as well, so equal base currents means equal collector currents. The practical result of all this is Q2‘s collector current mimicking whatever current magnitude has been established through the collector of Q1 by the potentiometer. In other words, current through Q2 mirrors the current through Q1. Changes in load resistance (resistance connecting the collector of Q2 to the positive side of the battery) have no effect on Q1‘s current, and consequently, have no effect upon the base-emitter voltage or base current of Q2. With a constant base current and a nearly constant β ratio, Q2 will drop as much or as little collector-emitter voltage as necessary to hold its collector (load) current constant. Thus, the current mirror circuit acts to regulate current at a value set by the potentiometer, without regard to load resistance. Well, that is how it is supposed to work, anyway. Reality isn’t quite so simple, as you are about to see. In the circuit diagram shown, the load circuit of Q2 is completed to the positive side of the battery through an ammeter, for easy current measurement. Rather than solidly connect the ammeter’s black probe to a definite point in the circuit, I’ve marked five test points, TP1 through TP5, for you to touch the black test probe to while measuring current. This allows you to quickly and effortlessly change load resistance: touching the probe to TP1 results in practically no load resistance, while touching it to TP5 results in approximately 14.5 kΩ of load resistance. To begin the experiment, touch the test probe to TP4 and adjust the potentiometer through its range of travel. You should see a small, changing current indicated by your ammeter as you move the potentiometer mechanism: no more than a few milliamps. Leave the potentiometer set to a position giving a round number of milliamps and move the meter’s black test probe to TP3. The current indication should be very nearly the same as before. Move the probe to TP2, then TP1. Again, you should see a nearly unchanged amount of current. Try adjusting the potentiometer to another position, giving a different current indication, and touch the meter’s black probe to test points TP1 through TP4, noting the stability of the current indications as you change load resistance. This demonstrates the current regulating behavior of this circuit. You should note that the current regulation isn’t perfect. Despite regulating the current at nearly the value for load resistances between 0 and 4.5 kΩ, there is some variation over this range. The regulation may be much worse if load resistance is allowed to rise too high. Try adjusting the potentiometer so that maximum current is obtained, as indicated with the ammeter test probe connected to TP1. Leaving the potentiometer at that position, move the meter probe to TP2, then TP3, then TP4, and finally TP5, noting the meter’s indication at each connection point. The current should be regulated at a nearly constant value until the meter probe is moved to the last test point, TP5. There, the current indication will be substantially lower than at the other test points. Why is this? Because too much load resistance has been inserted into Q2‘s circuit. Simply put, Q2 cannot “turn on” any more than it already has, to maintain the same amount of current with this great a load resistance as with lesser load resistances. This phenomenon is common to all current-regulator circuits: there is a limited amount of resistance a current regulator can handle before it saturates. This stands to reason, as any current regulator circuit capable of supplying a constant amount of current through any load resistance imaginable would require an unlimited source of voltage to do it! Ohm’s Law (E=IR) dictates the amount of voltage needed to push a given amount of current through a given amount of resistance, and with only 12 volts of power supply voltage at our disposal, a finite limit of load current and load resistance definitely exists for this circuit. For this reason, it may be helpful to think of current regulator circuits as being current limiter circuits, for all they can really do is limit current to some maximum value. An important caveat for current mirror circuits, in general, is that of equal temperature between the two transistors. The current “mirroring” taking place between the two transistors’ collector circuits depends on the base-emitter junctions of those two transistors having the exact same properties. As the “diode equation” describes, the voltage/current relationship for a PN junction strongly depends on junction temperature. The hotter a PN junction is, the more current it will pass for a given amount of voltage drop. If one transistor should become hotter than the other, it will pass more collector current than the other, and the circuit will no longer “mirror” current as expected. When building a real current mirror circuit using discrete transistors, the two transistors should be epoxy-glued together (back-to-back) so that they remain at approximately the same temperature. To illustrate this dependence on equal temperature, try grasping one transistor between your fingers to heat it up. What happens to the current through the load resistors as the transistor’s temperature increases? Now, let go of the transistor and blow on it to cool it down to ambient temperature. Grasp the other transistor between your fingers to heat it up. What does the load current do now? In this next phase of the experiment, we will intentionally allow one of the transistors to overheat and note the effects. To avoid damaging a transistor, this procedure should be conducted no longer than is necessary to observe load current begin to “run away.” To begin, adjust the potentiometer for minimum current. Next, replace the 10 kΩ Rlimit resistor with a 1.5 kΩ resistor. This will allow a higher current to pass through Q1, and consequently through Q2 as well. Place the ammeter’s black probe on TP1 and observe the current indication. Move the potentiometer in the direction of increasing current until you read about 10 mA through the ammeter. At that point, stop moving the potentiometer and just observe the current. You will notice current begin to increase all on its own, without further potentiometer motion! Break the circuit by removing the meter probe from TP1 when the current exceeds 30 mA, to avoid damaging transistor Q2. If you carefully touch both transistors with a finger, you should notice Q2 is warm, while Q1 is cool. Warning:if Q2‘s current has been allowed to “run away” too far or for too long a time, it may become very hot! You can receive a bad burn on your fingertip by touching an overheated semiconductor component, so be careful here! What just happened to make Q2 overheat and lose current control? By connecting the ammeter to TP1, all load resistance was removed, so Q2 had to drop full battery voltage between collector and emitter as it regulated current. Transistor Q1 at least had the 1.5 kΩ resistance of Rlimit in place to drop most of the battery voltage, so its power dissipation was far less than that of Q2. This gross imbalance of power dissipation caused Q2 to heat more than Q1. As the temperature increased, Q2 began to pass more current for the same amount of base-emitter voltage drop. This caused it to heat up even faster, as it was passing more collector current while still dropping the full 12 volts between collector and emitter. The effect is known as thermal runaway, and it is possible in many bipolar junction transistor circuits, not just current mirrors. COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): Vammeter is nothing more than a zero-volt DC battery strategically placed to intercept load current. This is nothing more than a trick to measure current in a SPICE simulation, as no dedicated “ammeter” component exists in the SPICE language. It is important to remember that SPICE only recognizes the first eight characters of a component’s name. The name “vammeter” is okay, but if we were to incorporate more than one current-measuring voltage source in the circuit and name them “vammeter1” and “vammeter2”, respectively, SPICE would see them as being two instances of the same component “vammeter” (seeing only the first eight characters) and halt with an error. Something to bear in mind when altering the netlist or programming your own SPICE simulation! You will have to experiment with different resistance values of Rload in this simulation to appreciate the current-regulating nature of the circuit. With Rlimit set to 10 kΩ and a power supply voltage of 12 volts, the regulated current through Rload will be 1.1 mA. SPICE shows the regulation to be perfect (isn’t the virtual world of computer simulation so nice?), the load current remaining at 1.1 mA for a wide range of load resistances. However, if the load resistance is increased beyond 10 kΩ, even this simulation shows the load current suffering a decrease as in real life.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.15%3A_JFET_Current_Regulator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • One N-channel junction field-effect transistor, models 2N3819 or J309 recommended (Radio Shack catalog # 276-2035 is the model 2N3819) • Two 6-volt batteries • One 10 kΩ potentiometer, single-turn, linear taper (Radio Shack catalog # 271-1715) • One 1 kΩ resistor • One 10 kΩ resistor • Three 1.5 kΩ resistors For this experiment you will need an N-channel JFET, not a P-channel!experiment you will need an N-channel JFET, not a P-channel! Beware that not all transistors share the same terminal designations, or pinouts, even if they share the same physical appearance. This will dictate how you connect the transistors together and to other components, so be sure to check the manufacturer’s specifications (component datasheet), easily obtained from the manufacturer’s website. Beware that it is possible for the transistor’s package and even the manufacturer’s datasheet to show incorrect terminal identification diagrams! Double-checking pin identities with your multimeter’s “diode check” function is highly recommended. For details on how to identify junction field-effect transistor terminals using a multimeter, consult chapter 5 of the Semiconductor volume (volume III) of this book series. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 5: “Junction Field-Effect Transistors” Lessons In Electric Circuits, Volume 3, chapter 3: “Diodes and Rectifiers” LEARNING OBJECTIVES • How to use a JFET as a current regulator • How the JFET is relatively immune to changes in temperature SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Previously in this chapter, you saw how a pair of bipolar junction transistors (BJTs) could be used to form a current mirror, whereby one transistor would try to maintain the same current through it as though the other, the other’s current level is established by a variable resistance. This circuit performs the same task of regulating current but uses a single junction field-effect transistor (JFET) instead of two BJTs. The two series resistors Radjust and Rlimit set the current regulation point, while the load resistors and the test points between them serve only to demonstrate constant current despite changes in load resistance. To begin the experiment, touch the test probe to TP4 and adjust the potentiometer through its range of travel. You should see a small, changing current indicated by your ammeter as you move the potentiometer mechanism: no more than a few milliamps. Leave the potentiometer set to a position giving a round number of milliamps and move the meter’s black test probe to TP3. The current indication should be very nearly the same as before. Move the probe to TP2, then TP1. Again, you should see a nearly unchanged amount of current. Try adjusting the potentiometer to another position, giving a different current indication, and touch the meter’s black probe to test points TP1 through TP4, noting the stability of the current indications as you change load resistance. This demonstrates the current regulating behavior of this circuit. TP5, at the end of a 10 kΩ resistor, is provided for introducing a large change in load resistance. Connecting the black test probe of your ammeter to that test point gives a combined load resistance of 14.5 kΩ, which will be too much resistance for the transistor to maintain the maximum regulated current through. To experience what I’m describing here, touch the black test probe to TP1 and adjust the potentiometer for maximum current. Now, move the black test probe to TP2, then TP3, then TP4. For all these test point positions, the current will remain approximately constant. However, when you touch the black probe to TP5, the current will fall dramatically. Why? Because at this level of load resistance, there is an insufficient voltage drop across the transistor to maintain regulation. In other words, the transistor will be saturated as it attempts to provide more current than the circuit resistance will allow. Move the black test probe back to TP1 and adjust the potentiometer for minimum current. Now, touch the black test probe to TP2, then TP3, then TP4, and finally TP5. What do you notice about the current indication at all these points? When the current regulation point is adjusted to a lesser value, the transistor is able to maintain regulation over a much larger range of load resistance. An important caveat with the BJT current mirror circuit is that both transistors must be at equal temperature for the two currents to be equal. With this circuit, however, transistor temperature is almost irrelevant. Try grasping the transistor between your fingers to heat it up, noting the load current with your ammeter. Try cooling it down afterward by blowing on it. Not only is the requirement of transistor matching eliminated (due to the use of just one transistor), but the thermal effects are all but eliminated as well due to the relative thermal immunity of the field-effect transistor. This behavior also makes field-effect transistors immune to thermal runaway; a decided advantage over bipolar junction transistors. An interesting application of this current-regulator circuit is the so-called constant-current diode. Described in the “Diodes and Rectifiers” chapter of volume III, this diode isn’t really a PN junction device at all. Instead, it is a JFET with a fixed resistance connected between the gate and source terminals: A normal PN-junction diode is included in series with the JFET to protect the transistor against damage from reverse-bias voltage, but otherwise the current-regulating facility of this device is entirely provided by the field-effect transistor. COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): SPICE does not allow for “sweeping” resistance values, so to demonstrate the current regulation of this circuit over a wide range of conditions, I’ve elected to sweep the source voltage from 6 to 12 volts in 0.1-volt steps. If you wish, you can set rload to different resistance values and verify that the circuit current remains constant. With an rlimit value of 1 kΩ, the regulated current will be 291.8 µA. This current figure will most likely not be the same as your actual circuit current, due to differences in JFET parameters. Many manufacturers give SPICE model parameters for their transistors, which may be typed in the .modelline of the netlist for a more accurate circuit simulation.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.16%3A_Differential_Amplifier.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two 6-volt batteries • Two NPN transistors—models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 10 kΩ potentiometers, single-turn, linear taper (Radio Shack catalog # 271-1715) • Two 22 kΩ resistors • Two 10 kΩ resistors • One 100 kΩ resistor • One 1.5 kΩ resistor Resistor values are not especially critical in this experiment, but have been chosen to provide high voltage gain for a “comparator-like” differential amplifier behavior. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” Lessons In Electric Circuits, Volume 3, chapter 8: “Operational Amplifiers” LEARNING OBJECTIVES • Basic design of a differential amplifier circuit. • Working definitions of differential and common-mode voltages SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This circuit forms the heart of most operational amplifier circuits: the differential pair. In the form shown here, it is a rather crude differential amplifier, quite nonlinear and unsymmetrical with regard to output voltage versus input voltage(s). With a high voltage gain created by a large collector/emitter resistor ratio (100 kΩ/1.5 kΩ), though, it acts primarily as a comparator: the output voltage rapidly changing value as the two input voltage signals approach equality. Measure the output voltage (voltage at the collector of Q2 with respect to ground) as the input voltages are varied. Note how the two potentiometers have different effects on the output voltage: one input tends to drive the output voltage in the same direction (noninverting), while the other tends to drive the output voltage in the opposite direction (inverting). This is the essential nature of a differential amplifier: two complementary inputs, with contrary effects on the output signal. Ideally, the output voltage of such an amplifier is strictly a function of the difference between the two input signals. This circuit falls considerably short of the ideal, as even a cursory test will reveal. An ideal differential amplifier ignores all common-mode voltage, which is whatever level of voltage common to both inputs. For example, if the inverting input is at 3 volts and the noninverting input at 2.5 volts, the differential voltage will be 0.5 volts (3 - 2.5) but the common-mode voltage will be 2.5 volts since that is the lowest input signal level. Ideally, this condition should produce the same output signal voltage as if the inputs were set at 3.5 and 3 volts, respectively (0.5 volts differential, with a 3-volt common-mode voltage). However, this circuit does not give the same result for the two different input signal scenarios. In other words, its output voltage depends on both the differential voltage and the common-mode voltage. As imperfect as this differential amplifier is, its behavior could be worse. Note how the input signal potentiometers have been limited by 22 kΩ resistors to an adjustable range of approximately 0 to 4 volts, given a power supply voltage of 12 volts. If you’d like to see how this circuit behaves without any input signal limiting, just bypass the 22 kΩ resistors with jumper wires, allowing full 0 to 12-volt adjustment range from each potentiometer. Do not worry about building up excessive heat while adjusting potentiometers in this circuit! Unlike the current mirror circuit, this circuit is protected from thermal runaway by the emitter resistor (1.5 kΩ), which doesn’t allow enough transistor current to cause any problem
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.17%3A_Simple_Op-Amp.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two 6-volt batteries • Four NPN transistors—models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two PNP transistors—models 2N2907 or 2N3906 recommended (Radio Shack catalog # 276-1604 is a package of fifteen PNP transistors ideal for this and other experiments) • Two 10 kΩ potentiometers, single-turn, linear taper (Radio Shack catalog # 271-1715) • One 270 kΩ resistor • Three 100 kΩ resistors • One 10 kΩ resistor CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” Lessons In Electric Circuits, Volume 3, chapter 8: “Operational Amplifiers” LEARNING OBJECTIVES • Design of a differential amplifier circuit using current mirrors. • Effects of negative feedback on a high-gain differential amplifier. SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This circuit design improves on the differential amplifier shown previously. Rather than use resistors to drop voltage in the differential pair circuit, a set of current mirrors is used instead, the result being higher voltage gain and more predictable performance. With a higher voltage gain, this circuit is able to function as a working operational amplifier or op-amp. Op-amps form the basis of a great many modern analog semiconductor circuits, so understanding the internal workings of an operational amplifier is important. PNP transistors Q1 and Q2 form a current mirror which tries to keep current split equally through the two differential pair transistors Q3 and Q4. NPN transistors Q5 and Q6 form another current mirror, setting the total differential pair current at a level predetermined by resistor Rprg. Measure the output voltage (voltage at the collector of Q4 with respect to ground) as the input voltages are varied. Note how the two potentiometers have different effects on the output voltage: one input tends to drive the output voltage in the same direction (noninverting), while the other tends to drive the output voltage in the opposite direction (inverting). You will notice that the output voltage is most responsive to changes in the input when the two input signals are nearly equal to each other. Once the circuit’s differential response has been proven (the output voltage sharply transitioning from one extreme level to another when one input is adjusted above and below the other input’s voltage level), you are ready to use this circuit as a real op-amp. A simple op-amp circuit called a voltage follower is a good configuration to try first. To make a voltage follower circuit, directly connect the output of the amplifier to its inverting input. This means connecting the collector and base terminals of Q4 together, and discarding the “inverting” potentiometer: Note the triangular symbol of the op-amp shown in the lower schematic diagram. The inverting and noninverting inputs are designated with (-) and (+) symbols, respectively, with the output terminal at the right apex. The feedback wire connecting output to inverting input is shown in red in the above diagrams. As a voltage follower, the output voltage should “follow” the input voltage very closely, deviating no more than a few hundredths of a volt. This is a much more precise follower circuit than that of a single common-collector transistor, described in an earlier experiment! A more complex op-amp circuit is called the noninverting amplifier, and it uses a pair of resistors in the feedback loop to “feedback” a fraction of the output voltage to the inverting input, causing the amplifier to output a voltage equal to some multiple of the voltage at the noninverting input. If we use two equal-value resistors, the feedback voltage will be 1/2 the output voltage, causing the output voltage to become twice the voltage impressed at the noninverting input. Thus, we have a voltage amplifier with a precise gain of 2: As you test this noninverting amplifier circuit, you may notice slight discrepancies between the output and input voltages. According to the feedback resistor values, the voltage gain should be exactly 2. However, you may notice deviations in the order of several hundredths of a volt between what the output voltage is and what it should be. These deviations are due to imperfections of the differential amplifier circuit and may be greatly diminished if we add more amplification stages to increase the differential voltage gain. However, one way we can maximize the precision of the existing circuit is to change the resistance of Rprg. This resistor sets the lower current mirror’s control point, and in so doing influences many performance parameters of the op-amp. Try substituting difference resistance values, ranging from 10 kΩ to 1 MΩ. Do not use a resistance less than 10 kΩ, or else the current mirror transistors may begin to overheat and thermally “run away.” Some operational amplifiers available in prepackaged units provide a way for the user to similarly “program” the differential pair’s current mirror and are called programmable op-amps. Most op-amps are not programmable and have their internal current mirror control points fixed by an internal resistance, trimmed to precise value at the factory.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.18%3A_Audio_Oscillator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two 6-volt batteries • Three NPN transistors—models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 0.1 µF capacitors (Radio Shack catalog # 272-135 or equivalent) • One 1 MΩ resistor • Two 100 kΩ resistors • One 1 kΩ resistor • Assortment of resistor pairs, less than 100 kΩ (ex: two 10 kΩ, two 5 kΩ, two 1 kΩ) • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • Audio detector with headphones CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • How to build an astable multivibrator circuit using discrete transistors SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS The proper name for this circuit is “astable multivibrator”. It is a simple, free-running oscillator circuit timed by the sizes of the resistors, capacitors, and power supply voltage. Unfortunately, its output waveform is very distorted, neither sine wave nor square. For the simple purpose of making an audio tone, however, distortion doesn’t matter much. With a 12 volt supply, 100 kΩ resistors, and 0.1 µF capacitors, the oscillation frequency will be in the low audio range. You may listen to this signal with the audio detector connected with one test probe to ground and the other to one of the transistor’s collector terminals. I recommend placing a 1 MΩ resistor in series with the audio detector to minimize both circuit loading effects and headphone loudness: The multivibrator itself is just two transistors, two resistors, and two cross-connecting capacitors. The third transistor shown in the schematic and illustration is there for driving the LED, to be used as a visual indicator of oscillator action. Use the probe wire connected to the base of this common-emitter amplifier to detect voltage at different parts of the circuit with respect to ground. Given the low oscillating frequency of this multivibrator circuit, you should be able to see the LED blink rapidly with the probe wire connected to the collector terminal of either multivibrator transistor. You may notice that the LED fails to blink with its probe wire touching the base of either multivibrator transistor, yet the audio detector tells you there is an oscillating voltage there. Why is this? The LED’s common-collector transistor amplifier is a voltage follower, meaning that it doesn’t amplify voltage. Thus, if the voltage under test is less than the minimum required by the LED to light up, it will not glow. Since the forward-biased base-emitter junction of an active transistor drops only about 0.7 volts, there is insufficient voltage at either transistor base to energize the LED. The audio detector, being extraordinarily sensitive, though, detects this low voltage signal easily. Feel free to substitute lower-value resistors in place of the two 100 kΩ units shown. What happens to the oscillation frequency when you do so? I recommend using resistors at least 1 kΩ in size to prevent excessive transistor current. One shortcoming of many oscillator circuits is its dependence on a minimum amount of power supply voltage. Too little voltage and the circuit ceases to oscillate. This circuit is no exception. You might want to experiment with lower supply voltages and determine the minimum voltage necessary for oscillation, as well as experience the effect supply voltage change has on oscillation frequency. One shortcoming specific to this circuit is the dependence on mismatched components for successful starting. In order for the circuit to begin oscillating, one transistor must turn on before the other one. Usually, there is enough mismatch in the various component values to enable this to happen, but it is possible for the circuit to “freeze” and fail to oscillate at power-up. If this happens, try different components (same values, but different units) in the circuit.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/05%3A_Discrete_Semiconductor_Circuits/5.19%3A_Vacuum_Tube_Audio_Amplifier.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • One 12AX7 dual triode vacuum tube • Two power transformers, 120VAC step-down to 12VAC (Radio Shack catalog # 273-1365, 273-1352, or 273-1511). • Bridge rectifier module (Radio Shack catalog # 276-1173) • Electrolytic capacitor, at least 47 µF, with a working voltage of at least 200 volts DC. • Automotive ignition coil • Audio speaker, 8 Ω impedance • Two 100 kΩ resistors • One 0.1 µF capacitor, 250 WVDC (Radio Shack catalog # 272-1053) • “Low-voltage AC power supply” as shown in AC Experiments chapter • One toggle switch, SPST (“Single-Pole, Single-Throw”) • Radio, tape player, musical keyboard, or other sources of audio voltage signal Where can you obtain a 12AX7 tube, you ask? These tubes are very popular for use in the “preamplifier” stages of many professional electric guitar amplifiers. Go to any good music store and you will find them available for a modest price (\$12 US or less). A Russian manufacturer named Sovtek makes these tubes new, so you need not rely on “New-Old-Stock” (NOS) components left over from defunct American manufacturers. This model of tube was very popular in its day and may be found in old “tubed” electronic test equipment (oscilloscopes, oscillators) if you happen to have access to such equipment. However, I strongly suggest buying a tube new rather than taking chances with tubes salvaged from antique equipment. It is important to select an electrolytic capacitor with sufficient working voltage (WVDC) to withstand the output of this amplifier’s power supply circuit (about 170 volts). I strongly recommend choosing a capacitor with a voltage rating well in excess of the expected operating voltage, so as to handle unexpected voltage surges or any other event that may tax the capacitor. I purchased the Radio Shack electrolytic capacitor assortment (catalog # 272-802), and it happened to contain two 47 µF, 250 WVDC capacitors. If you are not as fortunate, you may build this circuit using five capacitors, each rated at 50 WVDC, to substitute for one 250 WVDC unit: Bear in mind that the total capacitance for this five-capacitor network will be 1/5, or 20%, of each capacitor’s value. Also, to ensure even charging of capacitors in the network, be sure all capacitor values (in µF) and all resistor values are identical. An automotive ignition coil is a special-purpose high-voltage transformer used in car engines to produce tens of thousands of volts to “fire” the spark plugs. In this experiment, it is used (very unconventionally, I might add!) as an impedance-matching transformer between the vacuum tube and an 8 Ω audio speaker. The specific choice of “coil” is not critical, so long as it is in good operating condition. Here is a photograph of the coil I used for this experiment: The audio speaker need not be extravagant. I’ve used small “bookshelf” speakers, automotive (6"x9”) speakers, as well as a large (100 watt) 3-way stereo speaker for this experiment, and they all work fine. Do not use a set of headphones under any circumstances, as the ignition coil does not provide electrical isolation between the 170 volts DC of the “plate” power supply and the speaker, thus elevating the speaker connections to that voltage with respect to ground. Since obviously placing wires on your head with high voltage to ground would be very hazardous, please do not use headphones! You will need some source of audio-frequency AC as an input signal to this amplifier circuit. I recommend a small battery-powered radio or musical keyboard, with an appropriate cable plugged into the “headphone” or “audio out” jack to convey the signal to your amplifier. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 13: “Electron Tubes” Lessons In Electric Circuits, Volume 3, chapter 3: “Diodes and Rectifiers” Lessons In Electric Circuits, Volume 2, chapter 9: “Transformers” LEARNING OBJECTIVES • Using a vacuum tube (triode) as an audio amplifier • Using transformers in both step-down and step-up operation • How to build a high-voltage DC power supply • Using a transformer to match impedances SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Welcome to the world of vacuum tube electronics! While not exactly an application of semiconductor technology (power supply rectifier excepted), this circuit is used as an introduction to vacuum tube technology, and an interesting application for impedance-matching transformers. It should be noted that building and operating this circuit involves work with lethal voltages! You must exhibit the utmost care while working with this circuit, as 170 volts DC is capable of electrocuting you!! It is recommended that beginners seek qualified assistance (experienced electricians, electronics technicians, or engineers) if attempting to build this amplifier. WARNING: do not touch any wires or terminals while the amplifier circuit is energized! If you must make contact with the circuit at any point, turn off the “plate” power supply switch and wait for the filter capacitor to discharge below 30 volts before touching any part of the circuit. If testing circuit voltages with the power on, use only one hand if possible to avoid the possibility of an arm-to-arm electric shock. Building the high-voltage power supply Vacuum tubes require fairly high DC voltage applied between plate and cathode terminals in order to function efficiently. Although it is possible to operate the amplifier circuit described in this experiment on as low as 24 volts DC, the power output will be minuscule and the sound quality poor. The 12AX7 triode is rated at a maximum “plate voltage” (voltage applied between plate and cathode terminals) of 330 volts, so our power supply of 170 volts DC specified here is well within that maximum limit. I’ve operated this amplifier on as high as 235 volts DC and discovered that both sound quality and intensity improved slightly, but not enough in my estimation to warrant the additional hazard to experimenters. The power supply actually has two different power outputs: the “B+” DC output for plate power, and the “filament” power, which is only 12 volts AC. Tubes require power applied to a small filament (sometimes called a heater) in order to function, as the cathode must be hot enough to thermally emit electrons, and that doesn’t happen at room temperature! Using one power transformer to step household 120 volt AC power down to 12 volts AC provides low-voltage for the filaments, and another transformer connected in step-up fashion brings the voltage back up to 120 volts. You might be wondering, “why step the voltage back up to 120 volts with another transformer? Why not just tap off the wall socket plug to obtain 120 volt AC power directly, and then rectify that into 170 volts DC?” The answer to this is twofold: first, running power through two transformers inherently limits the amount of current that may be sent into an accidental short-circuit on the plate-side of the amplifier circuit. Second, it electrically isolates the plate circuit from the wiring system of your house. If we were to rectify wall-socket power with a diode bridge, it would make both DC terminals (+ and -) elevated in voltage from the safety ground connection of your house’s electrical system, thereby increasing the shock hazard. Note the toggle switch connected between the 12-volt windings of the two transformers, labeled “Plate supply switch.” This switch controls power to the step-up transformer, thereby controlling plate voltage to the amplifier circuit. Why not just use the main power switch connected to the 120-volt plug? Why has a second switch to shut off the DC high voltage, when shutting off one main switch would accomplish the same thing? The answer lies in proper vacuum tube operation: like incandescent light bulbs, vacuum tubes “wear” when their filaments are powered up and down repeatedly, so having this additional switch in the circuit allows you to shut off the DC high voltage (for safety when modifying or adjusting the circuit) without having to shut off the filament. Also, it is a good habit to wait for the tube to reach full operating temperature before applying plate voltage, and this second switch allows you to delay the application of plate voltage until the tube has had time to reach operating temperature. During operation, you should have a voltmeter connected to the “B+” output of the power supply (between the B+ terminal and ground), continuously providing indication of the power supply voltage. This meter will show you when the filter capacitor has discharged below the shock-hazard limit (30 volts) when you turn off the “Plate supply switch” to service the amplifier circuit. The “ground” terminal shown on the DC output of the power supply circuit need not connect to earth ground. Rather, it is merely a symbol showing a common connection with a corresponding ground terminal symbol in the amplifier circuit. In the circuit you build, there will be a piece of wire connecting these two “ground” points together. As always, the designation of certain common points in a circuit by means of a shared symbol is standard practice in electronic schematics. You will note that the schematic diagram shows a 100 kΩ resistor in parallel with the filter capacitor. This resistor is quite necessary, as it provides the capacitor a path for discharge when the AC power is turned off. Without this “bleeder” resistor in the circuit, the capacitor would likely retain a dangerous charge for a long time after “power-down,” posing an additional shock hazard to you. In the circuit I built—with a 47 µF capacitor and a 100 kΩ bleeder resistor—the time constant of this RC circuit was a brief 4.7 seconds. If you happen to find a larger filter capacitor value (good for minimizing unwanted power supply “hum” in the speaker), you will need to use a correspondingly smaller value of bleeder resistor, or wait longer for the voltage to bleed off each time you turn the “Plate supply” switch off. Be sure you have the power supply safely constructed and working reliably before attempting to power the amplifier circuit with it. This is good circuit-building practice in general: build and troubleshoot the power supply first, then build the circuit you intend to power with it. If the power supply does not function as it should, then neither will the powered circuit, no matter how well it may be designed and built. Building the amplifier One of the problems with building vacuum tube circuits in the 21st century is that sockets for these components can be difficult to find. Given the limited lifetime of most “receiver” tubes (a few years), most “tubed” electronic devices used sockets for mounting the tubes, so that they could be easily removed and replaced. Though tubes may still be obtained (from music supply stores) with relative ease, the sockets they plug into are considerably scarcer—your local Radio Shack will not have them in stock! How, then, do we build circuits with tubes, if we might not be able to obtain sockets for them to plug into? For small tubes, this problem may be circumvented by directly soldering short lengths of 22-gauge solid copper wire to the pins of the tube, thus enabling you to “plug” the tube into a solderless breadboard. Here is a photograph of my tube amplifier, showing the 12AX7 in an inverted position (pin-side-up). Please disregard the 10-segment LED bar graph to the left and the 8-position DIP switch assembly to the right in the photograph, as these are leftover components from a digital circuit experiment assembled previously on my breadboard. One benefit of mounting the tube in this position is ease of pin identification since most “pin connection diagrams” for tubes are shown from a bottom view: You will notice on the amplifier schematic that both triode elements inside the 12AX7’s glass envelope are being used, in parallel: plate connected to plate, grid-connected to grid, and cathode connected to cathode. This is done to maximize power output from the tube, but it is not necessary for demonstrating basic operation. You may use just one of the triodes, for simplicity, if you wish. The 0.1 µF capacitor shown on the schematic “couples” the audio signal source (radio, musical keyboard, etc.) to the tube’s grid(s), allowing AC to pass but blocking DC. The 100 kΩ resistor ensures that the average DC voltage between grid and cathode is zero, and cannot “float” to some high level. Typically, bias circuits are used to keep the grid slightly negative with respect to ground, but for this purpose, a bias circuit would introduce more complexity than its worth. When I tested my amplifier circuit, I used the output of a radio receiver, and later the output of a compact disk (CD) player, as the audio signal source. Using a “mono”-to-“phono” connector extension cord plugged into the headphone jack of the receiver/CD player, and alligator clip jumper wires connecting the “mono” tip of the cord to the input terminals of the tube amplifier, I was able to easily send the amplifier audio signals of varying amplitude to test its performance over a wide range of conditions: A transformer is essential at the output of the amplifier circuit for “matching” the impedances of vacuum tube and speaker. Since the vacuum tube is a high-voltage, low-current device, and most speakers are low-voltage, high-current devices, the mismatch between them would result in very audio low power output if they were directly connected. To successfully match the high-voltage, low-current source to the low-voltage, high current load, we must use a step-down transformer. Since the vacuum tube circuit’s Thevenin resistance ranges in the tens of thousands of ohms, and the speaker only has about 8 ohms impedance, we will need a transformer with an impedance ratio of about 10,000:1. Since the impedance ratio of a transformer is the square of its turns ratio (or voltage ratio), we’re looking for a transformer with a turns ratio of about 100:1. A typical automotive ignition coil has approximately this turns ratio, and it is also rated for extremely high voltage on the high-voltage winding, making it well suited for this application. The only bad aspect of using an ignition coil is that it provides no electrical isolation between primary and secondary windings, since the device is actually an autotransformer, with each winding sharing a common terminal at one end. This means that the speaker wires will be at a high DC voltage with respect to circuit ground. So long as we know this, and avoid touching those wires during operation, there will be no problem. Ideally, though, the transformer would provide complete isolation as well as impedance matching, and the speaker wires would be perfectly safe to touch during use. Remember, make all connections in the circuit with the power turned off! After checking connections visually and with an ohmmeter to ensure that the circuit is built as per the schematic diagram, apply power to the filaments of the tube and wait about 30 seconds for it to reach operating temperature. The both filaments should emit a soft, orange glow, visible from both the top and bottom views of the tube. Turn the volume control of your radio/CD player/musical keyboard signal source to minimum, then turn on the plate supply switch. The voltmeter you have connected between the power supply’s B+ output terminal and “ground” should register full voltage (about 170 volts). Now, increase the volume control on the signal source and listen to the speaker. If all is well, you should hear the correct sounds clearly through the speaker. Troubleshooting this circuit is best done with the sensitive audio detector described in the DC and AC chapters of this Experiments volume. Connect a 0.1 µF capacitor in series with each test lead to block DC from the detector, then connect one of the test leads to ground, while using the other test lead to check for audio signal at various points in the circuit. Use capacitors with a high voltage rating, like the one used on the input of the amplifier circuit: Using two coupling capacitors instead of just one adds an additional degree of safety, in helping to isolate the unit from any (high) DC voltage. Even without the extra capacitor, though, the detector’s internal transformer should provide sufficient electrical isolation for your safety in using it to test for signals in a high-voltage circuit like this, especially if you built your detector using a 120-volt power transformer (rather than an “audio output” transformer) as suggested. Use it to test for a good signal at the input, then at the grid pin(s) of the tube, then at the plate of the tube, etc. until the problem is found. Being capacitively coupled, the detector is also able to test for excessive power supply “hum:” touch the free test lead to the supply’s B+ terminal and listen for a loud 60 Hz humming noise. The noise should be very soft, not loud. If it is loud, the power supply is not filtered adequately enough and may need additional filter capacitance. After testing a point in the amplifier circuit with large DC voltage to ground, the coupling capacitors on the detector may build up substantial voltage. To discharge this voltage, briefly, touch the free test lead to the grounded test lead. A “pop” sound should be heard in the headphones as the coupling capacitors discharge. If you would rather use a voltmeter to test for the presence of audio signal, you may do so, setting it to a sensitive AC voltage range. The indication you get from a voltmeter, though, doesn’t tell you anything about the quality of the signal, just its mere presence. Bear in mind that most AC voltmeters will register a transient voltage when initially connected across a source of DC voltage, so don’t be surprised to see a “spike” (a strong, momentary voltage indication) at the very moment contact is made with the meter’s probes to the circuit, rapidly decreasing to the true AC signal value. You may be pleasantly surprised at the quality and depth of tone from this little amplifier circuit, especially given its low power output: less than 1 watt of audio power. Of course, the circuit is quite crude and sacrifices quality for simplicity and parts availability, but it serves to demonstrate the basic principle of vacuum tube amplification. Advanced hobbyists and students may wish to experiment with biasing networks, negative feedback, different output transformers, different power supply voltages, and even different tubes, to obtain more power and/or better sound quality. Here is a photo of a very similar amplifier circuit, built by the husband-and-wife team of Terry and Cheryl Goetz, illustrating what can be done when care and craftsmanship are applied to a project like this.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/06%3A_Analog_Integrated_Circuits/6.01%3A_Introduction_to_Analog_Integrated_Circuits.txt	princeton-nlp/TextbookChapters	Analog circuits are circuits dealing with signals free to vary from zero to full power supply voltage. This stands in contrast to digital circuits, which almost exclusively employ “all or nothing” signals: voltages restricted to values of zero and full supply voltage, with no valid state in between those extreme limits. Analog circuits are often referred to as linear circuits to emphasize the valid continuity of signal range forbidden in digital circuits, but this label is unfortunately misleading. Just because a voltage or current signal is allowed to vary smoothly between the extremes of zero and full power supply limits does not necessarily mean that all mathematical relationships between these signals are linear in the “straight-line” or “proportional” sense of the word. As you will see in this chapter, many so-called “linear” circuits are quite nonlinear in their behavior, either by the necessity of physics or by design. The circuits in this chapter make use of IC, or integrated circuit, components. Such components are actually networks of interconnected components manufactured on a single wafer of semiconducting material. Integrated circuits providing a multitude of pre-engineered functions are available at very low cost, benefitting students, hobbyists and professional circuit designers alike. Most integrated circuits provide the same functionality as “discrete” semiconductor circuits at higher levels of reliability and at a fraction of the cost. Usually, the discrete-component circuit construction is favored only when power dissipation levels are too high for integrated circuits to handle. Perhaps the most versatile and important analog integrated circuit for the student to master is the operational amplifier or op-amp. Essentially nothing more than a differential amplifier with very high voltage gain, op-amps are the workhorse of the analog design world. By cleverly applying feedback from the output of an op-amp to one or more of its inputs, a wide variety of behaviors may be obtained from this single device. Many different models of op-amp are available at low cost, but circuits described in this chapter will incorporate only commonly available op-amp models. 6.02: Voltage Comparator Parts and Materials • Operational amplifier, model 1458 or 353 recommended (Radio Shack catalog # 276-038 and 900-6298, respectively) • Three 6 volt batteries • Two 10 kΩ potentiometers, linear taper (Radio Shack catalog # 271-1715) • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • One 330 Ω resistor • One 470 Ω resistor This experiment only requires a single operational amplifier. The model 1458 and 353 are both “dual” op-amp units, with two complete amplifier circuits housed in the same 8-pin DIP package. I recommend that you purchase and use “dual” op-amps over “single” op-amps even if a project only requires one, because they are more versatile (the same op-amp unit can function in projects requiring only one amplifier as well as in projects requiring two). In the interest of purchasing and stocking the least number of components for your home laboratory, this makes sense. Leaning Objectives • How to use an op-amp as a comparator Instructions for Comparator Circuit A comparator circuit compares two voltage signals and determines which one is greater. The result of this comparison is indicated by the output voltage: if the op-amp’s output is saturated in the positive direction, the noninverting input (+) is a greater, or more positive, voltage than the inverting input (-), all voltages measured with respect to ground. If the op-amp’s voltage is near the negative supply voltage (in this case, 0 volts, or ground potential), it means the inverting input (-) has a greater voltage applied to it than the noninverting input (+). This behavior is much easier understood by experimenting with a comparator circuit than it is by reading someone’s verbal description of it. In this experiment, two potentiometers supply variable voltages to be compared by the op-amp. The output status of the op-amp is indicated visually by the LED. By adjusting the two potentiometers and observing the LED, one can easily comprehend the function of a comparator circuit. For greater insight into this circuit’s operation, you might want to connect a pair of voltmeters to the op-amp input terminals (both voltmeters referenced to ground) so that both input voltages may be numerically compared with each other, these meter indications compared to the LED status: Comparator circuits are widely used to compare physical measurements, provided those physical variables can be translated into voltage signals. For instance, if a small generator were attached to an anemometer wheel to produce a voltage proportional to wind speed, that wind speed signal could be compared with a “set-point” voltage and compared by an op-amp to drive a high wind speed alarm:
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/06%3A_Analog_Integrated_Circuits/6.03%3A_Precision_Voltage_Follower.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Operational amplifier, model 1458 or 353 recommended (Radio Shack catalog # 276-038 and 900-6298, respectively) • Three 6 volt batteries • One 10 kΩ potentiometer, linear taper (Radio Shack catalog # 271-1715) CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 8: “Operational Amplifiers” LEARNING OBJECTIVES • How to use an op-amp as a voltage follower • Purpose of negative feedback • Troubleshooting strategy SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS In the previous op-amp experiment, the amplifier was used in “open-loop” mode; that is, without any feedback from output to input. As such, the full voltage gain of the operational amplifier was available, resulting in the output voltage saturating for virtually any amount of differential voltage applied between the two input terminals. This is good if we desire comparator operation, but if we want the op-amp to behave as a true amplifier, we need it to exhibit a manageable voltage gain. Since we do not have the luxury of disassembling the integrated circuitry of the op-amp and changing resistor values to give a lesser voltage gain, we are limited to external connections and componentry. Actually, this is not a disadvantage as one might think, because the combination of extremely high open-loop voltage gain coupled with feedback allows us to use the op-amp for a much wider variety of purposes, much easier than if we were to exercise the option of modifying its internal circuitry.think, because the combination of extremely high open-loop voltage gain coupled with feedback allows us to use the op-amp for a much wider variety of purposes, much easier than if we were to exercise the option of modifying its internal circuitry. If we connect the output of an op-amp to its inverting (-) input, the output voltage will seek whatever level is necessary to balance the inverting input’s voltage with that applied to the noninverting (+) input. If this feedback connection is direct, as, in a straight piece of wire, the output voltage will precisely “follow” the noninverting input’s voltage. Unlike the voltage follower circuit made from a single transistor (see chapter 5: Discrete Semiconductor Circuits), which approximated the input voltage to within several tenths of a volt, this voltage follower circuit will output a voltage accurate to within mere microvolts of the input voltage! Measure the input voltage of this circuit with a voltmeter connected between the op-amp’s noninverting (+) input terminal and circuit ground (the negative side of the power supply), and the output voltage between the op-amp’s output terminal and circuit ground. Watch the op-amp’s output voltage follow the input voltage as you adjust the potentiometer through its range. You may directly measure the difference, or error, between output and input voltages by connecting the voltmeter between the op-amp’s two input terminals. Throughout most of the potentiometer’s range, this error voltage should be almost zero. Try moving the potentiometer to one of its extreme positions, far clockwise or far counterclockwise. Measure error voltage, or compare output voltage against input voltage. Do you notice anything unusual? If you are using the model 1458 or model 353 op-amp for this experiment, you should measure a substantial error voltage, or difference between output and input. Many op-amps, the specified models included, cannot “swing” their output voltage exactly to full power supply (“rail”) voltage levels. In this case, the “rail” voltages are +18 volts and 0 volts, respectively. Due to limitations in the 1458’s internal circuitry, its output voltage is unable to exactly reach these high and low limits. You may find that it can only go within a volt or two of the power supply “rails.” This is a very important limitation to understand when designing circuits using operational amplifiers. If full “rail-to-rail” output voltage swing is required in a circuit design, other op-amp models may be selected which offer this capability. The model 3130 is one such op-amp. Precision voltage follower circuits are useful if the voltage signal to be amplified cannot tolerate “loading;” that is, if it has a high source impedance. Since a voltage follower by definition has a voltage gain of 1, its purpose has nothing to do with amplifying voltage, but rather with amplifying a signal’s capacity to deliver current to a load. Voltage follower circuits have another important use for circuit builders: they allow for simple linear testing of an op-amp. One of the troubleshooting techniques I recommend is to simplify and rebuild. Suppose that you are building a circuit using one or more op-amps to perform some advanced function. If one of those op-amps seems to be causing a problem and you suspect it may be faulty, try re-connecting it as a simple voltage follower and see if it functions in that capacity. An op-amp that fails to work as a voltage follower certainly won’t work as anything more complex! COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): An ideal operational amplifier may be simulated in SPICE using a dependent voltage source (e1 in the netlist). The output nodes are specified first (2 0), then the two input nodes, non-inverting input first (1 2). Open-loop gain is specified last (999meg) in the dependent voltage source line. Because SPICE views the input impedance of a dependent source as infinite, some finite amount of resistance must be included to avoid an analysis error. This is the purpose of Rbogus: to provide DC path to ground for the Vinput voltage source. Such “bogus” resistances should be arbitrarily large. In this simulation, I chose 1 MΩ for an Rbogus value. A load resistor is included in the circuit for much the same reason: to provide a DC path for current at the output of the dependent voltage source. As you can see, SPICE doesn’t like open circuits! 6.04: Noninverting Amplifier PARTS AND MATERIALS • Operational amplifier, model 1458 or 353 recommended (Radio Shack catalog # 276-038 and 900-6298, respectively) • Three 6 volt batteries • Two 10 kΩ potentiometers, linear taper (Radio Shack catalog # 271-1715) CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 8: “Operational Amplifiers” LEARNING OBJECTIVES • How to use an op-amp as a single-ended amplifier • Using divided, negative feedback SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This circuit differs from the voltage follower in only one respect: output voltage is “fed back” to the inverting (-) input through a voltage-dividing potentiometer rather than being directly connected. With only a fractionof the output voltage fed back to the inverting input, the op-amp will output a corresponding multiple of the voltage sensed at the noninverting (+) input in keeping the input differential voltage near zero. In other words, the op-amp will now function as an amplifier with a controllable voltage gain, that gain is established by the position of the feedback potentiometer (R2). Set R2 to approximately mid-position. This should give a voltage gain of about 2. Measure both input and output voltage for several positions of the input potentiometer R1. Move R2 to a different position and re-take voltage measurements for several positions of R1. For any given R2 position, the ratio between output and input voltage should be the same. You will also notice that the input and output voltages are always positive with respect to ground. Because of the output voltage increases in a positive direction for a positive increase of the input voltage, this amplifier is referred to as noninverting. If the output and input voltages were related to one another in an inverse fashion (i.e. positive increasing input voltage results in positive decreasing or negative increasing output), then the amplifier would be known as an inverting type. The ability to leverage an op-amp in this fashion to create an amplifier with controllable voltage gain makes this circuit an extremely useful one. It would take quite a bit more design and troubleshooting effort to produce a similar circuit using discrete transistors. Try adjusting R2 for maximum and minimum voltage gain. What is the lowest voltage gain attainable with this amplifier configuration? Why do you think this is? COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim): With R1 and R2 set equally to 5 kΩ in the simulation, it mimics the feedback potentiometer of the real circuit at mid-position (50%). To simulate the potentiometer at the 75% position, set R2 to 7.5 kΩ and R1 to 2.5 kΩ.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/06%3A_Analog_Integrated_Circuits/6.05%3A_High-impedance_Voltmeter.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Operational amplifier, model TL082 recommended (Radio Shack catalog # 276-1715) • Operational amplifier, model LM1458 recommended (Radio Shack catalog # 276-038) • Four 6 volt batteries • One meter movement, 1 mA full-scale deflection (Radio Shack catalog #22-410) • 15 kΩ precision resistor • Four 1 MΩ resistors The 1 mA meter movement sold by Radio Shack is advertised as a 0-15 VDC meter but is actually a 1 mA movement sold with a 15 kΩ +/- 1% tolerance multiplier resistor. If you get this Radio Shack meter movement, you can use the included 15 kΩ resistor for the resistor specified in the parts list. This meter experiment is based on a JFET-input op-amp such as the TL082. The other op-amp (model 1458) is used in this experiment to demonstrate the absence of latch-up: a problem inherent to the TL082. You don’t need 1 MΩ resistors, exactly. Any very high resistance resistors will suffice. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 8: “Operational Amplifiers” LEARNING OBJECTIVES • Voltmeter loading: its causes and its solution • How to make a high-impedance voltmeter using an op-amp • What op-amp “latch-up” is and how to avoid it SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS An ideal voltmeter has infinite input impedance, meaning that it draws zero current from the circuit under test. This way, there will be no “impact” on the circuit as the voltage is being measured. The more current a voltmeter draws from the circuit under test, the more the measured voltage will “sag” under the loading effect of the meter, like a tire-pressure gauge releasing air out of the tire being measured: the more air released from the tire, the more the tire’s pressure will be impacted by the act of measurement. This loading is more pronounced on circuits of high resistance, like the voltage divider made of 1 MΩ resistors, shown in the schematic diagram. If you were to build a simple 0-15 volt range voltmeter by connecting the 1 mA meter movement in series with the 15 kΩ precision resistor, and try to use this voltmeter to measure the voltage at TP1, TP2, or TP3 (with respect to ground), you’d encounter severe measurement errors induced by meter “impact:” Try using the meter movement and 15 kΩ resistor as shown to measure these three voltages. Does the meter read falsely high or falsely low? Why do you think this is? If we were to increase the meter’s input impedance, we would diminish its current draw or “load” on the circuit under test and consequently improve its measurement accuracy. An op-amp with high-impedance inputs (using a JFET transistor input stage rather than a BJT input stage) works well for this application. Note that the meter movement is part of the op-amp’s feedback loop from output to inverting input. This circuit drives the meter movement with a current proportional to the voltage impressed at the noninverting (+) input, the requisite current supplied directly from the batteries through the op-amp’s power supply pins, not from the circuit under test through the test probe. The meter’s range is set by the resistor connecting the inverting (-) input to ground. Build the op-amp meter circuit as shown and re-take voltage measurements at TP1, TP2, and TP3. You should enjoy far better success this time, with the meter movement accurately measuring these voltages (approximately 3, 6, and 9 volts, respectively). You may witness the extreme sensitivity of this voltmeter by touching the test probe with one hand and the most positive battery terminal with the other. Notice how you can drive the needle upward on the scale simply by measuring battery voltage through your body resistance: an impossible feat with the original, unamplified voltmeter circuit. If you touch the test probe to ground, the meter should read exactly 0 volts. After you’ve proven this circuit to work, modify it by changing the power supply from dual to split. This entails removing the center-tap ground connection between the 2nd and 3rd batteries, and grounding the far negative battery terminal instead: This alteration in the power supply increases the voltages at TP1, TP2, and TP3 to 6, 12, and 18 volts, respectively. With a 15 kΩ range resistor and a 1 mA meter movement, measuring 18 volts will gently “peg” the meter, but you should be able to measure the 6 and 12-volt test points just fine. Try touching the meter’s test probe to ground. This should drive the meter needle to exactly 0 volts as before, but it will not! What is happening here is an op-amp phenomenon called latch-up: where the op-amp output drives to a positive voltage when the input common-mode voltage exceeds the allowable limit. In this case, as with many JFET-input op-amps, neither input should be allowed to come close to either power supply rail voltage. With a single supply, the op-amp’s negative power rail is at ground potential (0 volts), so grounding the test probe brings the noninverting (+) input exactly to that rail voltage. This is bad for a JFET op-amp, and drives the output strongly positive, even though it doesn’t seem like it should, based on how op-amps are supposed to function. When the op-amp ran on a “dual” supply (+12/-12 volts, rather than a “single” +24 volt supply), the negative power supply rail was 12 volts away from ground (0 volts), so grounding the test probe didn’t violate the op-amp’s common-mode voltage limit. However, with the “single” +24 volt supply, we have a problem. Note that some op-amps do not “latch-up” the way the model TL082 does. You may replace the TL082 with an LM1458 op-amp, which is pin-for-pin compatible (no breadboard wiring changes needed). The model 1458 will not “latch-up” when the test probe is grounded, although you may still get incorrect meter readings with the measured voltage exactly equal to the negative power supply rail. As a general rule, you should always be sure the op-amp’s power supply rail voltages exceed the expected input voltages.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/06%3A_Analog_Integrated_Circuits/6.06%3A_Integrator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Four 6 volt batteries • Operational amplifier, model 1458 recommended (Radio Shack catalog # 276-038) • One 10 kΩ potentiometer, linear taper (Radio Shack catalog # 271-1715) • Two capacitors, 0.1 µF each, non-polarized (Radio Shack catalog # 272-135) • Two 100 kΩ resistors • Three 1 MΩ resistors Just about any operational amplifier model will work fine for this integrator experiment, but I’m specifying the model 1458 over the 353 because the 1458 has much higher input bias currents. Normally, high input bias current is a bad characteristic for an op-amp to have in a precision DC amplifier circuit (and especially an integrator circuit!). However, I want the bias current to be high in order that its bad effects may be exaggerated, and so that you will learn one method of counteracting its effects. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 8: “Operational Amplifiers” LEARNING OBJECTIVES • Method for limiting the span of a potentiometer • Purpose of an integrator circuit • How to compensate for op-amp bias current SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS As you can see from the schematic diagram, the potentiometer is connected to the “rails” of the power source through 100 kΩ resistors, one on each end. This is to limit the span of the potentiometer so that full movement produces a fairly small range of input voltages for the op-amp to operate on. At one extreme of the potentiometer’s motion, a voltage of about 0.5 volts (with respect the ground point in the middle of the series battery string) will be produced at the potentiometer wiper. At the other extreme of motion, a voltage of about -0.5 volts will be produced. When the potentiometer is positioned dead-center, the wiper voltage should measure zero volts. Connect a voltmeter between the op-amp’s output terminal and the circuit ground point. Slowly move the potentiometer control while monitoring the output voltage. The output voltage should be changing at a rate established by the potentiometer’s deviation from zero (center) position. To use calculus terms, we would say that the output voltage represents the integral (with respect to time) of the input voltage function. That is, the input voltage level establishes the output voltage rate of change over time. This is precisely the opposite of differentiation, where the derivative of a signal or function is its instantaneous rate of change. If you have two voltmeters, you may readily see this relationship between input voltage and output voltage rate of change by measuring the wiper voltage (between the potentiometer wiper and ground) with one meter and the output voltage (between the op-amp output terminal and ground) with the other. Adjusting the potentiometer to give zero volts should result in the lowest output voltage rate-of-change. Conversely, the more voltage input to this circuit, the faster its output voltage will change, or “ramp.” Try connecting the second 0.1 µF capacitor in parallel with the first. This will double the amount of capacitance in the op-amp’s feedback loop. What effect does this have on the circuit’s integration rate for any given potentiometer position? Try connecting another 1 MΩ resistor in parallel with the input resistor (the resistor connecting the potentiometer wiper to the inverting terminal of the op-amp). This will half the integrator’s input resistance. What effect does this have on the circuit’s integration rate? Integrator circuits are one of the fundamental “building-block” functions of an analog computer. By connecting integrator circuits with amplifiers, summers, and potentiometers (dividers), almost any differential equation could be modeled, and solutions obtained by measuring voltages produced at various points in the network of circuits. Because differential equations describe so many physical processes, analog computers are used as simulators. Before the advent of modern digital computers, engineers used analog computers to simulate such processes as machinery vibration, rocket trajectory, and control system response. Even though analog computers are considered obsolete by modern standards, their constituent components still work well as learning tools for calculus concepts. Move the potentiometer until the op-amp’s output voltage is as close to zero as you can get it, and moving as slowly as you can make it. Disconnect the integrator input from the potentiometer wiper terminal and connect it instead to ground, like this: Applying exactly zero voltage to the input of an integrator circuit should, ideally, cause the output voltage rate-of-change to be zero. When you make this change to the circuit, you should notice the output voltage remaining at a constant level or changing very slowly. With the integrator input still shorted to ground, short past the 1 MΩ resistor connecting the op-amp’s noninverting (+) input to ground. There should be no need for this resistor in an ideal op-amp circuit, so by shorting past it, we will see what function it provides in this very real op-amp circuit: As soon as the “grounding” resistor is shorted with a jumper wire, the op-amp’s output voltage will start to change, or drift. Ideally, this should not happen, because the integrator circuit still has an input signal of zero volts. However, real operational amplifiers have a very small amount of current entering each input terminal called the bias current. These bias currents will drop voltage across any resistance in their path. Since the 1 MΩ input resistor conducts some amount of bias current regardless of input signal magnitude, it will drop voltage across its terminals due to bias current, thus “offsetting” the amount of signal voltage seen at the inverting terminal of the op-amp. If the other (noninverting) input is connected directly to ground as we have done here, this “offset” voltage incurred by voltage drop generated by bias current will cause the integrator circuit to slowly “integrate” as though it were receiving a very small input signal. The “grounding” resistor is better known as a compensating resistor because it acts to compensate for voltage errors created by bias current. Since the bias currents through each op-amp input terminal are approximately equal to each other, an equal amount of resistance placed in the path of each bias current will produce approximately the same voltage drop. Equal voltage drops seen at the complementary inputs of an op-amp cancel each other out, thus nulling the error otherwise induced by bias current. Remove the jumper wire shorting past the compensating resistor and notice how the op-amp output returns to a relatively stable state. It may still drift some, most likely due to bias voltage error in the op-amp itself, but that is another subject altogether! COMPUTER SIMULATION Schematic with SPICE node numbers: Netlist (make a text file containing the following text, verbatim):
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/06%3A_Analog_Integrated_Circuits/6.07%3A_555_Audio_Oscillator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two 6 volt batteries • One capacitor, 0.1 µF, non-polarized (Radio Shack catalog # 272-135) • One 555 timer IC (Radio Shack catalog # 276-1723) • Two light-emitting diodes (Radio Shack catalog # 276-026 or equivalent) • One 1 MΩ resistor • One 100 kΩ resistor • Two 510 Ω resistors • Audio detector with headphones • Oscilloscope (recommended, but not necessary) An oscilloscope would be useful in analyzing the waveforms produced by this circuit, but it is not essential. An audio detector is a very useful piece of test equipment for this experiment, especially if you don’t have an oscilloscope. CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • How to use the 555 timer as an astable multivibrator • Working knowledge of duty cycle SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS The “555” integrated circuit is a general-purpose timer useful for a variety of functions. In this experiment, we explore its use as an astable multivibrator or oscillator. Connected to a capacitor and two resistors as shown, it will oscillate freely, driving the LEDs on and off with a square-wave output voltage. This circuit works on the principle of alternately charging and discharging a capacitor. The 555 begins to discharge the capacitor by grounding the Disch terminal when the voltage detected by the Thresh terminal exceeds 2/3 the power supply voltage (Vcc). It stops discharging the capacitor when the voltage detected by the Trig terminal falls below 1/3 the power supply voltage. Thus, when both Thresh and Trig terminals are connected to the capacitor’s positive terminal, the capacitor voltage will cycle between 1/3 and 2/3 power supply voltage in a “sawtooth” pattern. During the charging cycle, the capacitor receives charging current through the series combination of the 1 MΩ and 100 kΩ resistors. As soon as the Disch terminal on the 555 timer goes to ground potential (a transistor inside the 555 connected between that terminal and ground turns on), the capacitor’s discharging current only has to go through the 100 kΩ resistor. The result is an RC time constant that is much longer for charging than for discharging, resulting in a charging time greatly exceeding the discharging time. The 555’s Out terminal produces a square-wave voltage signal that is “high” (nearly Vcc) when the capacitor is charging, and “low” (nearly 0 volts) when the capacitor is discharging. This alternating high/low voltage signal drives the two LEDs in opposite modes: when one is on, the other will be off. Because the capacitor’s charging and discharging times are unequal, the “high” and “low” times of the output’s square-wave waveform will be unequal as well. This can be seen in the relative brightness of the two LEDs: one will be much brighter than the other because it is on for a longer period of time during each cycle. The equality or inequality between “high” and “low” times of a square wave is expressed as that wave’s duty cycle. A square wave with a 50% duty cycle is perfectly symmetrical: its “high” time is precisely equal to its “low” time. A square wave that is “high” 10% of the time and “low” 90% of the time is said to have a 10% duty cycle. In this circuit, the output waveform has a “high” time exceeding the “low” time, resulting in a duty cycle greater than 50%. Use the audio detector (or an oscilloscope) to investigate the different voltage waveforms produced by this circuit. Try different resistor values and/or capacitor values to see what effects they have on output frequency or charge/discharge times.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/06%3A_Analog_Integrated_Circuits/6.08%3A_555_Ramp_Generator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two 6 volt batteries • One capacitor, 470 µF electrolytic, 35 WVDC (Radio Shack catalog # 272-1030 or equivalent) • One capacitor, 0.1 µF, non-polarized (Radio Shack catalog # 272-135) • One 555 timer IC (Radio Shack catalog # 276-1723) • Two PNP transistors—models 2N2907 or 2N3906 recommended (Radio Shack catalog # 276-1604 is a package of fifteen PNP transistors ideal for this and other experiments) • Two light-emitting diodes (Radio Shack catalog # 276-026 or equivalent) • One 100 kΩ resistor • One 47 kΩ resistor • Two 510 Ω resistors • Audio detector with headphones The voltage rating on the 470 µF capacitor is not critical, so long as it generously exceeds the maximum power supply voltage. In this particular circuit, that maximum voltage is 12 volts. Be sure you connect this capacitor in the circuit properly, respecting polarity! CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 13: “Capacitors” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • How to use the 555 timer as an astable multivibrator • A practical use for a current mirror circuit • Understanding the relationship between capacitor current and capacitor voltage rate-of-change SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Again, we are using a 555 timer IC as an astable multivibrator, or oscillator. This time, however, we will compare its operation in two different capacitor-charging modes: traditional RC and constant-current. Connecting test point #1 (TP1) to test point #3 (TP3) using a jumper wire. This allows the capacitor to charge through a 47 kΩ resistor. When the capacitor has reached 2/3 supply voltage, the 555 timer switches to “discharge” mode and discharges the capacitor to a level of 1/3 supply voltage almost immediately. The charging cycle begins again at this point. Measure voltage directly across the capacitor with a voltmeter (a digital voltmeter is preferred), and note the rate of capacitor charging over time. It should rise quickly at first, then taper off as it builds up to 2/3 supply voltage, just as you would expect from an RC charging circuit. Remove the jumper wire from TP3, and re-connect it to TP2. This allows the capacitor to be charged through the controlled-current leg of a current mirror circuit formed by the two PNP transistors. Measure voltage directly across the capacitor again, noting the difference in charging rate over time as compared to the last circuit configuration. By connecting TP1 to TP2, the capacitor receives a nearly constant charging current. Constant capacitor charging current yields a voltage curve that is linear, as described by the equation i = C(de/dt). If the capacitors current is constant, so will be its rate-of-change of voltage over time. The result is a “ramp” waveform rather than a “sawtooth” waveform: The capacitor’s charging current may be directly measured by substituting an ammeter in place of the jumper wire. The ammeter will need to be set to measure a current in the range of hundreds of microamps (tenths of a milliamp). Connected between TP1 and TP3, you should see a current that starts at a relatively high value at the beginning of the charging cycle, and tapers off toward the end. Connected between TP1 and TP2, however, the current will be much more stable. It is an interesting experiment at this point to change the temperature of either current mirror transistor by touching it with your finger. As the transistor warms, it will conduct more collector current for the same base-emitter voltage. If the controlling transistor (the one connected to the 100 kΩ resistor) is touched, the current decreases. If the controlled transistor is touched, the current increases. For the most stable current mirror operation, the two transistors should be cemented together so that their temperatures never differ by any substantial amount. This circuit works just as well at high frequencies as it does at low frequencies. Replace the 470 µF capacitor with a 0.1 µF capacitor, and use an audio detector to sense the voltage waveform at the 555’s output terminal. The detector should produce an audio tone that is easy to hear. The capacitor’s voltage will now be changing much too fast to view with a voltmeter in the DC mode, but we can still measure capacitor current with an ammeter. With the ammeter connected between TP1 and TP3 (RC mode), measure both DC microamps and AC microamps. Record these current figures on paper. Now, connect the ammeter between TP1 and TP2 (constant-current mode). Measure both DC microamps and AC microamps, noting any differences in current readings between this circuit configuration and the last one. Measuring AC current in addition to DC current is an easy way to determine which circuit configuration gives the most stable charging current. If the current mirror circuit were perfect—the capacitor charging current absolutely constant—there would be zero AC current measured by the meter.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/06%3A_Analog_Integrated_Circuits/6.09%3A_PWM_Power_Controller.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Four 6 volt batteries • One capacitor, 100 µF electrolytic, 35 WVDC (Radio Shack catalog # 272-1028 or equivalent) • One capacitor, 0.1 µF, non-polarized (Radio Shack catalog # 272-135) • One 555 timer IC (Radio Shack catalog # 276-1723) • Dual operational amplifier, model 1458 recommended (Radio Shack catalog # 276-038) • One NPN power transistor—(Radio Shack catalog # 276-2041 or equivalent) • Three 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • One 10 kΩ potentiometer, linear taper (Radio Shack catalog # 271-1715) • One 33 kΩ resistor • 12-volt automotive tail-light lamp • Audio detector with headphones CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 8: “Operational Amplifiers” Lessons In Electric Circuits, Volume 2, chapter 7: “Mixed-Frequency AC Signals” LEARNING OBJECTIVES • How to use the 555 timer as an astable multivibrator • How to use an op-amp as a comparator • How to use diodes to drop unwanted DC voltage • How to control power to a load by pulse-width modulation SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This circuit uses a 555 timer to generate a sawtooth voltage waveform across a capacitor, then compares that signal against a steady voltage provided by a potentiometer, using an op-amp as a comparator. The comparison of these two voltage signals produces a square-wave output from the op-amp, varying in duty cycle according to the potentiometer’s position. This variable duty cycle signal then drives the base of a power transistor, switching current on and off through the load. The 555’s oscillation frequency is much higher than the lamp filament’s ability to thermally cycle (heat and cool), so any variation in duty cycle, or pulse width, has the effect of controlling the total power dissipated by the load over time. Controlling electrical power through a load by means of quickly switching it on and off, and varying the “on” time, is known as pulse-width modulation, or PWM. It is a very efficient means of controlling electrical power because the controlling element (the power transistor) dissipates comparatively little power in switching on and off, especially if compared to the wasted power dissipated of a rheostat in a similar situation. When the transistor is in cutoff, its power dissipation is zero because there is no current through it. When the transistor is saturated, its dissipation is very low because there is little voltage dropped between collector and emitter while it is conducting current. PWM is a concept easier understood through experimentation than reading. It would be nice to view the capacitor voltage, potentiometer voltage, and op-amp output waveforms all on one (triple-trace) oscilloscope to see how they relate to one another, and to the load power. However, most of us have no access to a triple-trace oscilloscope, much less any oscilloscope at all, so an alternative method is to slow the 555 oscillator down enough that the three voltages may be compared with a simple DC voltmeter. Replace the 0.1 µF capacitor with one that is 100 µF or larger. This will slow the oscillation frequency down by a factor of at least a thousand, enabling you to measure the capacitor voltage slowly rise over time, and the op-amp output transition from “high” to “low” when the capacitor voltage becomes greater than the potentiometer voltage. With such a slow oscillation frequency, the load power will not be proportioned as before. Rather, the lamp will turn on and off at regular intervals. Feel free to experiment with other capacitor or resistor values to speed up the oscillations enough so the lamp never fully turns on or off, but is “throttled” by quick on-and-off pulsing of the transistor. When you examine the schematic, you will notice two operational amplifiers connected in parallel. This is done to provide maximum current output to the base terminal of the power transistor. A single op-amp (one-half of a 1458 IC) may not be able to provide sufficient output current to drive the transistor into saturation, so two op-amps are used in tandem. This should only be done if the op-amps in question are overload-protected, which the 1458 series of op-amps are. Otherwise, it is possible (though unlikely) that one op-amp could turn on before the other, and damage result from the two outputs short-circuiting each other (one driving “high” and the other driving “low” simultaneously). The inherent short-circuit protection offered by the 1458 allows for direct driving of the power transistor base without any need for a current-limiting resistor. The three diodes in series connecting the op-amps’ outputs to the transistor’s base are there to drop voltage and ensure the transistor falls into cutoff when the op-amp outputs go “low.” Because the 1458 op-amp cannot swing its output voltage all the way down to ground potential, but only to within about 2 volts of ground, a direct connection from the op-amp to the transistor would mean the transistor would never fully turn off. Adding three silicon diodes in series drops approximately 2.1 volts (0.7 volts times 3) to ensure there is minimal voltage at the transistor’s base when the op-amp outputs go “low.” It is interesting to listen to the op-amp output signal through an audio detector as the potentiometer is adjusted through its full range of motion. Adjusting the potentiometer has no effect on signal frequency, but it greatly affects duty cycle. Note the difference in tone quality, or timbre, as the potentiometer varies the duty cycle from 0% to 50% to 100%. Varying the duty cycle has the effect of changing the harmonic content of the waveform, which makes the tone sound different. You might notice a particular uniqueness to the sound heard through the detector headphones when the potentiometer is in the center position (50% duty cycle—50% load power), versus a kind of similarity in sound just above or below 50% duty cycle. This is due to the absence or presence of even-numbered harmonics. Any waveform that is symmetrical above and below its centerline, such as a square wave with a 50% duty cycle, contains no even-numbered harmonics, only odd-numbered. If the duty cycle is below or above 50%, the waveform will not exhibit this symmetry, and there will be even-numbered harmonics. The presence of these even-numbered harmonic frequencies can be detected by the human ear, as some of them correspond to octaves of the fundamental frequency and thus “fit” more naturally into the tone scheme.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/06%3A_Analog_Integrated_Circuits/6.10%3A_Class_B_Audio_Amplifier.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Four 6 volt batteries • Dual operational amplifier, model TL082 recommended (Radio Shack catalog # 276-1715) • One NPN power transistor in a TO-220 package—(Radio Shack catalog # 276-2020 or equivalent) • One PNP power transistor in a TO-220 package—(Radio Shack catalog # 276-2027 or equivalent) • One 1N914 switching diode (Radio Shack catalog # 276-1620) • One capacitor, 47 µF electrolytic, 35 WVDC (Radio Shack catalog # 272-1015 or equivalent) • Two capacitors, 0.22 µF, non-polarized (Radio Shack catalog # 272-1070) • One 10 kΩ potentiometer, linear taper (Radio Shack catalog # 271-1715) Be sure to use an op-amp that has a high slew rate. Avoid the LM741 or LM1458 for this reason. The closer matched the two transistors are, the better. If possible, try to obtain TIP41 and TIP42 transistors, which are closely matched NPN and PNP power transistors with dissipation ratings of 65 watts each. If you cannot get a TIP41 NPN transistor, the TIP3055 (available from Radio Shack) is a good substitute. Do not use very large (i.e. TO-3 case) power transistors, as the op-amp may have trouble driving enough current to their bases for good operation. CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 4: “Bipolar Junction Transistors” Lessons In Electric Circuits, Volume 3, chapter 8: “Operational Amplifiers” LEARNING OBJECTIVES • How to build a “push-pull” class B amplifier using complementary bipolar transistors • The effects of “crossover distortion” in a push-pull amplifier circuit • Using negative feedback via an op-amp to correct circuit nonlinearities SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This project is an audio amplifier suitable for amplifying the output signal from a small radio, tape player, CD player, or any other source of audio signals. For stereo operation, two identical amplifiers must be built, one for the left channel and other for the right channel. To obtain an input signal for this amplifier to amplify, just connect it to the output of a radio or other audio device like this: This amplifier circuit also works well in amplifying “line-level” audio signals from high-quality, modular stereo components. It provides a surprising amount of sound power when played through a large speaker, and maybe run without heatsinks on the transistors (though you should experiment with it a bit before deciding to forego heat sinks, as the power dissipation varies according to the type of speaker used). The goal of any amplifier circuit is to reproduce the input waveshape as accurately as possible. Perfect reproduction is impossible, of course, and any differences between the output and input waveshapes are known as distortion. In an audio amplifier, distortion may cause unpleasant tones to be superimposed on the true sound. There are many different configurations of audio amplifier circuitry, each with its own advantages and disadvantages. This particular circuit is called a “class B,” push-pull circuit. Most audio “power” amplifiers use a class B configuration, where one transistor provides power to the load during one-half of the waveform cycle (it pushes) and a second transistor provides power to the load for the other half of the cycle (it pulls). In this scheme, neither transistor remains “on” for the entire cycle, giving each one a time to “rest” and cool during the waveform cycle. This makes for a power-efficient amplifier circuit, but leads to a distinct type of nonlinearity known as “crossover distortion.” Shown here is a sine-wave shape, equivalent to a constant audio tone of constant volume: In a push-pull amplifier circuit, the two transistors take turns amplifying the alternate half-cycles of the waveform like this: If the “hand-off” between the two transistors is not precisely synchronized, though, the amplifier’s output waveform may look something like this instead of a pure sine wave: Here, distortion results from the fact that there is a delay between the time one transistor turns off and the other transistor turns on. This type of distortion, where the waveform “flattens” at the crossover point between positive and negative half-cycles, is called crossover distortion. One common method of mitigating crossover distortion is to bias the transistors so that their turn-on/turn-off points actually overlap, so that both transistors are in a state of conduction for a brief moment during the crossover period: This form of amplification is technically known as class AB rather than class B because each transistor is “on” for more than 50% of the time during a complete waveform cycle. The disadvantage to doing this, though, is increased power consumption of the amplifier circuit, because during the moments of time where both transistors are conducting, there is current conducted through the transistors that are not going through the load, but is merely being “shorted” from one power supply rail to the other (from -V to +V). Not only is this a waste of energy, but it dissipates more heat energy in the transistors. When transistors increase in temperature, their characteristics change (Vbe forward voltage drop, β, junction resistances, etc.), making proper biasing difficult. In this experiment, the transistors operate in pure class B mode. That is, they are never conducting at the same time. This saves energy and decreases heat dissipation, but lends itself to crossover distortion. The solution taken in this circuit is to use an op-amp with negative feedback to quickly drive the transistors through the “dead” zone producing crossover distortion and reduce the amount of “flattening” of the waveform during crossover. The first (leftmost) op-amp shown in the schematic diagram is nothing more than a buffer. A buffer helps to reduce the loading of the input capacitor/resistor network, which has been placed in the circuit to filter out any DC bias voltage out of the input signal, preventing any DC voltage from becoming amplified by the circuit and sent to the speaker where it might cause damage. Without the buffer op-amp, the capacitor/resistor filtering circuit reduces the low-frequency (“bass”) response of the amplifier and accentuates the high-frequency (“treble”). The second op-amp functions as an inverting amplifier whose gain is controlled by the 10 kΩ potentiometer. This does nothing more than providing a volume control for the amplifier. Usually, inverting op-amp circuits have their feedback resistor(s) connected directly from the op-amp output terminal to the inverting input terminal like this: If we were to use the resulting output signal to drive the base terminals of the push-pull transistor pair, though, we would experience significant crossover distortion, because there would be a “dead” zone in the transistors’ operation as the base voltage went from + 0.7 volts to - 0.7 volts: If you have already constructed the amplifier circuit in its final form, you may simplify it to this form and listen to the difference in sound quality. If you have not yet begun construction of the circuit, the schematic diagram shown above would be a good starting point. It will amplify an audio signal, but it will sound horrible! The reason for the crossover distortion is that when the op-amp output signal is between + 0.7 volts and - 0.7 volts, neither transistor will be conducting, and the output voltage to the speaker will be 0 volts for the entire 1.4 volts span of base voltage swing. Thus, there is a “zone” in the input signal range where no change in speaker output voltage will occur. Here is where intricate biasing techniques are usually introduced to the circuit to reduce this 1.4-volt “gap” in transistor input signal response. Usually, something like this is done: The two series-connected diodes will drop approximately 1.4 volts, equivalent to the combined Vbe forward voltage drops of the two transistors, resulting in a scenario where each transistor is just on the verge of turning on when the input signal is zero volts, eliminating the 1.4 volt “dead” signal zone that existed before. Unfortunately, though, this solution is not perfect: as the transistors heat up from conducting power to the load, their Vbe forward voltage drops will decrease from 0.7 volts to something less, such as 0.6 volts or 0.5 volts. The diodes, which are not subject to the same heating effect because they do not conduct any substantial current, will not experience the same change in forward voltage drop. Thus, the diodes will continue to provide the same 1.4-volt bias voltage even though the transistors require less bias voltage due to heating. The result will be that the circuit drifts into class AB operation, where both transistors will be in a state of conduction part of the time. This, of course, will result in more heat dissipation through the transistors, exacerbating the problem of forward voltage drop change. A common solution to this problem is the insertion of temperature-compensation “feedback” resistors in the emitter legs of the push-pull transistor circuit: This solution doesn’t prevent simultaneous turn-on of the two transistors, but merely reduces the severity of the problem and prevents thermal runaway. It also has the unfortunate effect of inserting resistance in the load current path, limiting the output current of the amplifier. The solution I opted for in this experiment is one that capitalizes on the principle of op-amp negative feedback to overcome the inherent limitations of the push-pull transistor output circuit. I use one diode to provide a 0.7-volt bias voltage for the push-pull pair. This is not enough to eliminate the “dead” signal zone, but it reduces it by at least 50%: Since the voltage drop of a single diode will always be less than the combined voltage drops of the two transistors’ base-emitter junctions, the transistors can never turn on simultaneously, thereby preventing class AB operation. Next, to help get rid of the remaining crossover distortion, the feedback signal of the op-amp is taken from the output terminal of the amplifier (the transistors’ emitter terminals) like this: The op-amp’s function is to output whatever voltage signal it has to in order to keep its two input terminals at the same voltage (0 volts differential). By connecting the feedback wire to the emitter terminals of the push-pull transistors, the op-amp has the ability to sense any “dead” zone where neither transistor is conducting, and output an appropriate voltage signal to the bases of the transistors to quickly drive them into conduction again to “keep up” with the input signal waveform. This requires an op-amp with a high slew rate (the ability to produce a fast-rising or fast-falling output voltage), which is why the TL082 op-amp was specified for this circuit. Slower op-amps such as the LM741 or LM1458 may not be able to keep up with the high dv/dt (voltage rate-of-change over time, also known as de/dt) necessary for low-distortion operation. Only a couple of capacitors are added to this circuit to bring it into its final form: a 47 µF capacitor connected in parallel with the diode helps to keep the 0.7 volt bias voltage constant despite large voltage swings in the op-amp’s output, while a 0.22 µF capacitor connected between the base and emitter of the NPN transistor helps reduce crossover distortion at low volume settings:
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/07%3A_Digital_Integrated_Circuits/7.01%3A_Introduction_to_Digital_Integrated_Circuits.txt	princeton-nlp/TextbookChapters	Digital circuits are circuits dealing with signals restricted to the extreme limits of zero and some full amount. This stands in contrast to analog circuits, in which signals are free to vary continuously between the limits imposed by power supply voltage and circuit resistances. These circuits find use in “true/false” logical operations and digital computation. The circuits in this chapter make use of IC, or integrated circuit, components. Such components are actually networks of interconnected components manufactured on a single wafer of semiconducting material. Integrated circuits providing a multitude of pre-engineered functions are available at very low cost, benefitting students, hobbyists and professional circuit designers alike. Most integrated circuits provide the same functionality as “discrete” semiconductor circuits at higher levels of reliability and at a fraction of the cost. Circuits in this chapter will primarily use CMOS technology, as this form of IC design allows for a broad range of power supply voltage while maintaining generally low power consumption levels. Though CMOS circuitry is susceptible to damage from static electricity (high voltages will puncture the insulating barriers in the MOSFET transistors), modern CMOS ICs are far more tolerant of electrostatic discharge than the CMOS ICs of the past, reducing the risk of chip failure by mishandling. Proper handling of CMOS involves the use of anti-static foam for storage and transport of IC’s, and measures to prevent static charge from building up on your body (use of a grounding wrist strap, or frequently touching a grounded object). Circuits using TTL technology require a regulated power supply voltage of 5 volts, and will not tolerate any substantial deviation from this voltage level. Any TTL circuits in this chapter will be adequately labeled as such, and it will be expected that you realize its unique power supply requirements. When building digital circuits using integrated circuit “chips,” it is highly recommended that you use a breadboard with power supply “rail” connections along the length. These are sets of holes in the breadboard that are electrically common along the entire length of the board. Connect one to the positive terminal of a battery, and the other to the negative terminal, and DC power will be available to any area of the breadboard via connection through short jumper wires: With so many of these integrated circuits having “reset,” “enable,” and “disable” terminals needing to be maintained in a “high” or “low” state, not to mention the VDD (or VCC) and ground power terminals which require connection to the power supply, having both terminals of the power supply readily available for connection at any point along the board’s length is very useful. Most breadboards that I have seen have these power supply “rail” holes, but some do not. Up until this point, I’ve been illustrating circuits using a breadboard lacking this feature, just to show how it isn’t absolutely necessary. However, digital circuits seem to require more connections to the power supply than other types of breadboard circuits, making this feature more than just a convenience. 7.02: Basic Gate Function Parts and Materials • 4011 quad NAND gate (Radio Shack catalog # 276-2411) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Ten-segment bar graph LED (Radio Shack catalog # 276-081) • One 6 volt battery • Two 10 kΩ resistors • Three 470 Ω resistors Caution! The 4011 IC is CMOS, and therefore sensitive to static electricity! Further Reading Lessons In Electric Circuits, Volume 4, chapter 3: “Logic Gates” Learning Objectives • Purpose of a “pulldown” resistor • How to experimentally determine the truth table of a gate • How to connect logic gates together • How to create different logical functions by using NAND gates Experiment Instructions To begin, connect a single NAND gate to two input switches and one LED, as shown. At first, the use of an 8-position switch and a 10-segment LED bar graph may seem excessive since only two switches and one LED are needed to show the operation of a single NAND gate. However, the presence of those extra switches and LEDs make it very convenient to expand the circuit and help make the circuit layout both clean and compact. It is highly recommended that you have a datasheet for the 4011 chip available when you build your circuit. Don’t just follow the illustration shown above! It is important that you develop the skill of reading datasheets, especially “pinout” diagrams when connecting IC terminals to other circuit elements. The datasheet’s connection diagram is an essential piece of information to have. Shown here is my own rendition of what any 4011 datasheet shows: In the breadboard illustration, I’ve shown the circuit built using the lower-left NAND gate: pin #‘s 1 and 2 are the inputs, and pin #3 is the output. Pin #‘s 14 and 7 conduct DC power to all four gate circuits inside the IC chip, “VDD” representing the positive side of the power supply (+V), and “Gnd” representing the negative side of the power supply (-V), or ground. Sometimes the negative power supply terminal will be labeled “VSS” instead of “Gnd” on a datasheet, but it means the same thing. Digital logic circuitry does not make use of split power supplies as op-amps do. Like op-amp circuits, though, ground is still the implicit point of reference for all voltage measurements. If I were to speak of a “high” signal being present on a certain pin of the chip, I would mean that there was full voltage between that pin and the negative side of the power supply (ground). Note how all inputs of the unused gates inside the 4011 chip are connected either to VDD or ground. This is not a mistake, but an act of intentional design. Since the 4011 is a CMOS integrated circuit, and CMOS circuit inputs left unconnected (floating) can assume any voltage level merely from intercepting a static electric charge from a nearby object, leaving inputs floating means that those unused gates may receive any random combinations of “high” and “low” signals. Why is this undesirable, if we aren’t using those gates? Who cares what signals they receive, if we are not doing anything with their outputs? The problem is if static voltage signals appear at the gate inputs that are not fully “high” or fully “low,” the gates’ internal transistors may begin to turn on in such a way as to draw excessive current. At worst, this could lead to damage of the chip. At best it means excessive power consumption. It matters little if we choose to connect these unused gate inputs “high” (VDD) or “low” (ground), so long as we connect them to one of those two places. In the breadboard illustration, I show all the top inputs connected to VDD, and all the bottom inputs (of the unused gates) connected to ground. This was done merely because those power supply rail holes were closer and did not require long jumper wires! Please note that none of the unused gate outputs have been connected to VDD or ground, and for good reason! If I were to do that, I may be forcing a gate to assume the opposite output state that it’s trying to achieve, which is a complicated way of saying that I would have created a short-circuit. Imagine a gate that is supposed to output a “high” logic level (for a NAND gate, this would be true if any of its inputs were “low”). If such a gate were to have its output terminal directly connected to ground, it could never reach a “high” state (being made electrically common to ground through the jumper wire connection). Instead, its upper (P-channel) output transistor would be turned on in vain, sourcing maximum current to a nonexistent load. This would very likely damage the gate! Gate output terminals, by their very nature, generate their own logic levels and never “float” in the same way that CMOS gate inputs do. The two 10 kΩ resistors are placed in the circuit to avoid floating input conditions on the used gate. With a switch closed, the respective input will be directly connected to VDD and therefore be “high.” With a switch open, the 10 kΩ “pulldown” resistor provides a resistive connection to ground, ensuring a secure “low” state at the gate’s input terminal. This way, the input will not be susceptible to stray static voltages. With the NAND gate connected to the two switches and one LED as shown, you are ready to develop a “truth table” for the NAND gate. Even if you already know what a NAND gate truth table looks like, this is a good exercise in experimentation: discovering a circuit’s behavioral principles by induction. Draw a truth table on a piece of paper like this: The “A” and “B” columns represent the two input switches, respectively. When the switch is on, its state is “high” or 1. When the switch is off, its state is “low,” or 0, as ensured by its pulldown resistor. The gate’s output, of course, is represented by the LED: whether it is lit (1) or unlit (0). After placing the switches in every possible combination of states and recording the LED’s status, compare the resulting truth table with what a NAND gate’s truth table should be. As you can imagine, this breadboard circuit is not limited to testing NAND gates. Any gate type may be tested with two switches, two pulldown resistors, and an LED to indicate output status. Just be sure to double-check the chip’s “pinout” diagram before substituting it pin-for-pin in place of the 4011. Not all “quad” gate chips have the same pin assignments! Additional Improvement An improvement you might want to make to this circuit is to assign a couple of LEDs to indicate input status, in addition to the one LED assigned to indicate the output. This makes operation a little more interesting to observe, and has the further benefit of indicating if a switch fails to close (or open) by showing the true input signal to the gate, rather than forcing you to infer input status from switch position:
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/07%3A_Digital_Integrated_Circuits/7.03%3A_NOR_Gate_S-R_Latch.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • 4001 quad NOR gate (Radio Shack catalog # 276-2401) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Ten-segment bar graph LED (Radio Shack catalog # 276-081) • One 6 volt battery • Two 10 kΩ resistors • Two 470 Ω resistors • Two 100 Ω resistors Caution! The 4001 IC is CMOS, and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 3: “Logic Gates” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • The effects of positive feedback in a digital circuit • What is meant by the “invalid” state of a latch circuit • What a race condition is in a digital circuit • The importance of valid “high” CMOS signal voltage levels SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS The 4001 integrated circuit is a CMOS quad NOR gate, identical in input, output, and power supply pin assignments to the 4011 quad NAND gate. Its “pinout,” or “connection,” diagram is as such: When two NOR gates are cross-connected as shown in the schematic diagram, there will be positive feedback from output to input. That is, the output signal tends to maintain the gate in its last output state. Just as in op-amp circuits, positive feedback creates hysteresis. This tendency for the circuit to remain in its last output state gives it a sort of “memory.” In fact, there are solid-state computer memory technologies based on circuitry like this! If we designate the left switch as the “Set” input and the right switch as the “Reset,” the left LED will be the “Q” output and the right LED the “Q-not” output. With the Set input “high” (switch on) and the Reset input “low,” Q will go “high” and Q-not will go “low.” This is known as the set state of the circuit. Making the Reset input “high” and the Set input “low” reverses the latch circuit’s output state: Q “low” and Q-not “high.” This is known as the reset state of the circuit. If both inputs are placed into the “low” state, the circuit’s Q and Q-not outputs will remain in their last states, “remembering” their prior settings. This is known as the latched state of the circuit. Because the outputs have been designated “Q” and “Q-not,” it is implied that their states will always be complementary (opposite). Thus, if something were to happen that forced both outputs to the same state, we would be inclined to call that mode of the circuit “invalid.” This is exactly what will happen if we make both Set and Reset inputs “high:” both Q and Q-not outputs will be forced to the same “low” logic state. This is known as the invalid or illegal state of the circuit, not because something has gone wrong, but because the outputs have failed to meet the expectations established by their labels. Since the “latched” state is a hysteretic condition whereby the last output states are “remembered,” one might wonder what will happen if the circuit powers up this way, with no previous state to hold. To experiment, place both switches in their off positions, making both Set and Reset inputs low, then disconnect one of the battery wires from the breadboard. Then, quickly make and break contact between that battery wire and its proper connection point on the breadboard, noting the status of the two LEDs as the circuit is powered up again and again: When a latch circuit such as this is powered up into its “latched” state, the gates race against each other for control. Given the “low” inputs, both gates try to output “high” signals. If one of the gates reaches its “high” output state before the other, that “high” state will be fed back to the other gate’s input to force its output “low,” and the race is won by the faster gate. Invariably, one gate wins the race, due to internal variations between gates in the chip, and/or external resistances and capacitances that act to delay one gate more than the other. What this usually means is that the circuit tends to power up in the same mode, over and over again. However, if you are persistent in your powering/un-powering cycles, you should see at least a few times where the latch circuit powers up latched in the opposite state from normal. Race conditions are generally undesirable in any kind of system, as they lead to unpredictable operation. They can be particularly troublesome to locate, as this experiment shows, because of the unpredictability they create. Imagine a scenario, for instance, where one of the two NOR gates was exceptionally slow-acting, due to a defect in the chip. This handicap would cause the other gate to win the power-up race every time. In other words, the circuit will be very predictable on power-up with both inputs “low.” However, suppose that the unusual chip was to be replaced by one with more evenly matched gates, or by a chip where the other NOR gate were consistently slower. Normal circuit behavior is not supposed to change when a component is replaced, but if race conditions are present, a change of components may very well do just that. Due to the inherent race tendency of an S-R latch, one should not design a circuit with the expectation of a consistent power-up state, but rather use external means to “force” the race so that the desired gate always “wins.” An interesting modification to try in this circuit is to replace one of the 470 Ω LED “dropping” resistors with a lower-value unit, such as 100 Ω. The obvious effect of this alteration will be increased LED brightness, as more current is allowed through. A not-so-obvious effect will also result, and it is this effect which holds great learning value. Try replacing one of the 470 Ω resistors with a 100 Ω resistor, and operate the input signal switches through all four possible setting combinations, noting the behavior of the circuit. You should note that the circuit refuses to latch in one of its states (either Set or Reset), but only in the other state, when the input switches are both set “low” (the “latch” mode). Why is this? Take a voltmeter and measure the output voltage of the gate whose output is “high” when both inputs are “low.” Note this voltage indication, then set the input switches in such a way that the other state (either Reset or Set) is forced, and measure the output voltage of the other gate when its output is “high.” Note the difference between the two gate output voltage levels, one gate loaded by an LED with a 470 Ω resistor, and the other loaded by an LED with a 100 Ω resistor. The one loaded down by the “heavier” load (100 Ω resistor) will be much less: so much less than this voltage will not be interpreted by the other NOR gate’s input as a “high” signal at all as it is fed back! All logic gates have permissible “high” and “low” input signal voltage ranges, and if the voltage of a digital signal falls outside this permissible range, it might not be properly interpreted by the receiving gate. In a latch circuit such as this, which depends on a solid “high” signal fed back from the output of one gate to the input of the other, a “weak” signal will not be able to maintain the positive feedback necessary to keep the circuit latched in one of its states. This is one reason I favor the use of a voltmeter as a logic “probe” for determining digital signal levels, rather than an actual logic probe with “high” and “low” lights. A logic probe may not indicate the presence of a “weak” signal, whereas a voltmeter definitely will by means of its quantitative indication. This type of problem, common in circuits where different “families” of integrated circuits are mixed (TTL and CMOS, for example), can only be found with test equipment providing quantitative measurements of signal level.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/07%3A_Digital_Integrated_Circuits/7.04%3A_NAND_Gate_S-R_Enabled_Latch.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • 4011 quad NAND gate (Radio Shack catalog # 276-2411) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Ten-segment bar graph LED (Radio Shack catalog # 276-081) • One 6 volt battery • Three 10 kΩ resistors • Two 470 Ω resistors Caution! The 4011 IC is CMOS, and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 3: “Logic Gates” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • Principle and function of an enabled latch circuit SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS Although this circuit uses NAND gates instead of NOR gates, its behavior is identical to that of the NOR gate S-R latch (a “high” Set input drives Q “high,” and a “high” Reset input drives Q-not “high”), except for the presence of a third input: the Enable. The purpose of the Enable input is to enable or disable the Set and Reset inputs from having effect over the circuit’s output status. When the Enable input is “high,” the circuit acts just like the NOR gate S-R latch. When the Enable input is “low,” the Set and Reset inputs are disabled and have no effect whatsoever on the outputs, leaving the circuit in its latched state. This kind of latch circuit (also called a gated S-R latch), may be constructed from two NOR gates and two AND gates, but the NAND gate design is easier to build since it makes use of all four gates in a single integrated circuit. 7.05: NAND Gate S-R Flip-Flop PARTS AND MATERIALS • 4011 quad NAND gate (Radio Shack catalog # 276-2411) • 4001 quad NOR gate (Radio Shack catalog # 276-2401) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Ten-segment bar graph LED (Radio Shack catalog # 276-081) • One 6 volt battery • Three 10 kΩ resistors • Two 470 Ω resistors Caution! The 4011 IC is CMOS, and therefore sensitive to static electricity! Although the parts list calls for a ten-segment LED unit, the illustration shows two individual LEDs being used instead. This is due to lack of room on my breadboard to mount the switch assembly, two integrated circuits, and the bar graph. If you have room on your breadboard, feel free to use the bar graph as called for in the parts list, and as shown in prior latch circuits. CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 3: “Logic Gates” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • The difference between a gated latch and a flip-flop • How to build a “pulse detector” circuit • Learn the effects of switch contact “bounce” on digital circuits SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS The only difference between a gated (or enabled) latch and a flip-flop is that a flip-flop is enabled only on the rising or falling edge of a “clock” signal, rather than for the entire duration of a “high” enable signal. Converting an enabled latch into a flip-flop simply requires that a “pulse detector” circuit be added to the Enable input so that the edge of a clock pulse generates a brief “high” Enable pulse: The single NOR gate and three inverter gates create this effect by exploiting the propagation delay time of multiple, cascaded gates. In this experiment, I use three NOR gates with paralleled inputs to create three inverters, thus using all four NOR gates of a 4001 integrated circuit: Normally, when using a NOR gate as an inverter, one input would be grounded while the other acts as the inverter input, to minimize input capacitance and increase speed. Here, however, slow response is desired, and so I parallel the NOR inputs to make inverters rather than use the more conventional method. Please note that this particular pulse detector circuit produces a “high” output pulse at every falling edge of the clock (input) signal. This means that the flip-flop circuit should be responsive to the Set and Reset input states only when the middle switch is moved from “on” to “off,” not from “off” to “on.” When you build this circuit, though, you may discover that the outputs respond to Set and Reset input signals during both transitions of the Clock input, not just when it is switched from a “high” state to a “low” state. The reason for this is contact bounce: the effect of a mechanical switch rapidly making-and-breaking when its contacts are first closed, due to the elastic collision of the metal contact pads. Instead of the Clock switch producing a single, clean low-to-high signal transition when closed, there will most likely be several low-high-low “cycles” as the contact pads “bounce” upon off-to-on actuation. The first high-to-low transition caused by bouncing will trigger the pulse detector circuit, enabling the S-R latch for that moment in time, making it responsive to the Set and Reset inputs. Ideally, of course, switches are perfect and bounce-free. In the real world, though, contact bounce is a very common problem for digital gate circuits operated by switch inputs and must be understood well if it is to be overcome.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/07%3A_Digital_Integrated_Circuits/7.06%3A_LED_Sequencer.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • 4017 decade counter/divider (Radio Shack catalog # 276-2417) • 555 timer IC (Radio Shack catalog # 276-1723) • Ten-segment bargraph LED (Radio Shack catalog # 276-081) • One SPST switch • One 6 volt battery • 10 kΩ resistor • 1 MΩ resistor • 0.1 µF capacitor (Radio Shack catalog # 272-135 or equivalent) • Coupling capacitor, 0.047 to 0.001 µF • Ten 470 Ω resistors • Audio detector with headphones Caution! The 4017 IC is CMOS, and therefore sensitive to static electricity! Any single-pole, single-throw switch is adequate. A household light switch will work fine and is readily available at any hardware store. The audio detector will be used to assess signal frequency. If you have access to an oscilloscope, the audio detector is unnecessary. CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 3: “Logic Gates” Lessons In Electric Circuits, Volume 4, chapter 4: “Switches” Lessons In Electric Circuits, Volume 4, chapter 11: “Counters” LEARNING OBJECTIVES • Use of a 555 timer circuit to produce “clock” pulses (astable multivibrator) • Use of a 4017 decade counter/divider circuit to produce a sequence of pulses • Use of a 4017 decade counter/divider circuit for frequency division • Using a frequency divider and timepiece (watch) to measure frequency • Purpose of a “pulldown” resistor • Learn the effects of switch contact “bounce” on digital circuits • Use of a 555 timer circuit to “debounce” a mechanical switch (monostable multivibrator) SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS The model 4017 integrated circuit is a CMOS counter with ten output terminals. One of these ten terminals will be in a “high” state at any given time, with all others being “low,” giving a “one-of-ten” output sequence. If low-to-high voltage pulses are applied to the “clock” (Clk) terminal of the 4017, it will increment its count, forcing the next output into a “high” state. With a 555 timer connected as an astable multivibrator (oscillator) of low frequency, the 4017 will cycle through its ten-count sequence, lighting up each LED, one at a time, and “recycling” back to the first LED. The result is a visually pleasing sequence of flashing lights. Feel free to experiment with resistor and capacitor values on the 555 timer to create different flash rates. Try disconnecting the jumper wire leading from the 4017’s “Clock” terminal (pin #14) to the 555’s “Output” terminal (pin #3) where it connects to the 555 timer chip, and hold its end in your hand. If there is sufficient 60 Hz power-line “noise” around you, the 4017 will detect it as a fast clock signal, causing the LEDs to blink very rapidly. Two terminals on the 4017 chip, “Reset” and “Clock Enable,” are maintained in a “low” state by means of a connection to the negative side of the battery (ground). This is necessary if the chip is to count freely. If the “Reset” terminal is made “high,” the 4017’s output will be reset back to 0 (pin #3 “high,” all other output pins “low”). If the “Clock Enable” is made “high,” the chip will stop responding to the clock signal and pause in its counting sequence. If the 4017’s “Reset” terminal is connected to one of its ten output terminals, its counting sequence will be cut short or truncated. You may experiment with this by disconnecting the “Reset” terminal from ground, then connecting a long jumper wire to the “Reset” terminal for easy connection to the outputs at the ten-segment LED bargraph. Notice how many (or how few) LEDs light up with the “Reset” connected to any one of the outputs: Counters such as the 4017 may be used as digital frequency dividers, to take a clock signal and produce a pulse occurring at some integer factor of the clock frequency. For example, if the clock signal from the 555 timer is 200 Hz, and the 4017 is configured for a full-count sequence (the “Reset” terminal connected to ground, giving a full, ten-step count), a signal with a period ten times as long (20 Hz) will be present at any of the 4017’s output terminals. In other words, each output terminal will cycle once for every ten cycles of the clock signal: a frequency ten times as slow. To experiment with this principle, connect your audio detector between output 0 (pin #3) of the 4017 and ground, through a very small capacitor (0.047 µF to 0.001 µF). The capacitor is used for “coupling” AC signals only, to that you may audibly detect pulses without placing a DC (resistive) load on the counter chip output. With the 4017 “Reset” terminal grounded, you will have a full-count sequence, and you will hear a “click” in the headphones every time the “0” LED lights up, corresponding to 1/10 of the 555’s actual output frequency: In fact, knowing this mathematical relationship between clicks heard in the headphone and the clock frequency allows us to measure the clock frequency to a fair degree of precision. Using a stopwatch or other timepiece, count the number of clicks heard in one full minute while connected to the 4017’s “0” output. Using a 1 MΩ resistor and 0.1 µF capacitor in the 555 timing circuit, and a power supply voltage of 13 volts (instead of 6), I counted 79 clicks in one minute from my circuit. Your circuit may produce slightly different results. Multiply the number of pulses counted at the “0” output by 10 to obtain the number of cycles produced by the 555 timer during that same time (my circuit: 79 x 10 = 790 cycles). Divide this number by 60 to obtain the number of timer cycles elapsed in each second (my circuit: 790/60 = 13.17). This final figure is the clock frequency in Hz. Now, leaving one test probe of the audio detector connected to ground, take the other test probe (the one with the coupling capacitor connected in series) and connect it to pin #3 of the 555 timer. The buzzing you hear is the undivided clock frequency: By connecting the 4017’s “Reset” terminal to one of the output terminals, a truncated sequence will result. If we are using the 4017 as a frequency divider, this means the output frequency will be a different factor of the clock frequency: 1/9, 1/8, 1/7, 1/6, 1/5, 1/4, 1/3, or 1/2, depending on which output terminal we connect the “Reset” jumper wire to. Re-connect the audio detector test probe to output “0” of the 4017 (pin #3), and connect the “Reset” terminal jumper to the sixth LED from the left on the bargraph. This should produce a 1/5 frequency division ratio: Counting the number of clicks heard in one minute again, you should obtain a number approximately twice as large as what was counted with the 4017 configured for a 1/10 ratio, because 1/5 is twice as large a ratio as 1/10. If you do not obtain a count that is exactly twice what you obtained before, it is because of error inherent to the method of counting cycles: coordinating your sense of hearing with the display of a stopwatch or other time-keeping device. Try replacing the 1 MΩ timing resistor in the 555 circuit with one of greatly lesser value, such as 10 kΩ. This will increase the clock frequency driving the 4017 chip. Use the audio detector to listen to the divided frequency at pin #3 of the 4017, noting the different tones produced as you move the “Reset” jumper wire to different outputs, creating different frequency division ratios. See if you can produce octaves by dividing the original frequency by 2, then by 4, and then by 8 (each descending octave represents one-half the previous frequency). Octaves are readily distinguished from other divided frequencies by their similar pitches to the original tone. A final lesson that may be learned from this circuit is that of switch contact “bounce.” For this, you will need a switch to provide clock signals to the 4017 chip, instead of the 555 timer. Re-connect the “Reset” jumper wire to ground to enable a full ten-step count sequence, and disconnect the 555’s output from the 4017’s “Clock” input terminal. Connect a switch in series with a 10 kΩ pulldown resistor, and connect this assembly to the 4017 “Clock” input as shown: The purpose of a “pulldown” resistor is to provide a definite “low” logic state when the switch contact opens. Without this resistor in place, the 4017’s “Clock” input wire would be floating whenever the switch contact was opened, leaving it susceptible to interference from stray static voltages or electrical “noise,” either one capable of making the 4017 count randomly. With the pulldown resistor in place, the 4017’s “Clock” input will have a definite, albeit resistive, connection to ground, providing a stable “low” logic state that precludes any interference from static electricity or “noise” coupled from nearby AC circuit wiring. Actuate the switch on and off, noting the action of the LEDs. With each off-to-on switch transition, the 4017 should increment once in its count. However, you may notice some strange behavior: sometimes, the LED sequence will “skip” one or even several steps with a single switch closure. Why is this? It is due to very rapid, mechanical “bouncing” of the switch contacts. When two metallic contacts are brought together rapidly as does happen inside most switches, there will be an elastic collision. This collision results in the contacts making and breaking very rapidly as they “bounce” off one another. Normally, this “bouncing” is much to rapid for you to see its effects, but in a digital circuit such as this where the counter chip is able to respond to very quick clock pulses, these “bounces” are interpreted as distinct clock signals, and the count incremented accordingly. One way to combat this problem is to use a timing circuit to produce a single pulse for any number of input pulse signals received within a short amount of time. The circuit is called a monostable multivibrator, and any technique eliminating the false pulses caused by switch contact “bounce” is called debouncing. The 555 timer circuit is capable of functioning as a debouncer, if the “Trigger” input is connected to the switch as such: Please note that since we are using the 555 once again to provide a clock signal to the 4017, we must re-connect pin #3 of the 555 chip to pin #14 of the 4017 chip! Also, if you have altered the values of the resistor or capacitor in the 555 timer circuit, you should return to the original 1 MΩ and 0.1 µF components. Actuate the switch again and note the counting behavior of the 4017. There should be no more “skipped” counts as there were before because the 555 timer outputs a single, crisp pulse for every on-to-off actuation (notice the inversion of operation here!) of the switch. It is important that the timing of the 555 circuit be appropriate: the time to charge the capacitor should be longer than the “settling” period of the switch (the time required for the contacts to stop bouncing), but not so long that the timer would “miss” a rapid sequence of switch actuation, if they were to occur.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/07%3A_Digital_Integrated_Circuits/7.07%3A_Simple_Combination_Lock.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • 4001 quad NOR gate (Radio Shack catalog # 276-2401) • 4070 quad XOR gate (Radio Shack catalog # 900-6906) • Two, eight-position DIP switches (Radio Shack catalog # 275-1301) • Two light-emitting diodes (Radio Shack catalog # 276-026 or equivalent) • Four 1N914 “switching” diodes (Radio Shack catalog # 276-1122) • Ten 10 kΩ resistors • Two 470 Ω resistors • Pushbutton switch, normally open (Radio Shack catalog # 275-1556) • Two 6 volt batteries Caution! Both the 4001 and 4070 ICs are CMOS, and therefore sensitive to static electricity! This experiment may be built using only one 8-position DIP switch, but the concept is easier to understand if two switch assemblies are used. The idea is, one switch acts to hold the correct code for unlocking the lock, while the other switch serves as a data entry point for the person trying to open the lock. In real life, of course, the switch assembly with the “key” code set on it must be hidden from the sight of the person opening the lock, which means it must be physically located elsewhere from where the data entry switch assembly is. This requires two switch assemblies. However, if you understand this concept clearly, you may build a working circuit with only one 8-position switch, using the left four switches for data entry and the right four switches to hold the “key” code. For extra effect, choose different colors of LED: green for “Go” and red for “No go.” CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 3: “Logic Gates” LEARNING OBJECTIVES • Using XOR gates as bit comparators • How to build simple gate functions with diodes and a pull-up/down resistor • Using NOR gates as controlled inverters SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This circuit illustrates the use of XOR (Exclusive-OR) gates as bit comparators. Four of these XOR gates compare the respective bits of two 4-bit binary numbers, each number “entered” into the circuit via a set of switches. If the two numbers match, bit for bit, the green “Go” LED will light up when the “Enter” pushbutton switch is pressed. If the two numbers do not exactly match, the red “No go” LED will light up when the “Enter” pushbutton is pressed. Because four bits provides a mere sixteen possible combinations, this lock circuit is not very sophisticated. If it were used in a real application such as a home security system, the “No go” output would have to be connected to some kind of siren or other alarming device so that the entry of an incorrect code would deter an unauthorized person from attempting another code entry. Otherwise, it would not take much time to try all combinations (0000 through 1111) until the correct one was found! In this experiment, I do not describe how to work this circuit into a real security system or lock mechanism, but only how to make it recognize a pre-entered code. The “key” code that must be matched at the data entry switch array should be hidden from view, of course. If this were part of a real security system, the data entry switch assembly would be located outside the door and the key code switch assembly behind the door with the rest of the circuitry. In this experiment, you will likely locate the two switch assemblies on two different breadboards, but it is entirely possible to build the circuit using just a single (8-position) DIP switch assembly. Again, the purpose of the experiment is not to make a real security system, but merely to introduce you to the principle of XOR gate code comparison. It is the nature of an XOR gate to output a “high” (1) signal if the input signals are not the same logic state. The four XOR gates’ output terminals are connected through a diode network which functions as a four-input OR gate: if any of the four XOR gates outputs a “high” signal—indicating that the entered code and the key code are not identical—then a “high” signal will be passed on to the NOR gate logic. If the two 4-bit codes are identical, then none of the XOR gate outputs will be “high,” and the pull-down resistor connected to the common sides of the diodes will provide a “low” signal state to the NOR logic. The NOR gate logic performs a simple task: prevent either of the LEDs from turning on if the “Enter” pushbutton is not pressed. Only when this pushbutton is pressed can either of the LEDs energize. If the Enter switch is pressed and the XOR outputs are all “low,” the “Go” LED will light up, indicating that the correct code has been entered. If the Enter switch is pressed and any of the XOR outputs are “high,” the “No go” LED will light up, indicating that an incorrect code has been entered. Again, if this were a real security system, it would be wise to have the “No go” output do something that deters an unauthorized person from discovering the correct code by trial-and-error. In other words, there should be some sort of penalty for entering an incorrect code. Let your imagination guide your design of this detail!
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/07%3A_Digital_Integrated_Circuits/7.08%3A_3-bit_Binary_Counter.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • 555 timer IC (Radio Shack catalog # 276-1723) • One 1N914 “switching” diode (Radio Shack catalog # 276-1122) • Two 10 kΩ resistors • One 100 µF capacitor (Radio Shack catalog # 272-1028) • 4027 dual J-K flip-flop (Radio Shack catalog # 900-4394) • Ten-segment bargraph LED (Radio Shack catalog # 276-081) • Three 470 Ω resistors • One 6 volt battery Caution! The 4027 IC is CMOS, and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” Lessons In Electric Circuits, Volume 4, chapter 11: “Counters” LEARNING OBJECTIVES • Using the 555 timer as a square-wave oscillator • How to make an asynchronous counter using J-K flip-flops SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS In a sense, this circuit “cheats” by using only two J-K flip-flops to make a three-bit binary counter. Ordinarily, three flip-flops would be used—one for each binary bit—but in this case, we can use the clock pulse (555 timer output) as a bit of its own. When you build this circuit, you will find that it is a “down” counter. That is, its count sequence goes from 111 to 110 to 101 to 100 to 011 to 010 to 001 to 000 and then back to 111. While it is possible to construct an “up” counter using J-K flip-flops, this would require additional components and introduce more complexity into the circuit. The 555 timer operates as a slow, square-wave oscillator with a duty cycle of approximately 50 percent. This duty cycle is made possible by the use of a diode to “bypass” the lower resistor during the capacitor’s charging cycle, so that the charging time constant is only RC and not 2RC as it would be without the diode in place. It is highly recommended, in this experiment as in all experiments, to build the circuit in stages: identify portions of the circuit with specific functions, and build those portions one at a time, testing each one and verifying its performance before building the next. A very common mistake of new electronics students is to build an entire circuit at once without testing sections of it during the construction process and then be faced with the possibility of several problems simultaneously when it comes time to finally apply power to it. Remember that a small amount of extra attention paid to detail near the beginning of a project is worth an enormous amount of troubleshooting work near the end! Students who make the mistake of not testing circuit portions before attempting to operate the entire circuit often (falsely) think that the time it would take to test those sections is not worth it, and then spend days trying to figure out what the problem(s) might be with their experiment. Following this philosophy, build the 555 timer circuit first, before even plugging the 4027 IC into the breadboard. Connect the 555’s output (pin #3) to the “Least Significant Bit” (LSB) LED so that you have visual indication of its status. Make sure that the output oscillates in a slow, square-wave pattern (LED is “lit” for about as long as it is “off” in a cycle), and that it is a reliable signal (no erratic behavior, no unexplained pauses). If the 555 timer is not working properly, neither will the rest of the counter circuit! Once the timer circuit has been proven good, proceed to plug the 4027 IC into the breadboard and complete the rest of the necessary connections between it, the 555 timer circuit, and the LED assembly.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/07%3A_Digital_Integrated_Circuits/7.09%3A_7-segment_Display.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • 4511 BCD-to-7seg latch/decoder/driver (Radio Shack catalog # 900-4437) • Common-cathode 7-segment LED display (Radio Shack catalog # 276-075) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Four 10 kΩ resistors • Seven 470 Ω resistors • One 6 volt battery Caution! The 4511 IC is CMOS, and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 9: “Combinational Logic Functions” LEARNING OBJECTIVES • How to use the 4511 7-segment decoder/display driver IC • Gain familiarity with the BCD code • How to use 7-segment LED assemblies to create decimal digit displays • How to identify and use both “active-low” and “active-high” logic inputs SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This experiment is more of an introduction to the 4511 decoder/display driver IC than it is a lesson in how to “build up” a digital function from lower-level components. Since 7-segment displays are very common components of digital devices, it is good to be familiar with the “driving” circuits behind them, and the 4511 is a good example of a typical driver IC. Its operating principle is to input a four-bit BCD (Binary-Coded Decimal) value and energize the proper output lines to form the corresponding decimal digit on the 7-segment LED display. The BCD inputs are designated A, B, C, and D in order from least-significant to most-significant. Outputs are labeled a, b, c, d, e, f, and g, each letter corresponding to a standardized segment designation for 7-segment displays. Of course, since each LED segment requires its own dropping resistor, we must use seven 470 Ω resistors placed in series between the 4511’s output terminals and the corresponding terminals of the display unit. Most 7-segment displays also provide for a decimal point (sometimes two!), a separate LED and terminal designated for its operation. All LEDs inside the display unit are made common to each other on one side, either cathode or anode. The 4511 display driver IC requires a common-cathode 7-segment display unit, and so that is what is used here. After building the circuit and applying power, operate the four switches in a binary counting sequence (0000 to 1111), noting the 7-segment display. A 0000 input should result in a decimal “0” display, a 0001 input should result in a decimal “1” display, and so on through 1001 (decimal “9”). What happens for the binary numbers 1010 (10) through 1111 (15)? Read the datasheet on the 4511 IC and see what the manufacturer specifies for operation above an input value of 9. In the BCD code, there is no real meaning for 1010, 1011, 1100, 1101, 1110, or 1111. These are binary values beyond the range of a single decimal digit, and so have no function in a BCD system. The 4511 IC is built to recognize this, and output (or not output!) accordingly. Three inputs on the 4511 chip have been permanently connected to either Vdd or ground: the “Lamp Test,” “Blanking Input,” and “Latch Enable.” To learn what these inputs do, remove the short jumpers connecting them to either power supply rail (one at a time!), and replace the short jumper with a longer one that can reach the other power supply rail. For example, remove the short jumper connecting the “Latch Enable” input (pin #5) to ground, and replace it with a long jumper wire that can reach all the way to the Vdd power supply rail. Experiment with making this input “high” and “low,” observing the results on the 7-segment display as you alter the BCD code with the four input switches. After you’ve learned what the input’s function is, connect it to the power supply rail enabling normal operation, and proceed to experiment with the next input (either “Lamp Test” or “Blanking Input”). Once again, the manufacturer’s datasheet will be informative as to the purpose of each of these three inputs. Note that the “Lamp Test” (LT) and “Blanking Input” (BI) input labels are written with boolean complementation bars over the abbreviations. Bar symbols designate these inputs as active-low, meaning that you must make each one “low” in order to invoke its particular function. Making an active-low input “high” places that particular input into a “passive” state where its function will not be invoked. Conversely, the “Latch Enable” (LE) input has no complementation bar written over its abbreviation, and correspondingly it is shown connected to ground (“low”) in the schematic so as to not invoke that function. The “Latch Enable” input is an active-high input, which means it must be made “high” (connected to Vdd) in order to invoke its function.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/08%3A_555_Timer_Circuits/8.01%3A_The_555_IC.txt	princeton-nlp/TextbookChapters	The 555 integrated circuit is the most popular chip ever manufactured. Independently manufactured by more than 10 manufacturers, still in current production, and almost 40 years old, this little circuit has withstood the test of time. It has been redesigned, improved, and reconfigured in many ways, yet the original design can be bought from many vendors. The design of this chip was right the first time. Originally conceived in 1970 and created by Hans R. Camenzind in 1971, over 1 billion of these ICs were made in 2003 with no apparent reduction in demand. It has been used in everything from toys to spacecraft. Due to its versatility, availability, and low cost it remains a hobbyist favorite. One of the secrets to its success is it is a true black box, its symbolized schematic is simple and accurate enough that designs using this simplification as a reference tend to work first time. You don’t need to understand every transistor in the base schematic to make it work. It has been used to derive the 556, a dual 555, each independent of the other in one 14 pin package, and is the inspiration of the 558, a quad timer in a 16 pin package. What few weak points the original design has have been addressed by redesigns into CMOS technology, with its dramatically reduced current and expanded voltage requirements, and yet the original version remains. Originally conceived as a simple timer, the 555 has been used for oscillators, waveform generators, VCO’s, FM discrimination, and a lot more. It really is an all purpose circuit. SOURCES 8.02: 555 Schmitt Trigger PARTS AND MATERIALS • One 9V Battery • Battery Clip (Radio Shack catalog # 270-325) • Mini Hook Clips (soldered to Battery Clip, Radio Shack catalog # 270-372) • One Potentiometer, 10 KΩ, 15-Turn (Radio Shack catalog # 271-343) • One 555 timer IC (Radio Shack catalog # 276-1723) • One red light-emitting diode (Radio Shack catalog # 276-041 or equivalent) • One green light-emitting diode (Radio Shack catalog # 276-022 or equivalent) • Two 1 KΩ Resistors • One DVM (Digital Volt Meter) or VOM (Volt Ohm Meter) CROSS-REFERENCES Lessons In Electric Circuits, Volume 3, chapter 8: “Positive Feedback” Lessons In Electric Circuits, Volume 4, chapter 3: “Logic Signal Voltage Levels” LEARNING OBJECTIVES • Learn how a Schmitt Trigger works • How to use the 555 timer as an Schmitt Trigger SCHEMATIC DIAGRAM Schmitt Triggers have a convention to show a gate that is also a Schmitt Trigger, shown below. The same schematic redrawn to reflect this convention looks something like this: ILLUSTRATION INSTRUCTIONS The 555 timer is probably one of the more versatile “black box” chips. Its 3 resistor voltage divider, 2 comparators, and built-in set-reset flip-flop are wired to form a Schmitt Trigger in this design. It’s interesting to note that the configuration isn’t even close to the op-amp configuration shown elsewhere, but the end result is identical. Try adjusting the potentiometer until the lights flip states, then measure the voltage. Compare this voltage to the power supply voltage. Adjust the potentiometer the other way until the LED’s flip states again, and measure the voltage. How close to the 1/3 and 2/3 marks did you get? Try substituting the 9V battery with a 6-volt battery, or two 6 volt batteries, and see how close the thresholds are to the 1/3 and 2/3 marks. Schmitt Triggers are a fundamental circuit with several uses. One is signal processing, they can pull digital data out of some extremely noisy environments. Other big uses will be shown in following projects, such as an extremely simple RC oscillator. THEORY OF OPERATION The defining characteristic of any Schmitt Trigger is its hysteresis. In this case, it is 1/3 and 2/3 of the power supply voltage, defined by the built-in resistor voltage divider on the 555. The built-in comparators C1 and C2 compare the input voltage to the references provided by the voltage divider and use the comparison to trip the built-in flip-flop, which drives the output driver, another nice feature of the 555. The 555 can drive up to 200ma off either side of the power supply rail, the output driver creates a very low conduction path to either side of the power supply connections. The circuit “shorts” each side of the LED circuit, leaving the other side to light up. The 5KΩ resistors are not very accurate. It is interesting to note that IC fabrication doesn’t generally allow precision resistors, but the resistors compared to each other are extremely close in value, which is critical to the circuit’s operation.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/08%3A_555_Timer_Circuits/8.03%3A_555_Hysteretic_Oscillator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • One 9V Battery • Battery Clip (Radio Shack catalog # 270-325) • Mini Hook Clips (soldered to Battery Clip, Radio Shack catalog # 270-372) • U1 - 555 timer IC (Radio Shack catalog # 276-1723) • D1 - Red light-emitting diode (Radio Shack catalog # 276-041 or equivalent) • D2 - Green light-emitting diode (Radio Shack catalog # 276-022 or equivalent) • R1,R2 - 1 KΩ 1/4W Resistors • R3 - 10 Ω 1/4W Resistor • R4 - 10 KΩ, 15-Turn Potentiometer (Radio Shack catalog # 271-343) • C1 - 1 µF Capacitor (Radio Shack catalog 272-1434 or equivalent) • C1 - 100 µF Capacitor (Radio Shack catalog 272-1028 or equivalent) CROSS-REFERENCES Lessons In Electric CircuitsVolume 1, chapter 16: Voltage and current calculations Lessons In Electric Circuits, Volume 1, chapter 16: Solving for unknown time Lessons In Electric Circuits, Volume 4, chapter 10: Multivibrators Lessons in Electric Circuits, Volume 3, chapter 8: Positive Feedback LEARNING OBJECTIVES • Learn how to use a Schmitt Trigger for a simple RC Oscillator • Learn a practical application for a RC time constant • Learn one of several 555 timer Astable Multivibrator Configurations SCHEMATIC DIAGRAM Here is one way of drawing the schematic: As mentioned in the previous experiment, there is also another convention, shown below: ILLUSTRATION INSTRUCTIONS This is one of the most basic RC oscillators. It is simple and very predictable. Any inverting Schmitt Trigger will work in this design, although the frequency will shift somewhat depending on the hysteresis of the gate. This circuit has a lower end frequency of 0.7 Hertz, which means each LED will alternate and be lit for just under a second each. As you turn the potentiometer counterclockwise the frequency will increase, going well into the high end audio range. You can verify this with the Audio Detector (Vol. VI, Chapter 3, Section 12) or a piezoelectric speaker, as you continue to turn the potentiometer the pitch of the sound will rise. You can increase the frequency 100 times by replacing the capacitor with the 1µF capacitor, which will also raise the maximum frequency well into the ultrasonic range, around 70Khz. The 555 does not go rail to rail (it doesn’t quite reach the upper supply voltage) because of its output Darlington transistors, and this causes the oscillators square wave to be not quite symmetrical. Can you see this looking at the LEDs? The higher the power supply voltage, the less pronounced this asymmetry is, while it gets worse with lower power supply voltages. If the output were true rail to rail it would be a 50% square wave, which can be attained if one uses the CMOS version of the 555, such as the TLC555 (Radio Shack P/N 276-1718). R3 was added to prevent shorting the IC output through C1, as the capacitor shorts the AC portion of the 555 output to ground. On a discharged battery it is not noticeable, but with a fresh 9V the 555 IC will get very hot. If you eliminate the resistor and adjust R4 for maximum frequency you can test this, it is not good for the battery or the 555, but they will survive a short test. THEORY OF OPERATION This is a hysteretic oscillator, which is a type of relaxation oscillator. It is also an astable multivibrator. It is a logical offshoot of the 555 Schmitt Trigger experiment shown earlier. The formula to calculate the frequency with this configuration using a 555 is: The 555 hysteresis is dependent on the supply voltage, so the frequency of the oscillator would be relatively independent of the supply voltage if it weren’t for the lack of rail to rail output. The output of a 555 either goes to ground, or relatively close to the plus voltage. This allows the resistor and capacitor to charge and discharge through the output pin. Since this is a digital type signal, the LEDs interact very little in its operation. The first pulse generated by the oscillator is a bit longer than the rest. This and the charge/discharge curves are shown in the following illustration, which also shows why the asymmetrical square wave is created.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/08%3A_555_Timer_Circuits/8.04%3A_555_Monostable_Multivibrator.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • One 9V Battery • Battery Clip (Radio Shack catalog # 270-325) • Mini Hook Clips (soldered to Battery Clip, Radio Shack catalog # 270-372) • A Watch with a second hand/display or a Stop Watch • A wire, 11/2” to 2” (3.8 mm to 5 mm) long, folded in half (shown as red wire in illustration) • U1 - 555 timer IC (Radio Shack catalog # 276-1723) • D1 - Red light-emitting diode (Radio Shack catalog # 276-041 or equivalent) • D2 - Green light-emitting diode (Radio Shack catalog # 276-022 or equivalent) • R1,R2 - 1 KΩ 1/4W Resistors • Rt - 27 KΩ 1/4W Resistor • Rt - 270 KΩ 1/4W Resistor • C1,C2 - 0.1 µF Capacitor (Radio Shack catalog 272-1069 or equivalent) • Ct - 10 µF Capacitor (Radio Shack catalog 272-1025 or equivalent) • Ct - 100 µF Capacitor (Radio Shack catalog 272-1028 or equivalent) CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 13: “Electric fields and capacitance” Lessons In Electric Circuits, Volume 1, chapter 13: “Capacitors and calculus” Lessons In Electric Circuits, Volume 1, chapter 16: “Voltage and current calculations” Lessons In Electric Circuits, Volume 1, chapter 16: “Solving for unknown time” Lessons In Electric Circuits, Volume 4, chapter 10: “Monostable multivibrators” LEARNING OBJECTIVES • Learn how a Monostable Multivibrator works • Learn a practical application for a RC time constant • How to use the 555 timer as a Monostable Multivibrator SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS This is one of the most basic 555 circuits. This circuit is part of this chips datasheet, complete with the math needed to design to specification, and is one of the reasons a 555 is referred to as a timer. The green LED shown on the illustration lights when the 555 output is high (i.e., switched to Vcc), and the red LED lights when the 555 output is low (switched to ground). This particular monostable multivibrator (also known as a monostable or timer) is not a retriggerable type. This means once triggered it will ignore further inputs during a timing cycle, with one exception, which will be discussed in the next paragraph. The timer starts when the input goes low or switched to the ground level, and the output goes high. You can prove this by connecting the red wire shown on the illustration between ground and point B, disconnecting it, and reconnecting it. It is an illegal condition for the input to stay low for this design past timeout. For this reason, R3 and C1 were added to create a signal conditioner, which will allow edge only triggering and prevent the illegal input. You can prove this by connecting the red wire between ground and point A. The timer will start when the wire is inserted into the protoboard between these two points, and ignore further contacts. If you force the timer input to stay low past timeout the output will stay high, even though the timer has finished. As soon as this ground is removed the timer will go low. Rt and Ct were selected for 3 seconds timing duration. You can verify this with a watch, 3 seconds is long enough that we slow humans can actually measure it. Try swapping Rt and Ct with the 27 KO resistor and the 100 µF capacitors. Since the answer to the formula is the same there should be no difference in how it operates. Next try swapping Rt with the 270 KO resistor, since the RC time constant is now 10 times greater you should get close to 30 seconds. The resistor and capacitor are probably 5% and 20% tolerance respectively, so the calculated times you measure can vary as much as 25%, though it will usually be much closer. Another nice feature of the 555 is its immunity from the power supply voltage. If you were to swap the 9V battery with a 6V or 12 battery you should get identical results, though the LED light intensity will change. C2 isn’t actually necessary. The 555 IC has this option in case the timer is being used in an environment where the power supply line is noisy. You can remove it and not notice a difference. The 555 itself is a source of noise since there is a very brief period of time that the transistors on both sides of the output are both conducting, creating a power surge (measured in nanoseconds) from the power supply. THEORY OF OPERATION Looking at the functional schematic shown (Figure below), you can see that pin 7 is a transistor going to ground. This transistor is simply a switch that normally conducts until pin 2 (which is connected through the comparator C1, which feeds the internal flip-flop) is brought low, allowing the capacitor Ct to start charging. Pin 7 stays off until the voltage on Ct charges to 2/3 of the power supply voltage, where the timer times out and pin 7 transistor turns on again, its normal state in this circuit. The following (Figure below) will show the sequence of switching, with red being the higher voltages and green being ground (0 volts), with the spectrum in between since this is fundamentally an analog circuit. This graph shows the charge curve across the Ct. Figure 1 is the starting and ending point for this circuit, where it is waiting for a trigger to start a timing cycle. At this point the pin 7 transistor is on, keeping the capacitor Ct discharged. Figure 2 shows what happens when the 555 receives a trigger, starting the sequence. Ct hasn’t had time to accumulate voltage, but the charging has started. Figure 3 shows the capacitor charging, during this time the circuit is in a stable configuration and the output is high. Figure 4 shows the circuit in the middle of switching off when it hits timeout. The capacitor has charged to 67%, the upper limit of the 555 circuit, causing its internal flip-flop to switch states. As shown, the transistor hasn’t switched yet, which will discharge Ct when it does. Figure 5 shows the circuit after it has settled down, which is basically the same as shown in Figure 1.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/08%3A_555_Timer_Circuits/8.05%3A_CMOS_555_Long_Duration_Minimum_Parts_Red_LED_Flasher.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two AAA Batteries • Battery Clip (Radio Shack catalog # 270-398B) • One DVM or VOM • U1 - T One CMOS TLC555 timer IC (Radio Shack catalog # 276-1718 or equivalent) • D1 - Red light-emitting diode (Radio Shack catalog # 276-041 or equivalent) • R1 - 1.5 MΩ 1/4W 5% Resistor • R2 - 47 KΩ 1/4W 5% Resistor • C1 - 1 µF Tantalum Capacitor (Radio Shack catalog 272-1025 or equivalent) • C2 - 100 µF Electrolytic Capacitor (Radio Shack catalog 272-1028 or equivalent) CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 16: “Voltage and current calculations” Lessons In Electric Circuits, Volume 1, chapter 16: “Solving for unknown time” Lessons In Electric Circuits, Volume 3, chapter 9 : “ElectroStatic Discharge” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • Learn a practical application for a RC time constant • Learn one of several 555 timer Astable Multivibrator Configurations • Working knowledge of duty cycle • Learn how to handle ESD sensitive parts SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS NOTE! This project uses a static sensitive part, the CMOS 555. If you do not use protection as described in Volume 3, Chapter 9, ElectroStatic Discharge, you run the risk of destroying it. The 555 is not a power hog, but it is a child of the 1970’s, created in 1971. It will suck a battery dry in days, if not hours. Fortunately, the design has been reinvented using CMOS technology. The new implementation isn’t perfect, as it lacks the fantastic current drive of the original, but for a CMOS device the output current is still very good. The main advantages include wider supply voltage range (power supply specifications are 2V to 18V, and it will work using an 11/2V battery) and low power. This project uses the TLC555, a Texas Instruments design. There are other CMOS 555’s out there, very similar but with some differences. These chips are designed to be drop-in replacements and do very well as long as the output is not substantially loaded. This design turns a deficit into an advantage as the current drive only gets worse at lower power supply voltages, its specifications are not more than 3ma for 2VDC. This design tries to make the batteries last as absolutely long as possible using several different approaches. The CMOS IC is extremely low current, and sends the LED a pulse of 30ms (which is a very short time but within persistence of human vision) as well as using a slow flash rate (1 second) using really large resistors to minimize current. With a duty cycle of 3%, this circuit spends most of its time off, and (assuming 20ma for the LED) the average current is 0.6ma. The big problem is using the built-in current limitation of this IC, as is it is not rated for a specific current, and the LED current can vary a lot between different CMOS ICs. It is possible to run into problems with electrolytic capacitors when dealing with very low currents (2µa in this case) in that the leakage can be excessive, a borderline failure condition. If your experiment seems to do this it might be fixed by charging across the battery, then discharging the capacitor C1 across any conductor several times. When you complete this circuit the LED should start flashing and would continue to do so for several months. If you use larger batteries, such as D cells, this duration will increase dramatically. To measure the current draw feeding the LED, connect C1+ to Vcc with a jumper (shown in red on the Illustration), which will turn the TLC555 on. Measure the amperage flowing from the battery to the circuit. The target current is 20ma, I measured 9ma to 24ma using different CMOS 555s. This isn’t critical, though it will affect the battery life. THEORY OF OPERATION An observant reader will note that this is fundamentally the same circuit that was used in the 555 AUDIO OSCILLATOR experiment. Many designs use the same basic designs and concepts several different ways, this is such a case. A conventional 555 IC would work in this design if the power supply weren’t so low and a LED current limiting resistor is used. Other than the type of transistors used the block diagram shown in Figure 1 is basically the same as a conventional 555. This particular oscillator depends on the pin 7 transistor, much like the 555 Monostable Multivibrator shown in an earlier experiment. The startup condition is with the capacitor discharged, the output high, and pin 7 transistor off. The capacitor starts charging as shown in Figure 2. When the voltage across pins 2 and 6 reaches 2/3 of the power supply the flip flop is reset via internal comparator C1, which turns on the Pin 7 transistor, and starts the capacitor C1 discharging through R2 as shown in Figure 3. The current shown through R1 is incidental, and not important other than it drains the battery. This is why this resistor value is so large. When the voltage across pins 2 and 6 reaches 1/3 of the power supply the flip-flop is set via internal comparator C2, when turns off the pin 7 transistor, allowing the capacitor to start charging again through R1 and R2, as shown in Figure 2. This cycle repeats. Capacitor C2 extends the life of the batteries, since it will store the voltage during the 97% of time the circuit is off, and provide the current during the 3% it is on. This simple addition will take the batteries beyond their useful life by a large margin. In running this experiment there was a feedback mechanism I hadn’t anticipated. The output current of the TLC555 is not proportional, as the power supply voltage goes down the output current reduces a lot more. My flasher lasted for 6 months before I terminated the experiment. It was still flashing, it was just very dim.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/08%3A_555_Timer_Circuits/8.06%3A_CMOS_555_Long_Duration_Blue_LED_Flasher.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two AAA Batteries • Battery Clip (Radio Shack catalog # 270-398B) • U1 - 1CMOS TLC555 timer IC (Radio Shack catalog # 276-1718 or equivalent) • Q1 - 2N3906 PNP Transistor (Radio Shack catalog #276-1604 (15 pack) or equivalent) • Q2 - 2N2222 NPN Transistor (Radio Shack catalog #276-1617 (15 pack) or equivalent) • CR1 - 1N914 Diode (Radio Shack catalog #276-1122 (10 pack) or equivalent, see Instructions) • D1 - Blue light-emitting diode (Radio Shack catalog # 276-311 or equivalent) • R1 - 1.5 MΩ 1/4W 5% Resistor • R2 - 47 KΩ 1/4W 5% Resistor • R3 - 2.2 KΩ 1/4W 5% Resistor • R4 - 620 Ω 1/4W 5% Resistor • R5 - 82 Ω 1/4W 5% Resistor • C1 - 1 µF Tantalum Capacitor (Radio Shack catalog 272-1025 or equivalent) • C2 - 100 µF Electrolytic Capacitor (Radio Shack catalog 272-1028 or equivalent) • C3 - 470 µF Electrolytic Capacitor (Radio Shack catalog 272-1030 or equivalent) CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 16: “Voltage and current calculations“ Lessons In Electric Circuits, Volume 1, chapter 16: “Solving for unknown time” Lessons In Electric Circuits, Volume 3, chapter 4 : “Bipolar Junction Transistors” Lessons In Electric Circuits, Volume 3, chapter 9 : “ElectroStatic Discharge” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • Learn a practical application for a RC time constant • Learn one of several 555 timer Astable Multivibrator Configurations • Working knowledge of duty cycle • How to handle ESD sensitive parts • How to use transistors to improve current gain • How to use a capacitor to double voltage with a switch SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS NOTE! This project uses a static sensitive part, the CMOS 555. If you do not use protection as described in Volume 3, Chapter 9, ElectroStatic Discharge, you run the risk of destroying it. This circuit builds on the previous two experiments, using their features and adding to them. Blue and white LEDs have a higher Vf (forward dropping voltage) than most, around 3.6V. 3V batteries can’t drive them without help, so extra circuitry is required. As in the previous circuits, the LED is given a 0.03 second (30ms) pulse. C3 is used to double the voltage of this pulse, but it can only do this for a short time. Measuring the current though the LED is impractical with this circuit because of this short duration, but blue LEDs are generally more predictable because they were invented later. This particular design can also be used with a single 1 1/2V battery. The base concept was created with a now obsolete IC, the LM3909, which used a red LED, the IC, and a capacitor. As with this circuit, it could flash a red LED for over a year with a single D cell. When newer red LEDs increased their Vf from 1.5V to 2.5V this old chip was no longer practical, and is still missed by many hobbyists. If you want to try a 11/2V battery change R5 to 10Ω and use a red LED with a better CR1 (see next paragraph) . CR1 is not the best choice for this component, it was selected because it is a common part and it works. Almost any diode will work in this application. Schottky and germanium diodes drop much less voltage, a silicon diode drops 0.6-0.7V, while a Schottky diode drops 0.1-0.2V, and a germanium diode drops 0.2V-0.3V. If these components are used the reduced voltage drop would translate into brighter LED intensity, as the circuits efficiency is increased. THEORY OF OPERATION Q2 is a switch, which this circuit uses. When Q2 is off C3 is charged to the battery voltage, minus the diode drop, as shown in Figure 1. Since the blue LED Vf is 3.4V to 3.6V it is effectively out of the circuit. Figure 2 shows what happens when Q2 turns on. The capacitor C3 + side is grounded, which moves the - side to -2.4V. The diode CR1 is now back biased, and is out of the circuit. The -2.4V is discharged through R5 and D1 to the +3.0V of the batteries. The 5.4V provides lots of extra voltage to light the blue LED. Long before C3 is discharged the circuit switches back and C3 starts charging again. In the LM3909 CR1 was a resistor. The diode was used to minimize current, by allowing R4 to be its maximum value. You may notice a dim blue glow in the blue LED when it is off. This demonstrates the difference between theory and practice, 3V is enough to cause some leakage through the blue LED, even though it is not conducting. If you were to measure this current it would be very small.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/08%3A_555_Timer_Circuits/8.07%3A_CMOS_555_Long_Duration_Flyback_LED_Flasher.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two AAA Batteries • Battery Clip (Radio Shack catalog # 270-398B) • U1, U2 - CMOS TLC555 timer IC (Radio Shack catalog # 276-1718 or equivalent) • Q1 - 2N3906 PNP Transistor (Radio Shack catalog #276-1604 (15 pack) or equivalent) • Q2 - 2N2222 NPN Transistor (Radio Shack catalog #276-1617 (15 pack) or equivalent) • D1 - Red light-emitting diode (Radio Shack catalog # 276-041 or equivalent) • D2 - Blue light-emitting diode (Radio Shack catalog # 276-311 or equivalent) • R1 - 1.5 MΩ 1/4W 5% Resistor • R2 - 47 KΩ 1/4W 5% Resistor • R3,R5 - 10 KΩ 1/4W 5% Resistor • R4 - 1 MΩ 1/4W 5% Resisto • r • R6 - 100 KΩ 1/4W 5% Resistor • R7 - 1 KΩ 1/4W 5% Resistor • C1 - 1 µF Tantalum Capacitor (Radio Shack catalog # 272-1025 or equivalent) • C2 - 100 pF Ceramic Disc Capacitor (Radio Shack catalog # 272-123) • C3 - 100 µF Electrolytic Capacitor (Radio Shack catalog 272-1028 or equivalent) • L1 - 200 µH Choke or Inductor (Exact value not critical, see end of chapter) CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 16: Title “Inductor transient response” Lessons In Electric Circuits, Volume 1, chapter 16: Title “Why L/R and not LR?” Lessons In Electric Circuits, Volume 3, chapter 4: Title “The common-emitter amplifier” Lessons In Electric Circuits, Volume 3, chapter 9: Title “Electrostatic Discharge” Lessons In Electric Circuits, Volume 4, chapter 10: Title “Monostable multivibrators” LEARNING OBJECTIVES • Learn another mode of operation for the 555 • How to handle ESD Parts • How to use a transistor for a simple gate (resistor transistor inverter) • How inductors can convert power using inductive flyback • How to make an inductor SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS NOTE! This project uses a static sensitive part, the CMOS 555. If you do not use protection as described in Volume 3, Chapter 9, ElectroStatic Discharge, you run the risk of destroying it. This particular experiment builds on another experiment, “Commutating diode” (Volume 6, chapter 5). It is worth reviewing that section before proceeding. This is the last of the long duration LED flasher series. They have shown how to use a CMOS 555 to flash an LED, and how to boost the voltage of the batteries to allow an LED with more voltage drop than the batteries to be used. Here we are doing the same thing, but with an inductor instead of a capacitor. The basic concept is adapted from another invention, the Joule Thief. A joule thief is a simple transistor oscillator that also uses inductive kickback to light an white light LED from a 11/2 battery, and the LED needs at least 3.6 volts to start conducting! Like the joule thief, it is possible to use 11/2 volts to get this circuit to work. However, since a CMOS 555 is rated for 2 volts minimum 11/2 volts is not recommended, but we can take advantage of the extreme efficiency of this circuit. If you want to learn more about the joule thief plenty of information can be found on the web. This circuit can also drive more that 1 or 2 LEDs in series. As the numbers of LEDs go up the ability of the batteries to last a long duration goes down, as the amount of voltage the inductor can generate is somewhat dependent on battery voltage. For the purposes of this experiment two dissimilar LEDs were used to demonstrate its independence of LED voltage drop. The high intensity of the blue LED swamps the red LED, but if you look closely you will find the red LED is at its maximum brightness. You can use pretty much whatever color of LEDs you choose for this experiment. Generally the high voltage created by inductive kickback is something to be eliminated. This circuit uses it, but if you make a mistake with the polarity of the LEDs the blue LED, which is more ESD sensitive, will likely die (this has been verified). An uncontrolled pulse from a coil resembles an ESD event. The transistor and the TLC555 can also be at risk. The inductor in this circuit is probably the least critical part in the design. The term inductor is generic, you can also find this component called a choke or a coil. A solenoid coil would also work, since that is also a type of inductor. So would the coil from a relay. Of all the components I have used, this is probably the least critical I’ve come across. Indeed, coils are probably the most practical component you can make yourself that exists. I’ll cover how to make a coil that will work in this design after the Theory of Operation, but the part shown on the illustration is a 200µH choke I bought from a local electronics retailer. THEORY OF OPERATION Both capacitors and inductors store energy. Capacitors try to maintain constant voltage, whereas inductors try to maintain constant current. Both resist change to their respective aspect. This is the basis for the flyback transformer, which is a common circuit used in old CRT circuits and other uses where high voltage is needed with a minimum of fuss. When you charge a coil a magnetic field expands around it, basically it is an electromagnet, and the magnetic field is stored energy. When the current stops this magnetic field collapses, created electricity as the field crosses the wires in the coil. This circuit uses two astable multivibrators. The first multivibrator controls the second. Both are designed for minimum current, as well as the inverter made using Q1. Both the oscillators are very similar, the first has been covered in previous experiments. The problem is it stays on, or is high, 97% of the time. On the previous circuits we used the low state to light the LED, in this case the high is what turns the second multivibrator on. Using a simple transistor inverter designed for extra low current solves this problem. This is actually a very old logic family, RTL, which is short for resistor transistor logic. The second multivibrator oscillates at 68.6 KHz, with a square wave that is around 50%. This circuit uses the exact same principals as is shown in the Minimum Parts LED Flasher. Again, the largest practical resistors are used to minimize current, and this means a really small capacitor for C2. This high frequency square wave is used to turn Q2 on and off as a simple switch. Figure 1 shows what happens when the Q2 is conducting, and the coil starts to charge. If Q2 were to stay on then an effective short across the batteries would result, but since this is part of an oscillator this won’t happen. Before the coil can reach it’s maximum current Q2 switches, and the switch is open. Figure 2 shows Q2 when it opens, and the coil is charged. The coil tries to maintain the current, but if there is no discharge path it can not do this. If there were no discharge path is the coil would create a high voltage pulse, seeking to maintain the current that was flowing through it, and this voltage would be quite high. However, we have a couple of LEDs in the discharge path, so the coils pulse quickly goes to the voltage drop of the combined LEDs, then dumps the rest of its charge as current. As a result there is no high voltage generated, but there is a conversion to the voltage required to light the LEDs. The LEDs are pulsed, and the light curve follows the discharge curve of the coil fairly closely. However, the human eye averages this light output to something we perceive as continuous light. PARTS AND MATERIALS • 26 Feet (8 Meters) of 26AWG Magnet Wire (Radio Shack catalog #278-1345 or equivalent) • 6/32X1.5 inch screw, a M4X30mm screw, or a nail of similar diameter cut down to size, steel or iron, but not stainless • Matching lock nut (optional) • Transparent Tape (optional, needed if using screws) • Super Glue • Soldering Iron, Solder As has been mentioned before, this is not a precision part. Inductors in general can have a large variance for many applications, and this one specifically can be off on the high side a large amount. The target here is greater than 220µH. If you are using a screw, use one layer of the transparent tape between the threads and the wire. This is to prevent the threads of the screw from cutting into the wire and shorting the coil out. If you are using a lock nut put it on the screw 1” (25mm) from the head of the screw. Starting around 1” from one end of the wire, use the glue to tack the wire on the head of the nail or screw as shown. Let the glue set. Wind the wire neatly and tightly 1” the length of screw, again tacking it in place with super glue. (Figure above). You can use a variable speed drill to help with this, as long as you are careful. Like all power appliances, it can bite you. Hold the wire tight until the glue sets, then start winding a second layer over the first. Continue this process until all of the wire except the last 1” is used, using the glue to occasionally tack the wire down. Arrange the wire on the last layer so the second inductor lead is on the other end of the screw away from the first. Tack this down for a final time with the glue. Let dry completely. Gently take a sharp blade and scrap the enamel off each end of the two leads. Tin the exposed copper with the soldering iron and the solder, and you now have a functional inductor that can be used in this experiment. Here is what the one I made looked like: Figure below. The connections shown are being used to measure the inductance, which worked out pretty close to 220µH.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_VI_-_Experiments_(Kuphaldt)/08%3A_555_Timer_Circuits/8.08%3A_CMOS_555_Long_Duration_Red_LED_Flasher.txt	princeton-nlp/TextbookChapters	PARTS AND MATERIALS • Two AAA Batteries • Battery Clip (Radio Shack catalog # 270-398B) • A DVM or VOM • U1 - CMOS TLC555 timer IC (Radio Shack catalog # 276-1718 or equivalent) • Q1 - 2N3906 PNP Transistor (Radio Shack catalog #276-1604 (15 pack) or equivalent) • Q2 - 2N2222 NPN Transistor (Radio Shack catalog #276-1617 (15 pack) or equivalent) • D1 - Red light-emitting diode (Radio Shack catalog # 276-041 or equivalent) • R1 - 1.5 MΩ 1/4W 5% Resistor • R2 - 47 KΩ 1/4W 5% Resistor • R3 - 2.2 KΩ 1/4W 5% Resistor • R4 - 27 Ω 1/4W 5% Resistor (or test select a better value) • C1 - 1 µF Tantalum Capacitor (Radio Shack catalog 272-1025 or equivalent) • C2 - 100 µF Electrolytic Capacitor (Radio Shack catalog 272-1028 or equivalent) CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 16: “Voltage and current calculations” Lessons In Electric Circuits, Volume 1, chapter 16: “Solving for unknown time” Lessons In Electric Circuits, Volume 3, chapter 4 : “Bipolar Junction Transistors” Lessons In Electric Circuits, Volume 3, chapter 9 : “ElectroStatic Discharge” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES • Learn a practical application for a RC time constant • Learn one of several 555 timer Astable Multivibrator Configurations • Working knowledge of duty cycle • How to handle ESD sensitive parts • How to use transistors to improve current gain • How to calculate the correct resistor for a LED SCHEMATIC DIAGRAM ILLUSTRATION INSTRUCTIONS NOTE! This project uses a static sensitive part, the CMOS 555. If you do not use protection as described in Volume 3, Chapter 9, ElectroStatic Discharge, you run the risk of destroying it. The circuit shown in the previous experiment, CMOS 555 Long Duration Minimum Parts Red LED Flasher, has one big drawback, which is a lack of LED current control. This experiment uses the same basic 555 schematic and adds transistorized drivers to correct this. The parts used for this transistor driver are non critical. It is designed to load the TLC555 to an absolute minimum and still turn on Q2 fully. This is important because as the battery voltage approaches 2V the drive from the TLC555 is reduced to its minimum values. Bipolar transistors can be good switches. Since LEDs can have so much variation R4 should be tweaked to match the specific LED used. The current is limited to 18.5ma with 27Ω and a Vf (LED forward dropping voltage) of 2.5V, an LED Vf of 2.1V will draw 33ma, and a LED Vf of 1.5 will draw 56ma. The latter is too much current, not to mention what that would do for the battery life. To correct this use 47Ω if the Vf is 2.1V, and 75Ω if the Vf is 1.5V, assuming the target current is 20ma. You can measure Vf by using the jumper shown in red in the illustration, which will turn the LED on full time. You can calculate the value of R4 by using the equation: R4 = (3V-Vf) / 0.02A It was mentioned in the previous experiment that capacitor C2 extended the life of the batteries. An interesting experiment is to remove this part periodically and see what happens. At first you will notice a dimming of the LED, and after a week or two the circuit will die without it, and resume working in a couple of seconds when it is replaced. This flasher will work for 3 months using fresh alkaline AAA batteries. THEORY OF OPERATION The CMOS 555 oscillator was explained fully in the previous experiment, so the transistor driver will be the focus of this explanation. The transistor driver combines elements of a common collector configuration on Q1, along with common emitter configuration on Q2. This allows for very high input resistance while allowing Q2 to turn on fully. The input resistance of the transistor is the β (gain) of the transistor times the emitter resistor. If Q1 has a gain of 50 (a minimum value) then the driver loads the TLC555 with more than 100KΩ. Transistors can have large variations in gain, even within the same family. When Q1 turns on 1ma is sent to Q2. This is more than enough to turn Q2 fully, which is referred to as saturation. Q2 is used as a simple switch for the LED.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/01%3A_Useful_Equations_And_Conversion_Factors/1.01%3A_DC_Circuit_Equations_and_Laws.txt	princeton-nlp/TextbookChapters	Power Equation of Ohm’s Law and Joule’s Law NOTE: the symbol “V” (“U” in Europe) is sometimes used to represent voltage instead of “E”. In some cases, an author or circuit designer may choose to exclusively use “V” for voltage, never using the symbol “E.” Other times the two symbols are used interchangeably, or “E” is used to represent voltage from a power source while “V” is used to represent voltage across a load (voltage “drop”). Kirchhoff’s Voltage and Current Laws “The algebraic sum of all voltages in a loop must equal zero.” Kirchhoff’s Voltage Law (KVL) “The algebraic sum of all currents entering and exiting a node must equal zero.” Kirchhoff’s Current Law (KCL) 1.02: Series Circuit Rules • Components in a series circuit share the same current: • Itotal = I1 = I2 = . . . In • Total resistance in a series circuit is equal to the sum of the individual resistances, making it greater than any of the individual resistances: • Rtotal = R1 + R2 + . . . Rn • Total voltage in a series circuit is equal to the sum of the individual voltage drops: • Etotal = E1 + E2 + . . . En 1.03: Parallel Circuit Rules • Components in a parallel circuit share the same voltage: • Etotal = E1 = E2 = . . . En • Total resistance in a parallel circuit is less than any of the individual resistances: • Rtotal = 1 / (1/R1 + 1/R2 + . . . 1/Rn) • Total current in a parallel circuit is equal to the sum of the individual branch currents: • Itotal = I1 + I2 + . . . In 1.05: Capacitor Sizing Equation A formula for capacitance in picofarads using practical dimensions: 1.06: Inductor Sizing Equation The Inductance Formula Wheeler’s formulas for inductance of air core coils which follow are useful for radio frequency inductors. The following formula for the inductance of a single layer air core solenoid coil is accurate to approximately 1% for 2r/l < 3. The thick coil formula is 1% accurate when the denominator terms are approximately equal. Wheeler’s spiral formula is 1% accurate for c>0.2r. While this is a “round wire” formula, it may still be applicable to printed circuit spiral inductors at reduced accuracy. The inductance in henries of a square printed circuit inductor is given by two formulas where p=q, and p≠q. The wire table provides “turns per inch” for enamel magnet wire for use with the inductance formulas for coils. 1.07: Time Constant Equations Value of time constant in series RC and RL circuits Time constant in seconds = RC Time constant in seconds = L/R 1.08: AC Circuit Equations ZL = R + jXL ZC = R - jXC Series and Parallel Impedances NOTE: All impedances must be calculated in complex number form for these equations to work. Resonance NOTE: This equation applies to a non-resistive LC circuit. In circuits containing resistance as well as inductance and capacitance, this equation applies only to series configurations and to parallel configurations where R is very small.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/01%3A_Useful_Equations_And_Conversion_Factors/1.10%3A_Metric_Prefixes_and_Unit_Conversions.txt	princeton-nlp/TextbookChapters	• Metric prefixes • Yotta = 1024 Symbol: Y • Zetta = 1021 Symbol: Z • Exa = 1018 Symbol: E • Peta = 1015 Symbol: P • Tera = 1012 Symbol: T • Giga = 109 Symbol: G • Mega = 106 Symbol: M • Kilo = 103 Symbol: k • Hecto = 102 Symbol: h • Deca = 101 Symbol: da • Deci = 10-1 Symbol: d • Centi = 10-2 Symbol: c • Milli = 10-3 Symbol: m • Micro = 10-6 Symbol: µ • Nano = 10-9 Symbol: n • Pico = 10-12 Symbol: p • Femto = 10-15 Symbol: f • Atto = 10-18 Symbol: a • Zepto = 10-21 Symbol: z • Yocto = 10-24 Symbol: y Conversion factors for temperature • oF = (oC)(9/5) + 32 • oC = (oF - 32)(5/9) • oR = oF + 459.67 • oK = oC + 273.15 Conversion equivalencies for volume 1 US gallon (gal) = 231.0 cubic inches (in3) = 4 quarts (qt) = 8 pints (pt) = 128 fluid ounces (fl. oz.) = 3.7854 liters (l) 1 Imperial gallon (gal) = 160 fluid ounces (fl. oz.) = 4.546 liters (l) Conversion equivalencies for distance 1 inch (in) = 2.540000 centimeter (cm) Conversion equivalencies for velocity 1 mile per hour (mi/h) = 88 feet per minute (ft/m) = 1.46667 feet per second (ft/s) = 1.60934 kilometer per hour (km/h) = 0.44704 meter per second (m/s) = 0.868976 knot (knot—international) Conversion equivalencies for weight 1 pound (lb) = 16 ounces (oz) = 0.45359 kilogram (kg) Conversion equivalencies for force 1 pound-force (lbf) = 4.44822 newton (N) Acceleration of gravity (free fall), Earth standard 9.806650 meters per second per second (m/s2) = 32.1740 feet per second per second (ft/s2) Conversion equivalencies for area 1 acre = 43560 square feet (ft2) = 4840 square yards (yd2) = 4046.86 square meters (m2) Conversion equivalencies for pressure 1 pound per square inch (psi) = 2.03603 inches of mercury (in. Hg) = 27.6807 inches of water (in. W.C.) = 6894.757 pascals (Pa) = 0.0680460 atmospheres (Atm) = 0.0689476 bar (bar) Conversion equivalencies for energy or work 1 british thermal unit (BTU—“International Table”) = 251.996 calories (cal—“International Table”) = 1055.06 joules (J) = 1055.06 watt-seconds (W-s) = 0.293071 watt-hour (W-hr) = 1.05506 x 1010 ergs (erg) = 778.169 foot-pound-force (ft-lbf) Conversion equivalencies for power 1 horsepower (hp—550 ft-lbf/s) = 745.7 watts (W) = 2544.43 british thermal units per hour (BTU/hr) = 0.0760181 boiler horsepower (hp—boiler) Conversion equivalencies for motor torque Locate the row corresponding to known unit of torque along the left of the table. Multiply by the factor under the column for the desired units. For example, to convert 2 oz-in torque to n-m, locate oz-in row at table left. Locate 7.062 x 10-3 at intersection of desired n-m units column. Multiply 2 oz-in x (7.062 x 10-3 ) = 14.12 x 10-3 n-m. Converting between units is easy if you have a set of equivalencies to work with. Suppose we wanted to convert an energy quantity of 2500 calories into watt-hours. What we would need to do is find a set of equivalent figures for those units. In our reference here, we see that 251.996 calories is physically equal to 0.293071 watt hour. To convert from calories into watt-hours, we must form a “unity fraction” with these physically equal figures (a fraction composed of different figures and different units, the numerator and denominator being physically equal to one another), placing the desired unit in the numerator and the initial unit in the denominator, and then multiply our initial value of calories by that fraction. Since both terms of the “unity fraction” are physically equal to one another, the fraction as a whole has a physical value of 1, and so does not change the true value of any figure when multiplied by it. When units are canceled, however, there will be a change in units. For example, 2500 calories multiplied by the unity fraction of (0.293071 w-hr / 251.996 cal) = 2.9075 watt-hours. The “unity fraction” approach to unit conversion may be extended beyond single steps. Suppose we wanted to convert a fluid flow measurement of 175 gallons per hour into liters per day. We have two units to convert here: gallons into liters, and hours into days. Remember that the word “per” in mathematics means “divided by,” so our initial figure of 175 gallons per hour means 175 gallons divided by hours. Expressing our original figure as such a fraction, we multiply it by the necessary unity fractions to convert gallons to liters (3.7854 liters = 1 gallon), and hours to days (1 day = 24 hours). The units must be arranged in the unity fraction in such a way that undesired units cancel each other out above and below fraction bars. For this problem it means using a gallons-to-liters unity fraction of (3.7854 liters / 1 gallon) and a hours-to-days unity fraction of (24 hours / 1 day): Our final (converted) answer is 15898.68 liters per day.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/02%3A_Color_Codes/2.01%3A_Resistor_Color_Codes.txt	princeton-nlp/TextbookChapters	Standard Resistor Values and Color Components and wires are coded with colors to identify their value and function. The colors brown, red, green, blue, and violet are used as tolerance codes on 5-band resistors only. All 5-band resistors use a colored tolerance band. The blank (20%) “band” is only used with the “4-band” code (3 colored bands + a blank “band”). \ Example #1 A resistor colored Yellow-Violet-Orange-Gold would be 47 kΩ with a tolerance of +/- 5%. Example #2 A resistor colored Green-Red-Gold-Silver would be 5.2 Ω with a tolerance of +/- 10%. Example #3 A resistor colored White-Violet-Black would be 97 Ω with a tolerance of +/- 20%. When you see only three color bands on a resistor, you know that it is actually a 4-band code with a blank (20%) tolerance band. Example #4 A resistor colored Orange-Orange-Black-Brown-Violet would be 3.3 kΩ with a tolerance of +/- 0.1%. Example #5 A resistor colored Brown-Green-Grey-Silver-Red would be 1.58 Ω with a tolerance of +/- 2%. Example #6 A resistor colored Blue-Brown-Green-Silver-Blue would be 6.15 Ω with a tolerance of +/- 0.25%. Preferred Values or E-series To make mass manufacturing of resistors easier, the IEC (International Electrotechnical Commision) defined tolerance and resistance values for resistors in 1952. These are referred to as preferred values or E-series, published in standard IEC 60063:1963. Capactors, Zener diodes, and inductors also use these standards. The purpose of this was so that when companies produce resistors with different values of resistance, they would equally space on a logarithmic scale. This helps the supplier with stocking different values. Resistors produced by different manufacturers are compatible for the same designs because of the use of standard values. Standard Resistor Value Series and Tolerances The standard E3, E6, E12, E24, E48 and E96 resistor values are listed below. *The calculated tolerance for this series is 36.60%, While the standard only specifies a tolerance greater than 20%, other sources indicate 40% or 50%. E3 Resistor Series These are the most widely used resistor series in the electronics industry. E96 Resistor Series and Beyond The E96 and E192 series of standard resistor values do exist, but they are not used as much as the Series mention previously. 2.02: Wiring Color Codes Wiring for AC and DC power distribution branch circuits are color-coded for the identification of individual wires. In some jurisdictions, all wire colors are specified in legal documents. In other jurisdictions, only a few conductor colors are so codified. In that case, local custom dictates the “optional” wire colors. IEC, AC: Most of Europe abides by IEC (International Electrotechnical Commission) wiring color codes for AC branch circuits. These are listed in the Table below. The older color codes in the table reflect the previous style which did not account for proper phase rotation. The protective ground wire (listed as green-yellow) is green with a yellow stripe. UK, AC: The United Kingdom now follows the IEC AC wiring color codes. The Table below lists these along with the obsolete domestic color codes. For adding new colored wiring to existing old colored wiring see Cook. [PCk] US, AC: The US National Electrical Code only mandates white (or grey) for the neutral power conductor and bare copper, green, or green with a yellow stripe for the protective ground. In principle, any other colors except these may be used for the power conductors. The colors adopted as a local practice are shown in the Table below. Black, red, and blue are used for 208 VAC three-phase; brown, orange, and yellow are used for 480 VAC. Conductors larger than #6 AWG are only available in black and are color taped at the ends. Canada: Canadian wiring is governed by the CEC (Canadian Electric Code). See Table below. The protective ground is green or green with a yellow stripe. The neutral is white, the hot (live or active) single-phase wires are black, and red in the case of a second active. Three-phase lines are red, black, and blue. IEC, DC: DC power installations, for example, solar power and computer data centers, use color-coding which follows the AC standards. The IEC color standard for DC power cables is listed in Table below, adapted from Table 2, Cook. [PCk] US DC power: The US National Electrical Code (for both AC and DC) mandates that the grounded neutral conductor of a power system be white or grey. The protective ground must be bare, green, or green-yellow striped. Hot (active) wires may be any other colors except these. However, common practice (per local electrical inspectors) is for the first hot (live or active) wire to be black and the second hot to be red. The recommendations in the Table below are by Wiles. [JWi] He makes no recommendation for ungrounded power system colors. Usage of the ungrounded system is discouraged for safety. However, red (+) and black (-) follows the coloring of the grounded systems in the table.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/02%3A_Color_Codes/2.03%3A_Wiring_Color_Codes_Infographic.txt	princeton-nlp/TextbookChapters	Wiring Color Codes Infographic. Released under the Creative Commons Attribution-ShareAlike License Looking for Wiring & Resistor Calculators? View our Wire & Resistor calculators in our Tools section. Basic Wire Color Code Information by Region Many of the wire identifications standards rely on color codes. Which standard should you be using for your project? It depends on your location, voltage, and other important factors. Note: Older installations may use different color codes. It is always a great idea to document the color code that’s being followed. This makes work safer, and any future maintenance needed, easier. U.S. Wiring Color Codes In the USA, color codes are usually utilized for power wires in “branch circuits,” the wiring between the last protective device like a circuit breaker and the load (like an appliance). AC Wire Colors For 120/208/240 Volts These are commonly found in home and office settings. • Phase 1 - Black • Phase 2 - Red • Phase 3 - Blue • Neutral - White • Ground - Green, Green with Yellow Stripe, or Bare Wire If one phase of your wiring is at a higher voltage than others, using a high-leg connection, wires should be marked orange for that phase. High-leg connections are typically uncommon in newer installations. AC Wire Colors For 277/480 Volt Industrial motors and equipment typically have higher voltage systems. • Phase 1 - Brown • Phase 2 - Orange • Phase 3 - Yellow • Neutral - Gray • Ground - Green, Green with Yellow Stripe, or Bare Wire It is very important to have a documented wire labeling system for higher voltage systems. Labels should include information regarding the circuit, and the appropriate disconnection point for lockout/tagout. Wire Colors for DC Power DC or Direct Current, is typically used in battery systems and solar power systems, instead of AC or Alternating Current. • Positive (non-ground) - Red • Negative (non-ground) - Black • Ground - White or Gray International Wiring Color Codes International wire color codes are often specified by law depending on your location, though most rely on common practice, below we cover Europe and Canada. Wire Color Codes for Europe (IEC) The International Electrotechnical Commission (or IEC) has established a wire color code for most European countries for AC “branch” circuits. • Phase 1 - Brown • Phase 2 - Black • Phase 3 - Grey • Neutral - Blue • Ground - Green with Yellow Stripe Canadian AC Wiring Color Codes Wiring Color code standards are set in place by the Canadian Electric Code (or CEC) in Canada. The color code is very similar to the U.S.A’s color code. • Phase 1 - Red • Phase 2 - Black • Phase 3 - Blue • Neutral - White • Ground - Green with Yellow Stripe When are Color Codes Applied to Wiring? The manufacturer of most narrow wires will color code them, utilizing insulation of different colors. Wires that are manufactured with black insulation are typically larger than #6 AWG. Color coding should always be added during installation with color bands that wrap around the wire. Self-laminating wire wraps and heat-shrink tubes should be utilized to create clean and professional labels for your projects. 3.01: Copper Wire Gauge Table Solid Cooper Wire Table Size Diameter (inches) Cross-sectional area (cir. mils) Cross-sectional area (sq. inches) Weight (lb/1000ft) 4/0 0.4600 211,600 0.1662 640.5 3/0 0.4096 167,800 0.1318 507.9 2/0 0.3648 133,100 0.1045 402.8 1/0 0.3249 105,500 0.08289 319.5 1 0.2893 83,690 0.06573 253.5 2 0.2576 66,370 0.05213 200.9 3 0.2294 52,630 0.04134 159.3 4 0.2043 41,740 0.03278 126.4 5 0.1819 33,100 0.02600 100.2 6 0.1620 26,250 0.02062 79.46 7 0.1443 20,820 0.01635 63.02 8 0.1285 16,510 0.01297 49.97 9 0.1144 13,090 0.01028 39.63 10 0.1019 10,380 0.008155 31.43 11 0.09074 8,234 0.006467 24.92 12 0.08081 6,530 0.005129 19.77 13 0.07196 5,178 0.004067 15.68 14 0.06408 4,107 0.003225 12.43 15 0.05707 3,257 0.002558 9.858 16 0.05082 2,583 0.002028 7.818 17 0.04526 2,048 0.001609 6.200 18 0.04030 1,624 0.001276 4.917 19 0.03589 1,288 0.001012 3.899 20 0.03196 1,022 0.0008023 3.092 21 0.02846 810.1 0.0006363 2.452 22 0.02535 642.5 0.0005046 1.945 23 0.02257 509.5 0.0004001 1.542 24 0.02010 404.0 0.0003173 1.233 25 0.01790 320.4 0.0002517 0.9699 26 0.01594 254.1 0.0001996 0.7692 27 0.01420 201.5 0.0001583 0.6100 28 0.01264 159.8 0.0001255 0.4837 29 0.01126 126.7 0.00009954 0.3836 30 0.01003 100.5 0.00007894 0.3042 31 0.008928 79.70 0.00006260 0.2413 32 0.007950 63.21 0.00004964 0.1913 33 0.007080 50.13 0.00003937 0.1517 34 0.006305 39.75 0.00003122 0.1203 35 0.005615 31.52 0.00002476 0.09542 36 0.005000 25.00 0.00001963 0.07567 37 0.004453 19.83 0.00001557 0.06001 38 0.003965 15.72 0.00001235 0.04759 39 0.003531 12.47 0.000009793 0.03774 40 0.003145 9.888 0.000007766 0.02993 41 0.002800 7.842 0.000006159 0.02374 42 0.002494 6.219 0.000004884 0.01882 43 0.002221 4.932 0.000003873 0.01493 44 0.001978 3.911 0.000003072 0.01184 3.02: Copper Wire Ampacity Table Ampacities of copper wire, in free air at 30o C: * = estimated values; normally, wire gages this small are not manufactured with these insulation types. 3.03: Coefficients of Specific Resistance Specific resistance at 20o C: * = Steel alloy at 99.5 percent iron, 0.5 percent carbon. 3.04: Temperature Coefficients of Resistance Temperature coefficient (α) per degree C: * = Steel alloy at 99.5 percent iron, 0.5 percent carbon 3.05: Critical Temperatures for Superconductors Critical temperatures given in Kelvins Note: all critical temperatures given at zero magnetic field strength. 3.06: Dielectric Strengths for Insulators Dielectric strength in kilovolts per inch (kV/in): * = Materials listed are specially prepared for electrical use
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/04%3A_Algebra_Reference/4.01%3A_Basic_identities.txt	princeton-nlp/TextbookChapters	Note: while division by zero is popularly thought to be equal to infinity, this is not technically true. In some practical applications it may be helpful to think the result of such a fraction approaching positive infinity as a positive denominator approaches zero (imagine calculating current I=E/R in a circuit with resistance approaching zero—current would approach infinity), but the actual fraction of anything divided by zero is undefined in the scope of either real or complex numbers. 4.02: Arithmetic Properties The associative property In addition and multiplication, terms may be arbitrarily associated with each other through the use of parentheses: The commutative property In addition and multiplication, terms may be arbitrarily interchanged, or commutated: 4.04: Radicals Definition of a radical When people talk of a “square root,” they’re referring to a radical with a root of 2. This is mathematically equivalent to a number raised to the power of 1/2. This equivalence is useful to know when using a calculator to determine a strange root. Suppose for example you needed to find the fourth root of a number, but your calculator lacks a “4th root” button or function. If it has a yx function (which any scientific calculator should have), you can find the fourth root by raising that number to the 1/4 power, or x0.25. It is important to remember that when solving for an even root (square root, fourth root, etc.) of any number, there are two valid answers. For example, most people know that the square root of nine is three, but negative three is also a valid answer, since (-3)2 = 9 just as 32 = 9. 4.05: Important Constants Euler’s number Euler’s constant is an important value for exponential functions, especially scientific applications involving decay (such as the decay of a radioactive substance). It is especially important in calculus due to its uniquely self-similar properties of integration and differentiation. Pi Pi (π) is defined as the ratio of a circle’s circumference to its diameter. Note: For both Euler’s constant (e) and pi (π), the spaces shown between each set of five digits have no mathematical significance. They are placed there just to make it easier for your eyes to “piece” the number into five-digit groups when manually copying. 4.06: Logarithms Definition of a logarithm “log” denotes a common logarithm (base = 10), while “ln” denotes a natural logarithm (base = e). Properties of logarithms These properties of logarithms come in handy for performing complex multiplication and division operations. They are an example of something called a transform function, whereby one type of mathematical operation is transformed into another type of mathematical operation that is simpler to solve. Using a table of logarithm figures, one can multiply or divide numbers by adding or subtracting their logarithms, respectively. then looking up that logarithm figure in the table and seeing what the final product or quotient is. Slide rules work on this principle of logarithms by performing multiplication and division through addition and subtraction of distances on the slide. Marks on a slide rule’s scales are spaced in a logarithmic fashion, so that a linear positioning of the scale or cursor results in a nonlinear indication as read on the scale(s). Adding or subtracting lengths on these logarithmic scales results in an indication equivalent to the product or quotient, respectively, of those lengths. Most slide rules were also equipped with special scales for trigonometric functions, powers, roots, and other useful arithmetic functions. 4.09: Sequences Arithmetic sequences An arithmetic sequence is a series of numbers obtained by adding (or subtracting) the same value with each step. A child’s counting sequence (1, 2, 3, 4, . . .) is a simple arithmetic sequence, where the common difference is 1: that is, each adjacent number in the sequence differs by a value of one. An arithmetic sequence counting only even numbers (2, 4, 6, 8, . . .) or only odd numbers (1, 3, 5, 7, 9, . . .) would have a common difference of 2. In the standard notation of sequences, a lower-case letter “a” represents an element (a single number) in the sequence. The term “an” refers to the element at the nth step in the sequence. For example, “a3” in an even-counting (common difference = 2) arithmetic sequence starting at 2 would be the number 6, “a” representing 4 and “a1” representing the starting point of the sequence (given in this example as 2). A capital letter “A” represents the sum of an arithmetic sequence. For instance, in the same even-counting sequence starting at 2, A4 is equal to the sum of all elements from a1 through a4, which of course would be 2 + 4 + 6 + 8, or 20. Geometric sequences A geometric sequence, on the other hand, is a series of numbers obtained by multiplying (or dividing) by the same value with each step. A binary place-weight sequence (1, 2, 4, 8, 16, 32, 64, . . .) is a simple geometric sequence, where the common ratio is 2: that is, each adjacent number in the sequence differs by a factor of two. 4.10: Factorials Definition of a factorial Denoted by the symbol “!” after an integer; the product of that integer and all integers in descent to 1. Example of a factorial:
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/04%3A_Algebra_Reference/4.11%3A_Solving_Simultaneous_Equations-_The_Substitution_Method_and_the_Addition_Method.txt	princeton-nlp/TextbookChapters	What are Simultaneous Equations and Systems of Equations? The terms simultaneous equations and systems of equations refer to conditions where two or more unknown variables are related to each other through an equal number of equations. Example: For this set of equations, there is but a single combination of values for x and y that will satisfy both. Either equation, considered separately, has an infinitude of valid (x,y) solutions, but together there is only one. Plotted on a graph, this condition becomes obvious: Each line is actually a continuum of points representing possible x and y solution pairs for each equation. Each equation, separately, has an infinite number of ordered pair (x,y) solutions. There is only one point where the two linear functions x + y = 24 and 2x - y = -6 intersect (where one of their many independent solutions happen to work for both equations), and that is where x is equal to a value of 6 and yis equal to a value of 18. Usually, though, graphing is not a very efficient way to determine the simultaneous solution set for two or more equations. It is especially impractical for systems of three or more variables. In a three-variable system, for example, the solution would be found by the point intersection of three planes in a three-dimensional coordinate space—not an easy scenario to visualize. Solving Simultaneous Equations Using The Substitution Method Several algebraic techniques exist to solve simultaneous equations. Perhaps the easiest to comprehend is the substitution method. Take, for instance, our two-variable example problem: In the substitution method, we manipulate one of the equations such that one variable is defined in terms of the other: Then, we take this new definition of one variable and substitute it for the same variable in the other equation. In this case, we take the definition of y, which is 24 - x and substitute this for the y term found in the other equation: Now that we have an equation with just a single variable (x), we can solve it using “normal” algebraic techniques: Now that x is known, we can plug this value into any of the original equations and obtain a value for y. Or, to save us some work, we can plug this value (6) into the equation we just generated to define y in terms of x, being that it is already in a form to solve for y: Applying the substitution method to systems of three or more variables involves a similar pattern, only with more work involved. This is generally true for any method of solution: the number of steps required for obtaining solutions increases rapidly with each additional variable in the system. To solve for three unknown variables, we need at least three equations. Consider this example: Being that the first equation has the simplest coefficients (1, -1, and 1, for x, y, and z, respectively), it seems logical to use it to develop a definition of one variable in terms of the other two. In this example, I’ll solve for x in terms of y and z: Now, we can substitute this definition of x where x appears in the other two equations: Reducing these two equations to their simplest forms: So far, our efforts have reduced the system from three variables in three equations to two variables in two equations. Now, we can apply the substitution technique again to the two equations 4y - z = 4 and -3y + 4z = 36 to solve for either y or z. First, I’ll manipulate the first equation to define z in terms of y: Next, we’ll substitute this definition of z in terms of y where we see z in the other equation: Now that y is a known value, we can plug it into the equation defining z in terms of y and obtain a figure for z: Now, with values for y and z known, we can plug these into the equation where we defined x in terms of y and z, to obtain a value for x: In closing, we’ve found values for x, y, and z of 2, 4, and 12, respectively, that satisfy all three equations. Solving Simultaneous Equations Using The Addition Method While the substitution method may be the easiest to grasp on a conceptual level, there are other methods of solution available to us. One such method is the so-called addition method, whereby equations are added to one another for the purpose of canceling variable terms. Let’s take our two-variable system used to demonstrate the substitution method: One of the most-used rules of algebra is that you may perform any arithmetic operation you wish to an equation so long as you do it equally to both sides. With reference to addition, this means we may add any quantity we wish to both sides of an equation—so long as its the same quantity—without altering the truth of the equation. An option we have, then, is to add the corresponding sides of the equations together to form a new equation. Since each equation is an expression of equality (the same quantity on either side of the = sign), adding the left-hand side of one equation to the left-hand side of the other equation is valid so long as we add the two equations’ right-hand sides together as well. In our example equation set, for instance, we may add x + y to 2x - y, and add 24 and -6 together as well to form a new equation. What benefit does this hold for us? Examine what happens when we do this to our example equation set: Because the top equation happened to contain a positive y term while the bottom equation happened to contain a negative y term, these two terms canceled each other in the process of addition, leaving no y term in the sum. What we have left is a new equation, but one with only a single unknown variable, x! This allows us to easily solve for the value of x: Once we have a known value for x, of course, determining y‘s value is a simply matter of substitution (replacing x with the number 6) into one of the original equations. In this example, the technique of adding the equations together worked well to produce an equation with a single unknown variable. What about an example where things aren’t so simple? Consider the following equation set: We could add these two equations together—this being a completely valid algebraic operation—but it would not profit us in the goal of obtaining values for x and y: The resulting equation still contains two unknown variables, just like the original equations do, and so we’re no further along in obtaining a solution. However, what if we could manipulate one of the equations so as to have a negative term that would cancel the respective term in the other equation when added? Then, the system would reduce to a single equation with a single unknown variable just as with the last (fortuitous) example. If we could only turn the y term in the lower equation into a - 2y term, so that when the two equations were added together, both y terms in the equations would cancel, leaving us with only an x term, this would bring us closer to a solution. Fortunately, this is not difficult to do. If we multiply each and every term of the lower equation by a -2, it will produce the result we seek: Now, we may add this new equation to the original, upper equation: Solving for x, we obtain a value of 3: Substituting this new-found value for x into one of the original equations, the value of y is easily determined: Using this solution technique on a three-variable system is a bit more complex. As with substitution, you must use this technique to reduce the three-equation system of three variables down to two equations with two variables, then apply it again to obtain a single equation with one unknown variable. To demonstrate, I’ll use the three-variable equation system from the substitution section: Being that the top equation has coefficient values of 1 for each variable, it will be an easy equation to manipulate and use as a cancellation tool. For instance, if we wish to cancel the 3x term from the middle equation, all we need to do is take the top equation, multiply each of its terms by -3, then add it to the middle equation like this: We can rid the bottom equation of its -5x term in the same manner: take the original top equation, multiply each of its terms by 5, then add that modified equation to the bottom equation, leaving a new equation with only y and z terms: At this point, we have two equations with the same two unknown variables, y and z: By inspection, it should be evident that the -z term of the upper equation could be leveraged to cancel the 4z term in the lower equation if only we multiply each term of the upper equation by 4 and add the two equations together: Taking the new equation 13y = 52 and solving for y (by dividing both sides by 13), we get a value of 4 for y. Substituting this value of 4 for y in either of the two-variable equations allows us to solve for z. Substituting both values of y and z into any one of the original, three-variable equations allows us to solve for x. The final result (I’ll spare you the algebraic steps since you should be familiar with them by now!) is that x = 2, y = 4, and z = 12.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/05%3A_Trigonometry_Reference/5.01%3A_Right_Triangle_Trigonometry.txt	princeton-nlp/TextbookChapters	A right triangle is defined as having one angle precisely equal to 90o (a right angle). Trigonometric Identities H is the Hypotenuse, always being opposite the right angle. Relative to angle x, O is the Opposite and A is the Adjacent. “Arc” functions such as “arcsin”, “arccos”, and “arctan” are the complements of normal trigonometric functions. These functions return an angle for a ratio input. For example, if the tangent of 45o is equal to 1, then the “arctangent” (arctan) of 1 is 45o. “Arc” functions are useful for finding angles in a right triangle if the side lengths are known. 5.04: Hyperbolic Functions Note: all angles (x) must be expressed in units of radians for these hyperbolic functions. There are 2π radians in a circle (360o). 6.02: Derivative of a Constant (“c” being a constant) 6.04: Derivatives of Power Functions of e Proportionality Constant When we say that a relationship or phenomenon is “exponential,” we are implying that some quantity—electric current, profits, population—increases more rapidly as the quantity grows. In other words, the rate of change with respect to a given variable is proportional to the value of that variable. This means that the derivative of an exponential function is equal to the original exponential function multiplied by a constant (k) that establishes proportionality. The proportionality constant is equal to the natural log of the base of the exponent: It follows, then, that if the natural log of the base is equal to one, the derivative of the function will be equal to the original function. This is exactly what happens with power functions of e: the natural log of e is 1, and consequently, the derivative of ex is ex. The “Chain” Rule When the exponential expression is something other than simply x, we apply the chain rule: First we take the derivative of the entire expression, then we multiply it by the derivative of the expression in the exponent. This technique can be used to find the rate of change of diode current with respect to diode voltage. The following equation provides an approximate relationship between the voltage across a diode ($V_D$)and the current through a diode($I_D$): (See the page on diodes and rectifiers for more information on the diode current–voltage equation; also, note that ($I_S$) is a constant, not a variable.) To find the rate of change of current with respect to voltage, we take the derivative: Thus, at a given value of diode voltage ($V_D$) , an incremental increase in voltage will create an increase in current equal to \frac{I_S}{0.026}e^\frac{V_D}{0.026}\] 6.07: The Antiderivative (Indefinite Integral) Notice something important here: taking the derivative of f(x) may precisely give you g(x), but taking the antiderivative of g(x) does not necessarily give you f(x) in its original form. Example: Note that the constant c is unknown! The original function f(x) could have been 3x2 + 5, 3x2 + 10, 3x2 + anything, and the derivative of f(x) would have still been 6x. Determining the antiderivative of a function, then, is a bit less certain than determining the derivative of a function. 6.09: Antiderivatives of Power Functions of e Note: this is a very unique and useful property of e. As in the case of derivatives, the antiderivative of such a function is that same function. In the case of the antiderivative, a constant term “c” is added to the end as well. 6.12: Differential Equations As opposed to normal equations where the solution is a number, a differential equation is one where the solution is actually a function, and which at least one derivative of that unknown function is part of the equation. As with finding antiderivatives of a function, we are often left with a solution that encompasses more than one possibility (consider the many possible values of the constant “c” typically found in antiderivatives). The set of functions which answer any differential equation is called the “general solution” for that differential equation. Any one function out of that set is referred to as a “particular solution” for that differential equation. The variable of reference for differentiation and integration within the differential equation is known as the “independent variable.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/07%3A_Using_The_spice_Circuit_Simulation_Program/7.01%3A_Introduction_to_SPICE.txt	princeton-nlp/TextbookChapters	“With Electronics Workbench, you can create circuit schematics that look just the same as those you’re already familiar with on paper—plus you can flip the power switch so the schematic behaves like a real circuit. With other electronics simulators, you may have to type in SPICE node lists as text files—an abstract representation of a circuit beyond the capabilities of all but advanced electronics engineers.” —(Electronics Workbench User’s guide—version 4, page 7) This introduction comes from the operating manual for a circuit simulation program called Electronics Workbench. Using a graphic interface, it allows the user to draw a circuit schematic and then have the computer analyze that circuit, displaying the results in graphic form. It is a very valuable analysis tool, but it has its shortcomings. For one, it and other graphic programs like it tend to be unreliable when analyzing complex circuits, as the translation from picture to computer code is not quite the exact science we would want it to be (yet). Secondly, due to its graphics requirements, it tends to need a significant amount of computational “horsepower” to run, and a computer operating system that supports graphics. Thirdly, these graphic programs can be costly. However, underneath the graphics skin of Electronics Workbench lies a robust (and free!) program called SPICE, which analyzes a circuit based on a text-file description of the circuit’s components and connections. What the user pays for with Electronics Workbench and other graphic circuit analysis programs is the convenient “point and click” interface, while SPICE does the actual mathematical analysis. By itself, SPICE does not require a graphic interface and demands little in system resources. It is also very reliable. The makers of Electronic Workbench would like you to think that using SPICE in its native text mode is a task suited for rocket scientists, but I’m writing this to prove them wrong. SPICE is fairly easy to use for simple circuits, and its non-graphic interface actually lends itself toward the analysis of circuits that can be difficult to draw. I think it was the programming expert Donald Knuth who quipped, “What you see is all you get” when it comes to computer applications. Graphics may look more attractive, but abstracted interfaces (text) are actually more efficient. This document is not intended to be an exhaustive tutorial on how to use SPICE. I’m merely trying to show the interested user how to apply it to the analysis of simple circuits, as an alternative to proprietary (\$\$\$) and buggy programs. Once you learn the basics, there are other tutorials better suited to take you further. Using SPICE—a program originally intended to develop integrated circuits—to analyze some of the really simple circuits showcased here may seem a bit like cutting butter with a chain saw, but it works! All options and examples have been tested on SPICE version 2g6 on both MS-DOS and Linux operating systems. As far as I know, I’m not using features specific to version 2g6, so these simple functions should work on most versions of SPICE. 7.02: History of SPICE SPICE is a computer program designed to simulate analog electronic circuits. Its original intent was for the development of integrated circuits, from which it derived its name: Simulation Program with Integrated Circuit Emphasis. The origin of SPICE traces back to another circuit simulation program called CANCER. Developed by professor Ronald Rohrer of U.C. Berkeley along with some of his students in the late 1960’s, CANCER continued to be improved through the early 1970’s. When Rohrer left Berkeley, CANCER was re-written and re-named to SPICE, released as version 1 to the public domain in May of 1972. Version 2 of SPICE was released in 1975 (version 2g6—the version used in this book—is a minor revision of this 1975 release). Instrumental in the decision to release SPICE as a public-domain computer program was professor Donald Pederson of Berkeley, who believed that all significant technical progress happens when information is freely shared. I for one thank him for his vision. A major improvement came about in March of 1985 with version 3 of SPICE (also released under public domain). Written in the C language rather than FORTRAN, version 3 incorporated additional transistor types (the MESFET, for example), and switch elements. Version 3 also allowed the use of alphabetical node labels rather than only numbers. Instructions written for version 2 of SPICE should still run in version 3, though. Despite the additional power of version 3, I have chosen to use version 2g6 throughout this book because it seems to be the easiest version to acquire and run on different computer systems.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/07%3A_Using_The_spice_Circuit_Simulation_Program/7.03%3A_Fundamentals_of_SPICE_programming.txt	princeton-nlp/TextbookChapters	Programming a circuit simulation with SPICE is much like programming in any other computer language: you must type the commands as text in a file, save that file to the computer’s hard drive, and then process the contents of that file with a program (compiler or interpreter) that understands such commands. In an interpreted computer language, the computer holds a special program called an interpreter that translates the program you wrote (the so-called source file) into the computer’s own language, on the fly, as its being executed: In a compiled computer language, the program you wrote is translated all at once into the computer’s own language by a special program called a compiler. After the program you’ve written has been “compiled,” the resulting executable file needs no further translation to be understood directly by the computer. It can now be “run” on a computer whether or not compiler software has been installed on that computer: SPICE is an interpreted language. In order for a computer to be able to understand the SPICE instructions you type, it must have the SPICE program (interpreter) installed: SPICE source files are commonly referred to as “netlists,” although they are sometimes known as “decks” with each line in the file being called a “card.” Cute, don’t you think? Netlists are created by a person like yourself typing instructions line-by-line using a word processor or text editor. Text editors are much preferred over word processors for any type of computer programming, as they produce pure ASCII text with no special embedded codes for text highlighting (like italic or boldface fonts), which are uninterpretable by interpreter and compiler software. As in general programming, the source file you create for SPICE must follow certain conventions of programming. It is a computer language in itself, albeit a simple one. Having programmed in BASIC and C/C++, and having some experience reading PASCAL and FORTRAN programs, it is my opinion that the language of SPICE is much simpler than any of these. It is about the same complexity as a markup language such as HTML, perhaps less so. There is a cycle of steps to be followed in using SPICE to analyze a circuit. The cycle starts when you first invoke the text editing program and make your first draft of the netlist. The next step is to run SPICE on that new netlist and see what the results are. If you are a novice user of SPICE, your first attempts at creating a good netlist will be fraught with small errors of syntax. Don’t worry—as every computer programmer knows, proficiency comes with lots of practice. If your trial run produces error messages or results that are obviously incorrect, you need to re-invoke the text editing program and modify the netlist. After modifying the netlist, you need to run SPICE again and check the results. The sequence, then, looks something like this: • Compose a new netlist with a text editing program. Save that netlist to a file with a name of your choice. • Run SPICE on that netlist and observe the results. • If the results contain errors, start up the text editing program again and modify the netlist. • Run SPICE again and observe the new results. • If there are still errors in the output of SPICE, re-edit the netlist again with the text editing program. Repeat this cycle of edit/run as many times as necessary until you are getting the desired results. • Once you’ve “debugged” your netlist and are getting good results, run SPICE again, only this time redirecting the output to a new file instead of just observing it on the computer screen. • Start up a text editing program or a word processor program and open the SPICE output file you just created. Modify that file to suit your formatting needs and either save those changes to disk and/or print them out on paper. To “run” a SPICE “program,” you need to type in a command at a terminal prompt interface, such as that found in MS-DOS, UNIX, or the MS-Windows DOS prompt option: `spice < example.cir ` The word “spice” invokes the SPICE interpreting program (providing that the SPICE software has been installed on the computer!), the “<” symbol redirects the contents of the source file to the SPICE interpreter, and example.cir is the name of the source file for this circuit example. The file extension “.cir” is not mandatory; I have seen “.inp” (for “input”) and just plain “.txt” work well, too. It will even work when the netlist file has no extension. SPICE doesn’t care what you name it, so long as it has a name compatible with the filesystem of your computer (for old MS-DOS machines, for example, the filename must be no more than 8 characters in length, with a 3 character extension, and no spaces or other non-alphanumerical characters). When this command is typed in, SPICE will read the contents of the example.cir file, analyze the circuit specified by that file, and send a text report to the computer terminal’s standard output (usually the screen, where you can see it scroll by). A typical SPICE output is several screens worth of information, so you might want to look it over with a slight modification of the command: `spice < example.cir \| more ` This alternative “pipes” the text output of SPICE to the “more” utility, which allows only one page to be displayed at a time. What this means (in English) is that the text output of SPICE is halted after one screen-full, and waits until the user presses a keyboard key to display the next screen-full of text. If you’re just testing your example circuit file and want to check for any errors, this is a good way to do it. `spice < example.cir > example.txt ` This second alternative (above) redirects the text output of SPICE to another file, called example.txt, where it can be viewed or printed. This option corresponds to the last step in the development cycle listed earlier. It is recommended by this author that you use this technique of “redirection” to a text file only after you’ve proven your example circuit netlist to work well, so that you don’t waste time invoking a text editor just to see the output during the stages of “debugging.” Once you have a SPICE output stored in a .txt file, you can use a text editor or (better yet!) a word processor to edit the output, deleting any unnecessary banners and messages, even specifying alternative fonts to highlight the headings and/or data for a more polished appearance. Then, of course, you can print the output to paper if you so desire. Being that the direct SPICE output is plain ASCII text, such a file will be universally interpretable on any computer whether SPICE is installed on it or not. Also, the plain text format ensures that the file will be very small compared to the graphic screen-shot files generated by “point-and-click” simulators. The netlist file format required by SPICE is quite simple. A netlist file is nothing more than a plain ASCII text file containing multiple lines of text, each line describing either a circuit component or special SPICE command. Circuit architecture is specified by assigning numbers to each component’s connection points in each line, connections between components designated by common numbers. Examine the following example circuit diagram and its corresponding SPICE file. Please bear in mind that the circuit diagram exists only to make the simulation easier for human beings to understand. SPICE only understands netlists: ```Example netlist v1 1 0 dc 15 r1 1 0 2.2k r2 1 2 3.3k r3 2 0 150 .end ``` Each line of the source file shown above is explained here: • v1 represents the battery (voltage source 1), positive terminal numbered 1, negative terminal numbered 0, with a DC voltage output of 15 volts. • r1 represents resistor R1 in the diagram, connected between points 1 and 0, with a value of 2.2 kΩ. • r2 represents resistor R2 in the diagram, connected between points 1 and 2, with a value of 3.3 kΩ. • r3 represents resistor R3 in the diagram, connected between points 2 and 0, with a value of 150 kΩ. Electrically common points (or “nodes”) in a SPICE circuit description share common numbers, much in the same way that wires connecting common points in a large circuit typically share common wire labels. To simulate this circuit, the user would type those six lines of text on a text editor and save them as a file with a unique name (such as example.cir). Once the netlist is composed and saved to a file, the user then processes that file with one of the command-line statements shown earlier (spice < example.cir), and will receive this text output on their computer’s screen: ```1*****10/10/99 **** spice 2g.6 3/15/83 ****07:32:42* 0example netlist 0 input listing temperature = 27.000 deg c v1 1 0 dc 15 r1 1 0 2.2k r2 1 2 3.3k r3 2 0 150 .end *10/10/99 ***** spice 2g.6 3/15/83 **07:32:42** 0example netlist 0 small signal bias solution temperature = 27.000 deg c node voltage node voltage ( 1) 15.0000 ( 2) 0.6522 voltage source currents name current v1 -1.117E-02 total power dissipation 1.67E-01 watts job concluded 0 total job time 0.02 1***10/10/99 **** spice 2g.6 3/15/83 **07:32:42* 0** input listing temperature = 27.000 deg c ``` SPICE begins by printing the time, date, and version used at the top of the output. It then lists the input parameters (the lines of the source file), followed by a display of DC voltage readings from each node (reference number) to ground (always reference number 0). This is followed by a list of current readings through each voltage source (in this case there’s only one, v1). Finally, the total power dissipation and computation time in seconds is printed. All output values provided by SPICE are displayed in scientific notation. The SPICE output listing shown above is a little verbose for most peoples’ taste. For a final presentation, it might be nice to trim all the unnecessary text and leave only what matters. Here is a sample of that same output, redirected to a text file (spice < example.cir > example.txt), then trimmed down judiciously with a text editor for final presentation and printed: ```example netlist v1 1 0 dc 15 r1 1 0 2.2k r2 1 2 3.3k r3 2 0 150 .end ``` ```node voltage node voltage ( 1) 15.0000 ( 2) 0.6522 ``` ```voltage source currents name current v1 -1.117E-02 ``` ```total power dissipation 1.67E-01 watts ``` One of the very nice things about SPICE is that both input and output formats are plain-text, which is the most universal and easy-to-edit electronic format around. Practically any computer will be able to edit and display this format, even if the SPICE program itself is not resident on that computer. If the user desires, he or she is free to use the advanced capabilities of word processing programs to make the output look fancier. Comments can even be inserted between lines of the output for further clarity to the reader. 7.04: The Command-line Interface If you’ve used DOS or UNIX operating systems before in a command-line shell environment, you may wonder why we have to use the “<” symbol between the word “spice” and the name of the netlist file to be interpreted. Why not just enter the file name as the first argument to the command “spice” as we do when we invoke the text editor? The answer is that SPICE has the option of an interactive mode, whereby each line of the netlist can be interpreted as it is entered through the computer’s Standard Input (stdin). If you simple type “spice” at the prompt and press [Enter], SPICE will begin to interpret anything you type in to it (live). For most applications, its nice to save your netlist work in a separate file and then let SPICE interpret that file when you’re ready. This is the way I encourage SPICE to be used, and so this is the way its presented in this lesson. In order to use SPICE this way in a command-line environment, we need to use the “<” redirection symbol to direct the contents of your netlist file to Standard Input (stdin), which SPICE can then process
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/07%3A_Using_The_spice_Circuit_Simulation_Program/7.05%3A_Circuit_Components.txt	princeton-nlp/TextbookChapters	Remember that this tutorial is not exhaustive by any means, and that all descriptions for elements in the SPICE language are documented here in condensed form. SPICE is a very capable piece of software with lots of options, and I’m only going to document a few of them. All components in a SPICE source file are primarily identified by the first letter in each respective line. Characters following the identifying letter are used to distinguish one component of a certain type from another of the same type (r1, r2, r3, rload, rpullup, etc.), and need not follow any particular naming convention, so long as no more than eight characters are used in both the component identifying letter and the distinguishing name. For example, suppose you were simulating a digital circuit with “pullup” and “pulldown” resistors. The name rpullup would be valid because it is seven characters long. The name rpulldown, however, is nine characters long. This may cause problems when SPICE interprets the netlist. You can actually get away with component names in excess of eight total characters if there are no other similarly-named components in the source file. SPICE only pays attention to the first eight characters of the first field in each line, so rpulldown is actually interpreted as rpulldow with the “n” at the end being ignored. Therefore, any other resistor having the first eight characters in its first field will be seen by SPICE as the same resistor, defined twice, which will cause an error (i.e. rpulldown1 and rpulldown2 would be interpreted as the same name, rpulldow). It should also be noted that SPICE ignores character case, so r1 and R1 are interpreted by SPICE as one and the same. SPICE allows the use of metric prefixes in specifying component values, which is a very handy feature. However, the prefix convention used by SPICE differs somewhat from standard metric symbols, primarily due to the fact that netlists are restricted to standard ASCII characters (ruling out Greek letters such as µ for the prefix “micro”) and that SPICE is case-insensitive, so “m” (which is the standard symbol for “milli”) and “M” (which is the standard symbol for “Mega”) are interpreted identically. Here are a few examples of prefixes used in SPICE netlists: r1 1 0 2t (Resistor R1, 2t = 2 Tera-ohms = 2 TΩ) r2 1 0 4g (Resistor R2, 4g = 4 Giga-ohms = 4 GΩ) r3 1 0 47meg (Resistor R3, 47meg = 47 Mega-ohms = 47 MΩ) r4 1 0 3.3k (Resistor R4, 3.3k = 3.3 kilo-ohms = 3.3 kΩ) r5 1 0 55m (Resistor R5, 55m = 55 milli-ohms = 55 mΩ) r6 1 0 10u (Resistor R6, 10u = 10 micro-ohms 10 µΩ) r7 1 0 30n (Resistor R7, 30n = 30 nano-ohms = 30 nΩ) r8 1 0 5p (Resistor R8, 5p = 5 pico-ohms = 5 pΩ) r9 1 0 250f (Resistor R9, 250f = 250 femto-ohms = 250 fΩ) Scientific notation is also allowed in specifying component values. For example: r10 1 0 4.7e3 (Resistor R10, 4.7e3 = 4.7 x 103 ohms = 4.7 kilo-ohms = 4.7 kΩ) r11 1 0 1e-12 (Resistor R11, 1e-12 = 1 x 10-12 ohms = 1 pico-ohm = 1 pΩ) The unit (ohms, volts, farads, henrys, etc.) is automatically determined by the type of component being specified. SPICE “knows” that all of the above examples are “ohms” because they are all resistors (r1, r2, r3, . . . ). If they were capacitors, the values would be interpreted as “farads,” if inductors, then “henrys,” etc. Passive components Capacitors `General form: c[name] [node1] [node2] [value] ic=[initial voltage] Example 1: c1 12 33 10u Example 2: c1 12 33 10u ic=3.5 ` Comments: The “initial condition” (ic=) variable is the capacitor’s voltage in units of volts at the start of DC analysis. It is an optional value, with the starting voltage assumed to be zero if unspecified. Starting current values for capacitors are interpreted by SPICE only if the .tran analysis option is invoked (with the “uic” option). INDUCTORS `General form: l[name] [node1] [node2] [value] ic=[initial current] Example 1: l1 12 33 133m Example 2: l1 12 33 133m ic=12.7m ` Comments: The “initial condition” (ic=) variable is the inductor’s current in units of amps at the start of DC analysis. It is an optional value, with the starting current assumed to be zero if unspecified. Starting current values for inductors are interpreted by SPICE only if the .tran analysis option is invoked. INDUCTOR COUPLING (transformers) `General form: k[name] l[name] l[name] [coupling factor] Example 1: k1 l1 l2 0.999 ` Comments: SPICE will only allow coupling factor values between 0 and 1 (non-inclusive), with 0 representing no coupling and 1 representing perfect coupling. The order of specifying coupled inductors (l1, l2 or l2, l1) is irrelevant. RESISTORS `General form: r[name] [node1] [node2] [value] Example: rload 23 15 3.3k ` Comments: In case you were wondering, there is no declaration of resistor power dissipation rating in SPICE. All components are assumed to be indestructible. If only real life were this forgiving! Active components All semiconductor components must have their electrical characteristics described in a line starting with the word “.model”, which tells SPICE exactly how the device will behave. Whatever parameters are not explicitly defined in the .model card will default to values pre-programmed in SPICE. However, the .modelcard must be included, and at least specify the model name and device type (d, npn, pnp, njf, pjf, nmos, or pmos). DIODES `General form: d[name] [anode] [cathode] [model] Example: d1 1 2 mod1 ` DIODE MODELS: ```General form: .model [modelname] d [parmtr1=x] [parmtr2=x] . . . Example: .model mod1 d Example: .model mod2 d vj=0.65 rs=1.3 ``` diodeparameter Parameter definitions: is = saturation current in amps rs = junction resistance in ohms n = emission coefficient (unitless) tt = transit time in seconds cjo = zero-bias junction capacitance in farads vj = junction potential in volts m = grading coefficient (unitless) eg = activation energy in electron-volts xti = saturation-current temperature exponent (unitless) kf = flicker noise coefficient (unitless) af = flicker noise exponent (unitless) fc = forward-bias depletion capacitance coefficient (unitless) bv = reverse breakdown voltage in volts ibv = current at breakdown voltage in amps Comments: The model name must begin with a letter, not a number. If you plan to specify a model for a 1N4003 rectifying diode, for instance, you cannot use “1n4003” for the model name. An alternative might be “m1n4003” instead. TRANSISTORS, bipolar junction—BJT `General form: q[name] [collector] [base] [emitter] [model] Example: q1 2 3 0 mod1 ` BJT TRANSISTOR MODELS: `General form: .model [modelname] [npn or pnp] [parmtr1=x] . . . Example: .model mod1 pnp Example: .model mod2 npn bf=75 is=1e-14 ` The model examples shown above are very nonspecific. To accurately model real-life transistors, more parameters are necessary. Take these two examples, for the popular 2N2222 and 2N2907 transistors (the “+”) characters represent line-continuation marks in SPICE, when you wish to break a single line (card) into two or more separate lines on your text editor: ` Example: .model m2n2222 npn is=19f bf=150 vaf=100 ikf=.18 + ise=50p ne=2.5 br=7.5 var=6.4 ikr=12m + isc=8.7p nc=1.2 rb=50 re=0.4 rc=0.4 cje=26p + tf=0.5n cjc=11p tr=7n xtb=1.5 kf=0.032f af=1 ` `Example: .model m2n2907 pnp is=1.1p bf=200 nf=1.2 vaf=50 + ikf=0.1 ise=13p ne=1.9 br=6 rc=0.6 cje=23p + vje=0.85 mje=1.25 tf=0.5n cjc=19p vjc=0.5 + mjc=0.2 tr=34n xtb=1.5 ` Parameter definitions: is = transport saturation current in amps bf = ideal maximum forward Beta (unitless) nf = forward current emission coefficient (unitless) vaf = forward Early voltage in volts ikf = corner for forward Beta high-current rolloff in amps ise = B-E leakage saturation current in amps ne = B-E leakage emission coefficient (unitless) br = ideal maximum reverse Beta (unitless) nr = reverse current emission coefficient (unitless) bar = reverse Early voltage in volts ikrikr = corner for reverse Beta high-current rolloff in amps iscisc = B-C leakage saturation current in amps nc = B-C leakage emission coefficient (unitless) rb = zero bias base resistance in ohms irb = current for base resistance halfway value in amps rbm = minimum base resistance at high currents in ohms re = emitter resistance in ohms rc = collector resistance in ohms cje = B-E zero-bias depletion capacitance in farads vje = B-E built-in potential in volts mje = B-E junction exponential factor (unitless) tf = ideal forward transit time (seconds) xtf = coefficient for bias dependence of transit time (unitless) vtf = B-C voltage dependence on transit time, in volts itf = high-current parameter effect on transit time, in amps ptf = excess phase at f=1/(transit time)(2)(pi) Hz, in degrees cjc = B-C zero-bias depletion capacitance in farads vjc = B-C built-in potential in volts mjc = B-C junction exponential factor (unitless) xjcj = B-C depletion capacitance fraction connected in base node (unitless) tr = ideal reverse transit time in seconds cjs = zero-bias collector-substrate capacitance in farads vjs = substrate junction built-in potential in volts mjs = substrate junction exponential factor (unitless) xtb = forward/reverse Beta temperature exponent eg = energy gap for temperature effect on transport saturation current in electron-volts xti = temperature exponent for effect on transport saturation current (unitless) kf = flicker noise coefficient (unitless) af = flicker noise exponent (unitless) fc = forward-bias depletion capacitance formula coefficient (unitless) Comments: Just as with diodes, the model name given for a particular transistor type must begin with a letter, not a number. That’s why the examples given above for the 2N2222 and 2N2907 types of BJTs are named “m2n2222” and “q2n2907” respectively. As you can see, SPICE allows for very detailed specification of transistor properties. Many of the properties listed above are well beyond the scope and interest of the beginning electronics student, and aren’t even useful apart from knowing the equations SPICE uses to model BJT transistors. For those interested in learning more about transistor modeling in SPICE, consult other books, such as Andrei Vladimirescu’s The Spice Book (ISBN 0-471-60926-9). JFET, junction field-effect transistor `General form: j[name] [drain] [gate] [source] [model] Example: j1 2 3 0 mod1 ` JFET TRANSISTOR MODELS: `General form: .model [modelname] [njf or pjf] [parmtr1=x] . . . Example: .model mod1 pjf Example: .model mod2 njf lambda=1e-5 pb=0.75 ` Parameter definitions: vto = threshold voltage in volts beta = transconductance parameter in amps/volts2 lambda = channel length modulation parameter in units of 1/volts rd = drain resistance in ohms rs = source resistance in ohms cgs = zero-bias G-S junction capacitance in farads cgd = zero-bias G-D junction capacitance in farads pb = gate junction potential in volts is = gate junction saturation current in amps kf = flicker noise coefficient (unitless) af = flicker noise exponent (unitless) fc = forward-bias depletion capacitance coefficient (unitless) MOSFET, transistor `General form: m[name] [drain] [gate] [source] [substrate] [model] Example: m1 2 3 0 0 mod1 ` MOSFET TRANSISTOR MODELS: `General form: .model [modelname] [nmos or pmos] [parmtr1=x] . . . Example: .model mod1 pmos Example: .model mod2 nmos level=2 phi=0.65 rd=1.5 Example: .model mod3 nmos vto=-1 (depletion) Example: .model mod4 nmos vto=1 (enhancement) Example: .model mod5 pmos vto=1 (depletion) Example: .model mod6 pmos vto=-1 (enhancement) ` Comments: In order to distinguish between enhancement mode and depletion-mode (also known as depletion-enhancement mode) transistors, the model parameter “vto” (zero-bias threshold voltage) must be specified. Its default value is zero, but a positive value (+1 volts, for example) on a P-channel transistor or a negative value (-1 volts) on an N-channel transistor will specify that transistor to be a depletion (otherwise known as depletion-enhancement) mode device. Conversely, a negative value on a P-channel transistor or a positive value on an N-channel transistor will specify that transistor to be an enhancement mode device. Remember that enhancement mode transistors are normally-off devices, and must be turned on by the application of gate voltage. Depletion-mode transistors are normally “on,” but can be “pinched off” as well as enhanced to greater levels of drain current by applied gate voltage, hence the alternate designation of “depletion-enhancement” MOSFETs. The “vto” parameter specifies the threshold gate voltage for MOSFET conduction. Sources AC SINEWAVE VOLTAGE SOURCES (when using .ac card to specify frequency): `General form: v[name] [+node] [-node] ac [voltage] [phase] sin Example 1: v1 1 0 ac 12 sin Example 2: v1 1 0 ac 12 240 sin (12 V ∠ 240o) ` Comments: This method of specifying AC voltage sources works well if you’re using multiple sources at different phase angles from each other, but all at the same frequency. If you need to specify sources at different frequencies in the same circuit, you must use the next method! AC SINEWAVE VOLTAGE SOURCES (when NOT using .ac card to specify frequency): `General form: v[name] [+node] [-node] sin([offset] [voltage] + [freq] [delay] [damping factor]) Example 1: v1 1 0 sin(0 12 60 0 0) ` Parameter definitions: offset = DC bias voltage, offsetting the AC waveform by a specified voltage. voltage = peak, or crest, AC voltage value for the waveform. freq = frequency in Hertz. delay = time delay, or phase offset for the waveform, in seconds. damping factor = a figure used to create waveforms of decaying amplitude. Comments: This method of specifying AC voltage sources works well if you’re using multiple sources at different frequencies from each other. Representing phase shift is tricky, though, necessitating the use of the delay factor. DC VOLTAGE SOURCES (when using .dc card to specify voltage): `General form: v[name] [+node] [-node] dc Example 1: v1 1 0 dc ` Comments: If you wish to have SPICE output voltages not in reference to node 0, you must use the .dcanalysis option, and to use this option you must specify at least one of your DC sources in this manner. DC VOLTAGE SOURCES (when NOT using .dc card to specify voltage): `General form: v[name] [+node] [-node] dc [voltage] Example 1: v1 1 0 dc 12 ` Comments: Nothing noteworthy here! PULSE VOLTAGE SOURCES `General form: v[name] [+node] [-node] pulse ( [p] [td] [tr] + [tf] [pw] [pd]) ` Parameter definitions: i = initial value p = pulse value td = delay time (all time parameters in units of seconds) tr = rise time tf = fall time pw = pulse width pd = period `Example 1: v1 1 0 pulse (-3 3 0 0 0 10m 20m) ` Comments: Example 1 is a perfect square wave oscillating between -3 and +3 volts, with zero rise and fall times, a 20 millisecond period, and a 50 percent duty cycle (+3 volts for 10 ms, then -3 volts for 10 ms). AC SINEWAVE CURRENT SOURCES (when using .ac card to specify frequency): `General form: i[name] [+node] [-node] ac [current] [phase] sin Example 1: i1 1 0 ac 3 sin (3 amps) Example 2: i1 1 0 ac 1m 240 sin (1 mA ∠ 240o) ` Comments: The same comments apply here (and in the next example) as for AC voltage sources. AC SINEWAVE CURRENT SOURCES (when NOT using .ac card to specify frequency): `General form: i[name] [+node] [-node] sin([offset] + [current] [freq] 0 0) Example 1: i1 1 0 sin(0 1.5 60 0 0) ` DC CURRENT SOURCES (when using .dc card to specify current): `General form: i[name] [+node] [-node] dc Example 1: i1 1 0 dc ` DC CURRENT SOURCES (when NOT using .dc card to specify current): `General form: i[name] [+node] [-node] dc [current] Example 1: i1 1 0 dc 12 ` Comments: Even though the books all say that the first node given for the DC current source is the positive node, that’s not what I’ve found to be in practice. In actuality, a DC current source in SPICE pushes current in the same direction as a voltage source (battery) would with its negative node specified first. PULSE CURRENT SOURCES `General form: i[name] [+node] [-node] pulse ( [p] [td] [tr] + [tf] [pw] [pd]) ` Parameter definitions: i = initial value p = pulse value td = delay time tr = rise time tf = fall time pw = pulse width pd = period `Example 1: i1 1 0 pulse (-3m 3m 0 0 0 17m 34m) ` Comments: Example 1 is a perfect square wave oscillating between -3 mA and +3 mA, with zero rise and fall times, a 34 millisecond period, and a 50 percent duty cycle (+3 mA for 17 ms, then -3 mA for 17 ms). VOLTAGE SOURCES (dependent): `General form: e[name] [out+node] [out-node] [in+node] [in-node] + [gain] Example 1: e1 2 0 1 2 999k ` Comments: Dependent voltage sources are great to use for simulating operational amplifiers. Example 1 shows how such a source would be configured for use as a voltage follower, inverting input connected to output (node 2) for negative feedback, and the noninverting input coming in on node 1. The gain has been set to an arbitrarily high value of 999,000. One word of caution, though: SPICE does not recognize the input of a dependent source as being a load, so a voltage source tied only to the input of an independent voltage source will be interpreted as “open.” See op-amp circuit examples for more details on this. CURRENT SOURCES (dependent):
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/07%3A_Using_The_spice_Circuit_Simulation_Program/7.06%3A_Analysis_Options.txt	princeton-nlp/TextbookChapters	AC ANALYSIS: `General form: .ac [curve] [points] [start] [final] Example 1: .ac lin 1 1000 1000 ` Comments: The [curve] field can be “lin” (linear), “dec” (decade), or “oct” (octave), specifying the (non)linearity of the frequency sweep. specifies how many points within the frequency sweep to perform analyses at (for decade sweep, the number of points per decade; for octave, the number of points per octave). The [start] and [final] fields specify the starting and ending frequencies of the sweep, respectively. One final note: the “start” value cannot be zero! DC ANALYSIS: `General form: .dc [source] [start] [final] [increment] Example 1: .dc vin 1.5 15 0.5 ` Comments: The .dc card is necessary if you want to print or plot any voltage between two nonzero nodes. Otherwise, the default “small-signal” analysis only prints out the voltage between each nonzero node and node zero. TRANSIENT ANALYSIS: `General form: .tran [increment] [stop_time] [start_time] + [comp_interval] Example 1: .tran 1m 50m uic Example 2: .tran .5m 32m 0 .01m ` Comments: Example 1 has an increment time of 1 millisecond and a stop time of 50 milliseconds (when only two parameters are specified, they are increment time and stop time, respectively). Example 2 has an increment time of 0.5 milliseconds, a stop time of 32 milliseconds, a start time of 0 milliseconds (no delay on start), and a computation interval of 0.01 milliseconds. Default value for start time is zero. Transient analysis always beings at time zero, but storage of data only takes place between start time and stop time. Data output interval is increment time, or (stop time - start time)/50, which ever is smallest. However, the computing interval variable can be used to force a computational interval smaller than either. For large total interval counts, the itl5 variable in the .optionscard may be set to a higher number. The “uic” option tells SPICE to “use initial conditions.” PLOT OUTPUT: `General form: .plot [type] [output1] [output2] . . . [output n] Example 1: .plot dc v(1,2) i(v2) Example 2: .plot ac v(3,4) vp(3,4) i(v1) ip(v1) Example 3: .plot tran v(4,5) i(v2) ` Comments: SPICE can’t handle more than eight data point requests on a single .plot or .print card. If requesting more than eight data points, use multiple cards! Also, here’s a major caveat when using SPICE version 3: if you’re performing AC analysis and you ask SPICE to plot an AC voltage as in example #2, the v(3,4) command will only output the real component of a rectangular-form complex number! SPICE version 2 outputs the polar magnitude of a complex number: a much more meaningful quantity if only a single quantity is asked for. To coerce SPICE3 to give you polar magnitude, you will have to re-write the .print or .plot argument as such: vm(3,4). PRINT OUTPUT: `General form: .print [type] [output1] [output2] . . . [output n] Example 1: .print dc v(1,2) i(v2) Example 2: .print ac v(2,4) i(vinput) vp(2,3) Example 3: .print tran v(4,5) i(v2) ` Comments: SPICE can’t handle more than eight data point requests on a single .plot or .print card. If requesting more than eight data points, use multiple cards! FOURIER ANALYSIS: `General form: .four [freq] [output1] [output2] . . . [output n] Example 1: .four 60 v(1,2) ` Comments: The .four card relies on the .tran card being present somewhere in the deck, with the proper time periods for analysis of adequate cycles. Also, SPICE may “crash” if a .plot analysis isn’t done along with the .four analysis, even if all .tran parameters are technically correct. Finally, the .four analysis option only works when the frequency of the AC source is specified in that source’s card line, and not in an .ac analysis option line. It helps to include a computation interval variable in the .tran card for better analysis precision. A Fourier analysis of the voltage or current specified is performed up to the 9th harmonic, with the [freq] specification being the fundamental, or starting frequency of the analysis spectrum. MISCELLANEOUS: `General form: .options [option1] [option2] Example 1: .options limpts=500 Example 2: .options itl5=0 Example 3: .options method=gear Example 4: .options list Example 5: .options nopage Example 6: .options numdgt=6 ` Comments: There are lots of options that can be specified using this card. Perhaps the one most needed by beginning users of SPICE is the “limpts” setting. When running a simulation that requires more than 201 points to be printed or plotted, this calculation point limit must be increased or else SPICE will terminate analysis. The example given above (limpts=500) tells SPICE to allocate enough memory to handle at least 500 calculation points in whatever type of analysis is specified (DC, AC, or transient). In example 2, we see an iteration variable (itl5) being set to a value of 0. There are actually six different iteration variables available for user manipulation. They control the iteration cycle limits for solution of nonlinear equations. The variable itl5 sets the maximum number of iterations for a transient analysis. Similar to the limpts variable, itl5 usually needs to be set when a small computation interval has been specified on a .tran card. Setting itl5 to a value of 0 turns off the limit entirely, allowing the computer infinite iteration cycles (infinite time) to compute the analysis. Warning: this may result in long simulation times! Example 3 with “method=gear” sets the numerical integration method used by SPICE. The default is “trapezoid” rather than “gear,” trapezoid being a simple geometric approximation of area under a curve found by slicing up the curve into trapezoids to approximate the shape. The “gear” method is based on second-order or better polynomial equations and is named after C.W. Gear (Numerical Integration of Stiff Ordinary Equations, Report 221, Department of Computer Science, University of Illinois, Urbana). The Gear method of integration is more demanding of the computer (computationally “expensive”) and will sometimes give slightly different results from the trapezoid method. The “list” option shown in example 4 gives a verbose summary of all circuit components and their respective values in the final output. By default, SPICE will insert ASCII page-break control codes in the output to separate different sections of the analysis. Specifying the “nopage” option (example 5) will prevent such pagination. The “numdgt” option shown in example 6 specifies the number of significant digits output when using one of the “.print” data output options. SPICE defaults at a precision of 4 significant digits. WIDTH CONTROL: `General form: .width in=[columns] out=[columns] Example 1: .width out=80 `
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/07%3A_Using_The_spice_Circuit_Simulation_Program/7.07%3A_SPICE_Quirks.txt	princeton-nlp/TextbookChapters	“Garbage in, garbage out.” —Anonymous SPICE is a very reliable piece of software, but it does have its little quirks that take some getting used to. By “quirk” I mean a demand placed upon the user to write the source file in a particular way in order for it to work without giving error messages. I do not mean any kind of fault with SPICE which would produce erroneous or misleading results: that would be more properly referred to as a “bug.” Speaking of bugs, SPICE has a few of them as well. Some (or all) of these quirks may be unique to SPICE version 2g6, which is the only version I’ve used extensively. They may have been fixed in later versions. A good beginning SPICE demands that the source file begins with something other than the first “card” in the circuit description “deck.” This first character in the source file can be a linefeed, title line, or a comment: there just has to be something there before the first component-specifying line of the file. If not, SPICE will refuse to do an analysis at all, claiming that there is a serious error (such as improper node connections) in the “deck.” A good ending SPICE demands that the .end line at the end of the source file not be terminated with a linefeed or carriage return character. In other words, when you finish typing “.end” you should not hit the [Enter] key on your keyboard. The cursor on your text editor should stop immediately to the right of the “d” after the “.end” and go no further. Failure to heed this quirk will result in a “missing .end card” error message at the end of the analysis output. The actual circuit analysis is not affected by this error, so I normally ignore the message. However, if you’re looking to receive a “perfect” output, you must pay heed to this idiosyncrasy. Must have a node 0 You are given much freedom in numbering circuit nodes, but you must have a node 0 somewhere in your netlist in order for SPICE to work. Node 0 is the default node for circuit ground, and it is the point of reference for all voltages specified at single node locations. When simple DC analysis is performed by SPICE, the output will contain a listing of voltages at all non-zero nodes in the circuit. The point of reference (ground) for all these voltage readings is node 0. For example: ```node voltage node voltage ( 1) 15.0000 ( 2) 0.6522 ``` In this analysis, there is a DC voltage of 15 volts between node 1 and ground (node 0), and a DC voltage of 0.6522 volts between node 2 and ground (node 0). In both these cases, the voltage polarity is negative at node 0 with reference to the other node (in other words, both nodes 1 and 2 are positive with respect to node 0). Avoid open circuits SPICE cannot handle open circuits of any kind. If your netlist specifies a circuit with an open voltage source, for example, SPICE will refuse to perform an analysis. A prime example of this type of error is found when “connecting” a voltage source to the input of a voltage-dependent source (used to simulate an operational amplifier). SPICE needs to see a complete path for current, so I usually tie a high-value resistor (call it rbogus!) across the voltage source to act as a minimal load. Avoid certain component loops SPICE cannot handle certain uninterrupted loops of components in a circuit, namely voltage sources and inductors. The following loops will cause SPICE to abort analysis: `netlist l1 2 4 10m l2 2 4 50m l3 2 4 25m ` `netlist v1 1 0 dc 12 l1 1 0 150m ` `netlist c1 5 6 33u c2 6 7 47u ` The reason SPICE can’t handle these conditions stems from the way it performs DC analysis: by treating all inductors as shorts and all capacitors as opens. Since short-circuits (0 Ω) and open circuits (infinite resistance) either contain or generate mathematical infinitudes, a computer simply cannot deal with them, and so SPICE will discontinue analysis if any of these conditions occur. In order to make these component configurations acceptable to SPICE, you must insert resistors of appropriate values into the appropriate places, eliminating the respective short-circuits and open-circuits. If a series resistor is required, choose a very low resistance value. Conversely, if a parallel resistor is required, choose a very high resistance value. For example: To fix the parallel inductor problem, insert a very low-value resistor in series with each offending inductor. `original netlist l1 2 4 10m l2 2 4 50m l3 2 4 25m ` `fixed netlist rbogus1 2 3 1e-12 rbogus2 2 5 1e-12 l1 3 4 10m l2 2 4 50m l3 5 4 25m ` The extremely low-resistance resistors Rbogus1 and Rbogus2 (each one with a mere 1 pico-ohm of resistance) “break up” the direct parallel connections that existed between L1, L2, and L3. It is important to choose very low resistances here so that circuit operation is not substantially impacted by the “fix.” To fix the voltage source / inductor loop, insert a very low-value resistor in series with the two components. `original netlist v1 1 0 dc 12 l1 1 0 150m ` `fixed netlist v1 1 0 dc 12 l1 2 0 150m rbogus 1 2 1e-12 ` As in the previous example with parallel inductors, it is important to make the correction resistor (Rbogus) very low in resistance, so as to not substantially impact circuit operation. To fix the series capacitor circuit, one of the capacitors must have a resistor shunting across it. SPICE requires a DC current path to each capacitor for analysis. `original netlist c1 5 6 33u c2 6 7 47u ` `fixed netlist c1 5 6 33u c2 6 7 47u rbogus 6 7 9e12 ` The Rbogus value of 9 Tera-ohms provides a DC current path to C1 (and around C2) without substantially impacting the circuit’s operation. Current measurement Although printing or plotting of voltage is quite easy in SPICE, the output of current values is a bit more difficult. Voltage measurements are specified by declaring the appropriate circuit nodes. For example, if we desire to know the voltage across a capacitor whose leads connect between nodes 4 and 7, we might make out .print statement look like this: `c1 4 7 22u .print ac v(4,7) ` However, if we wanted to have SPICE measure the current through that capacitor, it wouldn’t be quite so easy. Currents in SPICE must be specified in relation to a voltage source, not any arbitrary component. For example: `c1 4 7 22u vinput 6 4 ac 1 sin .print ac i(vinput) ` This .print card instructs SPICE to print the current through voltage source Vinput, which happens to be the same as the current through our capacitor between nodes 4 and 7. But what if there is no such voltage source in our circuit to reference for current measurement? One solution is to insert a shunt resistor into the circuit and measure voltage across it. In this case, I have chosen a shunt resistance value of 1 Ω to produce 1 volt per amp of current through C1: `c1 4 7 22u rshunt 6 4 1 .print ac v(6,4) ` However, the insertion of an extra resistance into our circuit large enough to drop a meaningful voltage for the intended range of current might adversely affect things. A better solution for SPICE is this, although one would never seek such a current measurement solution in real life: `c1 4 7 22u vbogus 6 4 dc 0 .print ac i(vbogus) ` Inserting a “bogus” DC voltage source of zero volts doesn’t affect circuit operation at all, yet it provides a convenient place for SPICE to take a current measurement. Interestingly enough, it doesn’t matter that Vbogus is a DC source when we’re looking to measure AC current! The fact that SPICE will output an AC current reading is determined by the “ac” specification in the .print card and nothing more. It should also be noted that the way SPICE assigns a polarity to current measurements is a bit odd. Take the following circuit as an example: `example v1 1 0 r1 1 2 5k r2 2 0 5k .dc v1 10 10 1 .print dc i(v1) .end ` With 10 volts total voltage and 10 kΩ total resistance, you might expect SPICE to tell you there’s going to be 1 mA (1e-03) of current through voltage source V1, but in actuality, SPICE will output a figure of negative 1 mA (-1e-03)! SPICE regards current out of the negative end of a DC voltage source (the normal direction) to be a negative value of current rather than a positive value of current. There are times I’ll throw in a “bogus” voltage source in a DC circuit like this simply to get SPICE to output a positive current value: `example v1 1 0 r1 1 2 5k r2 2 3 5k vbogus 3 0 dc 0 .dc v1 10 10 1 .print dc i(vbogus) .end ` Notice how Vbogus is positioned so that the circuit current will enter its positive side (node 3) and exit its negative side (node 0). This orientation will ensure a positive output figure for circuit current. Fourier analysis When performing a Fourier (frequency-domain) analysis on a waveform, I have found it necessary to either print or plot the waveform using the .print or .plot cards, respectively. If you don’t print or plot it, SPICE will pause for a moment during analysis and then abort the job after outputting the “initial transient solution.” Also, when analyzing a square wave produced by the “pulse” source function, you must give the waveform some finite rise and fall time, or else the Fourier analysis results will be incorrect. For some reason, a perfect square wave with zero rise/fall time produces significant levels of even harmonics according to SPICE’s Fourier analysis option, which is not true for real square waves.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/07%3A_Using_The_spice_Circuit_Simulation_Program/7.08%3A_Example_Circuits_and_Netlists.txt	princeton-nlp/TextbookChapters	The following circuits are pre-tested netlists for SPICE 2g6, complete with short descriptions when necessary. (See Chapter 2’s Computer Simulation of Electric Circuits for more information on netlists in SPICE.) Feel free to “copy” and “paste” any of the netlists to your own SPICE source file for analysis and/or modification. My goal here is twofold: to give practical examples of SPICE netlist design to further understanding of SPICE netlist syntax, and to show how simple and compact SPICE netlists can be in analyzing simple circuits. All output listings for these examples have been “trimmed” of extraneous information, giving you the most succinct presentation of the SPICE output as possible. I do this primarily to save space in this document. Typical SPICE outputs contain lots of headers and summary information not necessarily germane to the task at hand. So don’t be surprised when you run a simulation on your own and find that the output doesn’t exactly look like what I have shown here! Example multiple-source DC resistor network circuit, part 1 Without a .dc card and a .print or .plot card, the output for this netlist will only display voltages for nodes 1, 2, and 3 (with reference to node 0, of course). Netlist: ```Multiple dc sources v1 1 0 dc 24 v2 3 0 dc 15 r1 1 2 10k r2 2 3 8.1k r3 2 0 4.7k .end ``` Output: ```node voltage node voltage node voltage ( 1) 24.0000 ( 2) 9.7470 ( 3) 15.0000 ``` `voltage source currents name current v1 -1.425E-03 v2 -6.485E-04 ` ```total power dissipation 4.39E-02 watts ``` Example multiple-source DC resistor network circuit, part 2 By adding a .dc analysis card and specifying source V1 from 24 volts to 24 volts in 1 step (in other words, 24 volts steady), we can use the .print card analysis to print out voltages between any two points we desire. Oddly enough, when the .dc analysis option is invoked, the default voltage printouts for each node (to ground) disappears, so we end up having to explicitly specify them in the .print card to see them at all. Netlist: ```Multiple dc sources v1 1 0 v2 3 0 15 r1 1 2 10k r2 2 3 8.1k r3 2 0 4.7k .dc v1 24 24 1 .print dc v(1) v(2) v(3) v(1,2) v(2,3) .end ``` Output: `v1 v(1) v(2) v(3) v(1,2) v(2,3) 2.400E+01 2.400E+01 9.747E+00 1.500E+01 1.425E+01 -5.253E+00 ` Example RC time-constant circuit For DC analysis, the initial conditions of any reactive component (C or L) must be specified (voltage for capacitors, current for inductors). This is provided by the last data field of each capacitor card (ic=0). To perform a DC analysis, the .tran (”transient”) analysis option must be specified, with the first data field specifying time increment in seconds, the second specifying total analysis timespan in seconds, and the “uic” telling it to “use initial conditions” when analyzing. Netlist: ```RC time delay circuit v1 1 0 dc 10 c1 1 2 47u ic=0 c2 1 2 22u ic=0 r1 2 0 3.3k .tran .05 1 uic .print tran v(1,2) .end ``` Output: `time v(1,2) 0.000E+00 7.701E-06 5.000E-02 1.967E+00 1.000E-01 3.551E+00 1.500E-01 4.824E+00 2.000E-01 5.844E+00 2.500E-01 6.664E+00 3.000E-01 7.322E+00 3.500E-01 7.851E+00 4.000E-01 8.274E+00 4.500E-01 8.615E+00 5.000E-01 8.888E+00 5.500E-01 9.107E+00 6.000E-01 9.283E+00 6.500E-01 9.425E+00 7.000E-01 9.538E+00 7.500E-01 9.629E+00 8.000E-01 9.702E+00 8.500E-01 9.761E+00 9.000E-01 9.808E+00 9.500E-01 9.846E+00 1.000E+00 9.877E+00 ` Plotting and analyzing a simple AC sinewave voltage circuit This exercise does show the proper setup for plotting instantaneous values of a sine-wave voltage source with the .plot function (as a transient analysis). Not surprisingly, the Fourier analysis in this deck also requires the .tran (transient) analysis option to be specified over a suitable time range. The time range in this particular deck allows for a Fourier analysis with rather poor accuracy. The more cycles of the fundamental frequency that the transient analysis is performed over, the more precise the Fourier analysis will be. This is not a quirk of SPICE, but rather a basic principle of waveforms. Netlist: `v1 1 0 sin(0 15 60 0 0) rload 1 0 10k * change tran card to the following for better Fourier precision * .tran 1m 30m .01m and include .options card: * .options itl5=30000 .tran 1m 30m .plot tran v(1) .four 60 v(1) .end ` Output: `time v(1) -2.000E+01 -1.000E+01 0.000E+00 1.000E+01 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.000E+00 0.000E+00 . . * . . 1.000E-03 5.487E+00 . . . * . . 2.000E-03 1.025E+01 . . . * . 3.000E-03 1.350E+01 . . . . * . 4.000E-03 1.488E+01 . . . . . 5.000E-03 1.425E+01 . . . . . 6.000E-03 1.150E+01 . . . . * . 7.000E-03 7.184E+00 . . . * . . 8.000E-03 1.879E+00 . . . * . . 9.000E-03 -3.714E+00 . . * . . . 1.000E-02 -8.762E+00 . . * . . . 1.100E-02 -1.265E+01 . * . . . . 1.200E-02 -1.466E+01 . * . . . . 1.300E-02 -1.465E+01 . * . . . . 1.400E-02 -1.265E+01 . * . . . . 1.500E-02 -8.769E+00 . . * . . . 1.600E-02 -3.709E+00 . . * . . . 1.700E-02 1.876E+00 . . . * . . 1.800E-02 7.191E+00 . . . * . . 1.900E-02 1.149E+01 . . . . * . 2.000E-02 1.425E+01 . . . . * . 2.100E-02 1.489E+01 . . . . . 2.200E-02 1.349E+01 . . . . . 2.300E-02 1.026E+01 . . . * . 2.400E-02 5.491E+00 . . . * . . 2.500E-02 1.553E-03 . . * . . 2.600E-02 -5.514E+00 . . * . . . 2.700E-02 -1.022E+01 . * . . . 2.800E-02 -1.349E+01 . * . . . . 2.900E-02 -1.495E+01 . * . . . . 3.000E-02 -1.427E+01 . * . . . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ` ` fourier components of transient response v(1) dc component = -1.885E-03 harmonic frequency fourier normalized phase normalized no (hz) component component (deg) phase (deg) 1 6.000E+01 1.494E+01 1.000000 -71.998 0.000 2 1.200E+02 1.886E-02 0.001262 -50.162 21.836 3 1.800E+02 1.346E-03 0.000090 102.674 174.671 4 2.400E+02 1.799E-02 0.001204 -10.866 61.132 5 3.000E+02 3.604E-03 0.000241 160.923 232.921 6 3.600E+02 5.642E-03 0.000378 -176.247 -104.250 7 4.200E+02 2.095E-03 0.000140 122.661 194.658 8 4.800E+02 4.574E-03 0.000306 -143.754 -71.757 9 5.400E+02 4.896E-03 0.000328 -129.418 -57.420 total harmonic distortion = 0.186350 percent ` Example simple AC resistor-capacitor circuit The .ac card specifies the points of ac analysis from 60Hz to 60Hz, at a single point. This card, of course, is a bit more useful for multi-frequency analysis, where a range of frequencies can be analyzed in steps. The .print card outputs the AC voltage between nodes 1 and 2, and the AC voltage between node 2 and ground. Netlist: `Demo of a simple AC circuit v1 1 0 ac 12 sin r1 1 2 30 c1 2 0 100u .ac lin 1 60 60 .print ac v(1,2) v(2) .end ` Output: `freq v(1,2) v(2) 6.000E+01 8.990E+00 7.949E+00 ` Example low-pass filter circuit This low-pass filter blocks AC and passes DC to the Rload resistor. Typical of a filter used to suppress ripple from a rectifier circuit, it actually has a resonant frequency, technically making it a band-pass filter. However, it works well anyway to pass DC and block the high-frequency harmonics generated by the AC-to-DC rectification process. Its performance is measured with an AC source sweeping from 500 Hz to 15 kHz. If desired, the .print card can be substituted or supplemented with a .plot card to show AC voltage at node 4 graphically. Netlist: `Lowpass filter v1 2 1 ac 24 sin v2 1 0 dc 24 rload 4 0 1k l1 2 3 100m l2 3 4 250m c1 3 0 100u .ac lin 30 500 15k .print ac v(4) .plot ac v(4) .end ` `freq v(4) 5.000E+02 1.935E-01 1.000E+03 3.275E-02 1.500E+03 1.057E-02 2.000E+03 4.614E-03 2.500E+03 2.402E-03 3.000E+03 1.403E-03 3.500E+03 8.884E-04 4.000E+03 5.973E-04 4.500E+03 4.206E-04 5.000E+03 3.072E-04 5.500E+03 2.311E-04 6.000E+03 1.782E-04 6.500E+03 1.403E-04 7.000E+03 1.124E-04 7.500E+03 9.141E-05 8.000E+03 7.536E-05 8.500E+03 6.285E-05 9.000E+03 5.296E-05 9.500E+03 4.504E-05 1.000E+04 3.863E-05 1.050E+04 3.337E-05 1.100E+04 2.903E-05 1.150E+04 2.541E-05 1.200E+04 2.237E-05 1.250E+04 1.979E-05 1.300E+04 1.760E-05 1.350E+04 1.571E-05 1.400E+04 1.409E-05 1.450E+04 1.268E-05 1.500E+04 1.146E-05 ` `freq v(4) 1.000E-06 1.000E-04 1.000E-02 1.000E+00 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5.000E+02 1.935E-01 . . . * . 1.000E+03 3.275E-02 . . . * . 1.500E+03 1.057E-02 . . * . 2.000E+03 4.614E-03 . . * . . 2.500E+03 2.402E-03 . . * . . 3.000E+03 1.403E-03 . . * . . 3.500E+03 8.884E-04 . . * . . 4.000E+03 5.973E-04 . . * . . 4.500E+03 4.206E-04 . . * . . 5.000E+03 3.072E-04 . . * . . 5.500E+03 2.311E-04 . . * . . 6.000E+03 1.782E-04 . . * . . 6.500E+03 1.403E-04 . .* . . 7.000E+03 1.124E-04 . * . . 7.500E+03 9.141E-05 . * . . 8.000E+03 7.536E-05 . . . . 8.500E+03 6.285E-05 . . . . 9.000E+03 5.296E-05 . * . . . 9.500E+03 4.504E-05 . * . . . 1.000E+04 3.863E-05 . * . . . 1.050E+04 3.337E-05 . * . . . 1.100E+04 2.903E-05 . * . . . 1.150E+04 2.541E-05 . * . . . 1.200E+04 2.237E-05 . * . . . 1.250E+04 1.979E-05 . * . . . 1.300E+04 1.760E-05 . * . . . 1.350E+04 1.571E-05 . * . . . 1.400E+04 1.409E-05 . * . . . 1.450E+04 1.268E-05 . * . . . 1.500E+04 1.146E-05 . * . . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ` Example multiple-source AC network circuit One of the idiosyncrasies of SPICE is its inability to handle any loop in a circuit exclusively composed of series voltage sources and inductors. Therefore, the “loop” of V1-L1-L2-V2-V1 is unacceptable. To get around this, I had to insert a low-resistance resistor somewhere in that loop to break it up. Thus, we have Rbogusbetween 3 and 4 (with 1 pico-ohm of resistance), and V2 between 4 and 0. The circuit above is the original design, while the circuit below has Rbogus inserted to avoid the SPICE error. Netlist: `Multiple ac source v1 1 0 ac 55 0 sin v2 4 0 ac 43 25 sin l1 1 2 450m c1 2 0 330u l2 2 3 150m rbogus 3 4 1e-12 .ac lin 1 30 30 .print ac v(2) .end ` Output: `freq v(2) 3.000E+01 1.413E+02 ` Example AC phase shift demonstration circuit The currents through each leg are indicated by the voltage drops across each respective shunt resistor (1 amp = 1 volt through 1 Ω), output by the v(1,2) and v(1,3) terms of the .print card. The phase of the currents through each leg are indicated by the phase of the voltage drops across each respective shunt resistor, output by the vp(1,2) and vp(1,3) terms in the .print card. Netlist: `phase shift v1 1 0 ac 4 sin rshunt1 1 2 1 rshunt2 1 3 1 l1 2 0 1 r1 3 0 6.3k .ac lin 1 1000 1000 .print ac v(1,2) v(1,3) vp(1,2) vp(1,3) .end ` Output: `freq v(1,2) v(1,3) vp(1,2) vp(1,3) 1.000E+03 6.366E-04 6.349E-04 -9.000E+01 0.000E+00 ` Example transformer circuit SPICE understands transformers as a set of mutually coupled inductors. Thus, to simulate a transformer in SPICE, you must specify the primary and secondary windings as separate inductors, then instruct SPICE to link them together with a “k” card specifying the coupling constant. For ideal transformer simulation, the coupling constant would be unity (1). However, SPICE can’t handle this value, so we use something like 0.999 as the coupling factor. Note that all winding inductor pairs must be coupled with their own k cards in order for the simulation to work properly. For a two-winding transformer, a single k card will suffice. For a three-winding transformer, three k cards must be specified (to link L1 with L2, L2 with L3, and L1 with L3). The L1/L2 inductance ratio of 100:1 provides a 10:1 step-down voltage transformation ratio. With 120 volts in we should see 12 volts out of the L2 winding. The L1/L3 inductance ratio of 100:25 (4:1) provides a 2:1 step-down voltage transformation ratio, which should give us 60 volts out of the L3 winding with 120 volts in. Netlist: `transformer v1 1 0 ac 120 sin rbogus0 1 6 1e-3 l1 6 0 100 l2 2 4 1 l3 3 5 25 k1 l1 l2 0.999 k2 l2 l3 0.999 k3 l1 l3 0.999 r1 2 4 1000 r2 3 5 1000 rbogus1 5 0 1e10 rbogus2 4 0 1e10 .ac lin 1 60 60 .print ac v(1,0) v(2,0) v(3,0) .end ` Output: `freq v(1) v(2) v(3) 6.000E+01 1.200E+02 1.199E+01 5.993E+01 ` In this example, Rbogus0 is a very low-value resistor, serving to break up the source/inductor loop of V1/L1. Rbogus1 and Rbogus2 are very high-value resistors necessary to provide DC paths to a ground on each of the isolated circuits. Note as well that one side of the primary circuit is directly grounded. Without these ground references, SPICE will produce errors! Example full-wave bridge rectifier circuit Diodes, like all semiconductor components in SPICE, must be modeled so that SPICE knows all the nitty-gritty details of how they’re supposed to work. Fortunately, SPICE comes with a few generic models, and the diode is the most basic. Notice the .model card which simply specifies “d” as the generic diode model for mod1. Again, since we’re plotting the waveforms here, we need to specify all parameters of the AC source in a single card and print/plot all values using the .tran option. Netlist: `fullwave bridge rectifier v1 1 0 sin(0 15 60 0 0) rload 1 0 10k d1 1 2 mod1 d2 0 2 mod1 d3 3 1 mod1 d4 3 0 mod1 .model mod1 d .tran .5m 25m .plot tran v(1,0) v(2,3) .end ` Output: `legend: : v(1) +: v(2,3) time v(1) ()--------- -2.000E+01 -1.000E+01 0.000E+00 1.000E+01 2.000E+01 (+)--------- -5.000E+00 0.000E+00 5.000E+00 1.000E+01 1.500E+01 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.000E+00 0.000E+00 . + * . . 5.000E-04 2.806E+00 . . + . * . . 1.000E-03 5.483E+00 . . + * . . 1.500E-03 7.929E+00 . . . + * . . 2.000E-03 1.013E+01 . . . +* . 2.500E-03 1.198E+01 . . . . * + . 3.000E-03 1.338E+01 . . . . * + . 3.500E-03 1.435E+01 . . . . * +. 4.000E-03 1.476E+01 . . . . * + 4.500E-03 1.470E+01 . . . . * + 5.000E-03 1.406E+01 . . . . * + . 5.500E-03 1.299E+01 . . . . * + . 6.000E-03 1.139E+01 . . . . + . 6.500E-03 9.455E+00 . . . + . . 7.000E-03 7.113E+00 . . . + * . . 7.500E-03 4.591E+00 . . +. * . . 8.000E-03 1.841E+00 . . + . * . . 8.500E-03 -9.177E-01 . . + . . . 9.000E-03 -3.689E+00 . . + . . . 9.500E-03 -6.380E+00 . . * . + . . 1.000E-02 -8.784E+00 . . * . + . . 1.050E-02 -1.075E+01 . . . .+ . 1.100E-02 -1.255E+01 . . . . + . 1.150E-02 -1.372E+01 . * . . . + . 1.200E-02 -1.460E+01 . * . . . + 1.250E-02 -1.476E+01 .* . . . + 1.300E-02 -1.460E+01 . * . . . + 1.350E-02 -1.373E+01 . * . . . + . 1.400E-02 -1.254E+01 . * . . . + . 1.450E-02 -1.077E+01 . . . .+ . 1.500E-02 -8.726E+00 . . . + . . 1.550E-02 -6.293E+00 . . * . + . . 1.600E-02 -3.684E+00 . . x . . . 1.650E-02 -9.361E-01 . . + . . . 1.700E-02 1.875E+00 . . + . . . 1.750E-02 4.552E+00 . . +. * . . 1.800E-02 7.170E+00 . . . + * . . 1.850E-02 9.401E+00 . . . + . . 1.900E-02 1.146E+01 . . . . + . 1.950E-02 1.293E+01 . . . . * + . 2.000E-02 1.414E+01 . . . . * +. 2.050E-02 1.464E+01 . . . . * + 2.100E-02 1.483E+01 . . . . * + 2.150E-02 1.430E+01 . . . . * +. 2.200E-02 1.344E+01 . . . . * + . 2.250E-02 1.195E+01 . . . . + . 2.300E-02 1.016E+01 . . . + . 2.350E-02 7.917E+00 . . . + * . . 2.400E-02 5.460E+00 . . + * . . 2.450E-02 2.809E+00 . . + . * . . 2.500E-02 -8.297E-04 . + * . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ` Example common-base BJT transistor amplifier circuit This analysis sweeps the input voltage (Vin) from 0 to 5 volts in 0.1 volt increments, then prints out the voltage between the collector and emitter leads of the transistor v(2,3). The transistor (Q1) is an NPN with a forward Beta of 50. Netlist: `Common-base BJT amplifier vsupply 1 0 dc 24 vin 0 4 dc rc 1 2 800 re 3 4 100 q1 2 0 3 mod1 .model mod1 npn bf=50 .dc vin 0 5 0.1 .print dc v(2,3) .plot dc v(2,3) .end ` Output: `vin v(2,3) 0.000E+00 2.400E+01 1.000E-01 2.410E+01 2.000E-01 2.420E+01 3.000E-01 2.430E+01 4.000E-01 2.440E+01 5.000E-01 2.450E+01 6.000E-01 2.460E+01 7.000E-01 2.466E+01 8.000E-01 2.439E+01 9.000E-01 2.383E+01 1.000E+00 2.317E+01 1.100E+00 2.246E+01 1.200E+00 2.174E+01 1.300E+00 2.101E+01 1.400E+00 2.026E+01 1.500E+00 1.951E+01 1.600E+00 1.876E+01 1.700E+00 1.800E+01 1.800E+00 1.724E+01 1.900E+00 1.648E+01 2.000E+00 1.572E+01 2.100E+00 1.495E+01 2.200E+00 1.418E+01 2.300E+00 1.342E+01 2.400E+00 1.265E+01 2.500E+00 1.188E+01 2.600E+00 1.110E+01 2.700E+00 1.033E+01 2.800E+00 9.560E+00 2.900E+00 8.787E+00 3.000E+00 8.014E+00 3.100E+00 7.240E+00 3.200E+00 6.465E+00 3.300E+00 5.691E+00 3.400E+00 4.915E+00 3.500E+00 4.140E+00 3.600E+00 3.364E+00 3.700E+00 2.588E+00 3.800E+00 1.811E+00 3.900E+00 1.034E+00 4.000E+00 2.587E-01 4.100E+00 9.744E-02 4.200E+00 7.815E-02 4.300E+00 6.806E-02 4.400E+00 6.141E-02 4.500E+00 5.657E-02 4.600E+00 5.281E-02 4.700E+00 4.981E-02 4.800E+00 4.734E-02 4.900E+00 4.525E-02 5.000E+00 4.346E-02 ` `vin v(2,3) 0.000E+00 1.000E+01 2.000E+01 3.000E+01 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.000E+00 2.400E+01 . . . * . 1.000E-01 2.410E+01 . . . * . 2.000E-01 2.420E+01 . . . * . 3.000E-01 2.430E+01 . . . * . 4.000E-01 2.440E+01 . . . * . 5.000E-01 2.450E+01 . . . * . 6.000E-01 2.460E+01 . . . * . 7.000E-01 2.466E+01 . . . * . 8.000E-01 2.439E+01 . . . * . 9.000E-01 2.383E+01 . . . * . 1.000E+00 2.317E+01 . . . * . 1.100E+00 2.246E+01 . . . * . 1.200E+00 2.174E+01 . . . * . 1.300E+00 2.101E+01 . . .* . 1.400E+00 2.026E+01 . . * . 1.500E+00 1.951E+01 . . . . 1.600E+00 1.876E+01 . . . . 1.700E+00 1.800E+01 . . * . . 1.800E+00 1.724E+01 . . * . . 1.900E+00 1.648E+01 . . * . . 2.000E+00 1.572E+01 . . * . . 2.100E+00 1.495E+01 . . * . . 2.200E+00 1.418E+01 . . * . . 2.300E+00 1.342E+01 . . * . . 2.400E+00 1.265E+01 . . * . . 2.500E+00 1.188E+01 . . * . . 2.600E+00 1.110E+01 . . * . . 2.700E+00 1.033E+01 . * . . 2.800E+00 9.560E+00 . . . . 2.900E+00 8.787E+00 . . . . 3.000E+00 8.014E+00 . * . . . 3.100E+00 7.240E+00 . * . . . 3.200E+00 6.465E+00 . * . . . 3.300E+00 5.691E+00 . * . . . 3.400E+00 4.915E+00 . * . . . 3.500E+00 4.140E+00 . * . . . 3.600E+00 3.364E+00 . * . . . 3.700E+00 2.588E+00 . * . . . 3.800E+00 1.811E+00 . * . . . 3.900E+00 1.034E+00 .* . . . 4.000E+00 2.587E-01 * . . . 4.100E+00 9.744E-02 * . . . 4.200E+00 7.815E-02 * . . . 4.300E+00 6.806E-02 * . . . 4.400E+00 6.141E-02 * . . . 4.500E+00 5.657E-02 * . . . 4.600E+00 5.281E-02 * . . . 4.700E+00 4.981E-02 * . . . 4.800E+00 4.734E-02 * . . . 4.900E+00 4.525E-02 * . . . 5.000E+00 4.346E-02 * . . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ` Example common-source JFET amplifier circuit with self-bias Netlist: `common source jfet amplifier vin 1 0 sin(0 1 60 0 0) vdd 3 0 dc 20 rdrain 3 2 10k rsource 4 0 1k j1 2 1 4 mod1 .model mod1 njf .tran 1m 30m .plot tran v(2,0) v(1,0) .end ` Output: `legend: : v(2) +: v(1) time v(2) ()--------- 1.400E+01 1.600E+01 1.800E+01 2.000E+01 2.200E+01 (+)--------- -1.000E+00 -5.000E-01 0.000E+00 5.000E-01 1.000E+00 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.000E+00 1.708E+01 . . * + . . 1.000E-03 1.609E+01 . .* . + . . 2.000E-03 1.516E+01 . * . . . + . 3.000E-03 1.448E+01 . * . . . + . 4.000E-03 1.419E+01 .* . . . + 5.000E-03 1.432E+01 . * . . . +. 6.000E-03 1.490E+01 . * . . . + . 7.000E-03 1.577E+01 . * . . +. . 8.000E-03 1.676E+01 . . * . + . . 9.000E-03 1.768E+01 . . + . . . 1.000E-02 1.841E+01 . + . . . . 1.100E-02 1.890E+01 . + . . * . . 1.200E-02 1.912E+01 .+ . . * . . 1.300E-02 1.912E+01 .+ . . * . . 1.400E-02 1.890E+01 . + . . * . . 1.500E-02 1.842E+01 . + . . * . . 1.600E-02 1.768E+01 . . + . . . 1.700E-02 1.676E+01 . . . + . . 1.800E-02 1.577E+01 . * . . +. . 1.900E-02 1.491E+01 . * . . . + . 2.000E-02 1.432E+01 . * . . . +. 2.100E-02 1.419E+01 .* . . . + 2.200E-02 1.449E+01 . * . . . + . 2.300E-02 1.516E+01 . * . . . + . 2.400E-02 1.609E+01 . .* . + . . 2.500E-02 1.708E+01 . . * + . . 2.600E-02 1.796E+01 . . + * . . 2.700E-02 1.861E+01 . + . . * . . 2.800E-02 1.900E+01 . + . . * . . 2.900E-02 1.916E+01 + . . * . . 3.000E-02 1.908E+01 .+ . . * . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ` Example inverting op-amp circuit To simulate an ideal operational amplifier in SPICE, we use a voltage-dependent voltage source as a differential amplifier with extremely high gain. The “e” card sets up the dependent voltage source with four nodes, 3 and 0 for voltage output, and 1 and 0 for voltage input. No power supply is needed for the dependent voltage source, unlike a real operational amplifier. The voltage gain is set at 999,000 in this case. The input voltage source (V1) sweeps from 0 to 3.5 volts in 0.05 volt steps. Netlist: `Inverting opamp v1 2 0 dc e 3 0 0 1 999k r1 3 1 3.29k r2 1 2 1.18k .dc v1 0 3.5 0.05 .print dc v(3,0) .end ` Output: `v1 v(3) 0.000E+00 0.000E+00 5.000E-02 -1.394E-01 1.000E-01 -2.788E-01 1.500E-01 -4.182E-01 2.000E-01 -5.576E-01 2.500E-01 -6.970E-01 3.000E-01 -8.364E-01 3.500E-01 -9.758E-01 4.000E-01 -1.115E+00 4.500E-01 -1.255E+00 5.000E-01 -1.394E+00 5.500E-01 -1.533E+00 6.000E-01 -1.673E+00 6.500E-01 -1.812E+00 7.000E-01 -1.952E+00 7.500E-01 -2.091E+00 8.000E-01 -2.231E+00 8.500E-01 -2.370E+00 9.000E-01 -2.509E+00 9.500E-01 -2.649E+00 1.000E+00 -2.788E+00 1.050E+00 -2.928E+00 1.100E+00 -3.067E+00 1.150E+00 -3.206E+00 1.200E+00 -3.346E+00 1.250E+00 -3.485E+00 1.300E+00 -3.625E+00 1.350E+00 -3.764E+00 1.400E+00 -3.903E+00 1.450E+00 -4.043E+00 1.500E+00 -4.182E+00 1.550E+00 -4.322E+00 1.600E+00 -4.461E+00 1.650E+00 -4.600E+00 1.700E+00 -4.740E+00 1.750E+00 -4.879E+00 1.800E+00 -5.019E+00 1.850E+00 -5.158E+00 1.900E+00 -5.297E+00 1.950E+00 -5.437E+00 2.000E+00 -5.576E+00 2.050E+00 -5.716E+00 2.100E+00 -5.855E+00 2.150E+00 -5.994E+00 2.200E+00 -6.134E+00 2.250E+00 -6.273E+00 2.300E+00 -6.413E+00 2.350E+00 -6.552E+00 2.400E+00 -6.692E+00 2.450E+00 -6.831E+00 2.500E+00 -6.970E+00 2.550E+00 -7.110E+00 2.600E+00 -7.249E+00 2.650E+00 -7.389E+00 2.700E+00 -7.528E+00 2.750E+00 -7.667E+00 2.800E+00 -7.807E+00 2.850E+00 -7.946E+00 2.900E+00 -8.086E+00 2.950E+00 -8.225E+00 3.000E+00 -8.364E+00 3.050E+00 -8.504E+00 3.100E+00 -8.643E+00 3.150E+00 -8.783E+00 3.200E+00 -8.922E+00 3.250E+00 -9.061E+00 3.300E+00 -9.201E+00 3.350E+00 -9.340E+00 3.400E+00 -9.480E+00 3.450E+00 -9.619E+00 3.500E+00 -9.758E+00 ` Example noninverting op-amp circuit Another example of a SPICE quirk: since the dependent voltage source “e” isn’t considered a load to voltage source V1, SPICE interprets V1 to be open-circuited and will refuse to analyze it. The fix is to connect Rbogus in parallel with V1 to act as a DC load. Being directly connected across V1, the resistance of Rbogus is not crucial to the operation of the circuit, so 10 kΩ will work fine. I decided not to sweep the V1input voltage at all in this circuit for the sake of keeping the netlist and output listing simple. Netlist: `noninverting opamp v1 2 0 dc 5 rbogus 2 0 10k e 3 0 2 1 999k r1 3 1 20k r2 1 0 10k .end ` Output: `node voltage node voltage node voltage ( 1) 5.0000 ( 2) 5.0000 ( 3) 15.0000 ` Example instrumentation amplifier circuit Note the very high-resistance Rbogus1 and Rbogus2 resistors in the netlist (not shown in schematic for brevity) across each input voltage source, to keep SPICE from thinking V1 and V2 were open-circuited, just like the other op-amp circuit examples. Netlist: `Instrumentation amplifier v1 1 0 rbogus1 1 0 9e12 v2 4 0 dc 5 rbogus2 4 0 9e12 e1 3 0 1 2 999k e2 6 0 4 5 999k e3 9 0 8 7 999k rload 9 0 10k r1 2 3 10k rgain 2 5 10k r2 5 6 10k r3 3 7 10k r4 7 9 10k r5 6 8 10k r6 8 0 10k .dc v1 0 10 1 .print dc v(9) v(3,6) .end ` Output: `v1 v(9) v(3,6) 0.000E+00 1.500E+01 -1.500E+01 1.000E+00 1.200E+01 -1.200E+01 2.000E+00 9.000E+00 -9.000E+00 3.000E+00 6.000E+00 -6.000E+00 4.000E+00 3.000E+00 -3.000E+00 5.000E+00 9.955E-11 -9.956E-11 6.000E+00 -3.000E+00 3.000E+00 7.000E+00 -6.000E+00 6.000E+00 8.000E+00 -9.000E+00 9.000E+00 9.000E+00 -1.200E+01 1.200E+01 1.000E+01 -1.500E+01 1.500E+01 ` Example op-amp integrator circuit with sinewave input Netlist: `Integrator with sinewave input vin 1 0 sin (0 15 60 0 0) r1 1 2 10k c1 2 3 150u ic=0 e 3 0 0 2 999k .tran 1m 30m uic .plot tran v(1,0) v(3,0) .end ` Output: `legend: : v(1) +: v(3) time v(1) ()-------- -2.000E+01 -1.000E+01 0.000E+00 1.000E+01 (+)-------- -6.000E-02 -4.000E-02 -2.000E-02 0.000E+00 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.000E+00 6.536E-08 . . * + . 1.000E-03 5.516E+00 . . . * +. . 2.000E-03 1.021E+01 . . . + * . 3.000E-03 1.350E+01 . . . + . * . 4.000E-03 1.495E+01 . . + . . . 5.000E-03 1.418E+01 . . + . . . 6.000E-03 1.150E+01 . + . . . * . 7.000E-03 7.214E+00 . + . . * . . 8.000E-03 1.867E+00 .+ . . * . . 9.000E-03 -3.709E+00 . + . * . . . 1.000E-02 -8.805E+00 . + . * . . . 1.100E-02 -1.259E+01 . * + . . . 1.200E-02 -1.466E+01 . * . + . . . 1.300E-02 -1.471E+01 . * . +. . . 1.400E-02 -1.259E+01 . * . . + . . 1.500E-02 -8.774E+00 . . * . + . . 1.600E-02 -3.723E+00 . . * . +. . 1.700E-02 1.870E+00 . . . * + . 1.800E-02 7.188E+00 . . . * + . . 1.900E-02 1.154E+01 . . . + . * . 2.000E-02 1.418E+01 . . .+ . * . 2.100E-02 1.490E+01 . . + . . . 2.200E-02 1.355E+01 . . + . . . 2.300E-02 1.020E+01 . + . . * . 2.400E-02 5.496E+00 . + . . * . . 2.500E-02 -1.486E-03 .+ . * . . 2.600E-02 -5.489E+00 . + . * . . . 2.700E-02 -1.021E+01 . + * . . . 2.800E-02 -1.355E+01 . * . + . . . 2.900E-02 -1.488E+01 . * . + . . . 3.000E-02 -1.427E+01 . * . .+ . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ` Example op-amp integrator circuit with squarewave input Netlist: `Integrator with squarewave input vin 1 0 pulse (-1 1 0 0 0 10m 20m) r1 1 2 1k c1 2 3 150u ic=0 e 3 0 0 2 999k .tran 1m 50m uic .plot tran v(1,0) v(3,0) .end ` Output: <(1) +: v(3) time v(1) ()————-1.000E+00 -5.000E-01 0.000E+00 5.000E-01 1.000E+00 (+)————-1.000E-01 -5.000E-02 0.000E+00 5.000E-02 1.000E-01 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.000E+00 -1.000E+00 . + . . 1.000E-03 1.000E+00 . . + . * 2.000E-03 1.000E+00 . . + . . * 3.000E-03 1.000E+00 . . + . . * 4.000E-03 1.000E+00 . . + . . * 5.000E-03 1.000E+00 . . + . . * 6.000E-03 1.000E+00 . . + . . * 7.000E-03 1.000E+00 . . + . . * 8.000E-03 1.000E+00 . .+ . . * 9.000E-03 1.000E+00 . +. . . * 1.000E-02 1.000E+00 . + . . . * 1.100E-02 1.000E+00 . + . . . * 1.200E-02 -1.000E+00 * + . . . . 1.300E-02 -1.000E+00 * + . . . . 1.400E-02 -1.000E+00 * +. . . . 1.500E-02 -1.000E+00 * .+ . . . 1.600E-02 -1.000E+00 * . + . . . 1.700E-02 -1.000E+00 * . + . . . 1.800E-02 -1.000E+00 * . + . . . 1.900E-02 -1.000E+00 * . + . . . 2.000E-02 -1.000E+00 * . + . . . 2.100E-02 1.000E+00 . . + . . * 2.200E-02 1.000E+00 . . + . . * 2.300E-02 1.000E+00 . . + . . * 2.400E-02 1.000E+00 . . + . . * 2.500E-02 1.000E+00 . . + . . * 2.600E-02 1.000E+00 . .+ . . * 2.700E-02 1.000E+00 . +. . . * 2.800E-02 1.000E+00 . + . . . * 2.900E-02 1.000E+00 . + . . . * 3.000E-02 1.000E+00 . + . . . * 3.100E-02 1.000E+00 . + . . . * 3.200E-02 -1.000E+00 * + . . . . 3.300E-02 -1.000E+00 * + . . . . 3.400E-02 -1.000E+00 * + . . . . 3.500E-02 -1.000E+00 * + . . . . 3.600E-02 -1.000E+00 * +. . . . 3.700E-02 -1.000E+00 * .+ . . . 3.800E-02 -1.000E+00 * . + . . . 3.900E-02 -1.000E+00 * . + . . . 4.000E-02 -1.000E+00 * . + . . . 4.100E-02 1.000E+00 . . + . . * 4.200E-02 1.000E+00 . . + . . * 4.300E-02 1.000E+00 . . + . . * 4.400E-02 1.000E+00 . .+ . . * 4.500E-02 1.000E+00 . +. . . * 4.600E-02 1.000E+00 . + . . . * 4.700E-02 1.000E+00 . + . . . * 4.800E-02 1.000E+00 . + . . . * 4.900E-02 1.000E+00 . + . . . * 5.000E-02 1.000E+00 + . . . * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/08%3A_Troubleshooting_--_Theory_And_Practice/8.01%3A_Questions_to_Ask_Before_Proceeding.txt	princeton-nlp/TextbookChapters	• Has the system ever worked before? If yes, has anything happened to it since then that could cause the problem? • Has this system proven itself to be prone to certain types of failure? • How urgent is the need for repair? • What are the safety concerns, before I start troubleshooting? • What are the process quality concerns, before I start troubleshooting (what can I do without causing interruptions in production)? These preliminary questions are not trivial. Indeed, they are essential to expedient and safe troubleshooting. They are especially important when the system to be trouble-shot is large, dangerous, and/or expensive. Sometimes the troubleshooter will be required to work on a system that is still in full operation (perhaps the ultimate example of this is a doctor diagnosing a live patient). Once the cause or causes are determined to a high degree of certainty, there is the step of corrective action. Correcting a system fault without significantly interrupting the operation of the system can be very challenging, and it deserves thorough planning. When there is high risk involved in taking corrective action, such as is the case with performing surgery on a patient or making repairs to an operating process in a chemical plant, it is essential for the worker(s) to plan ahead for possible trouble. One question to ask before proceeding with repairs is, “how and at what point(s) can I abort the repairs if something goes wrong?” In risky situations, it is vital to have planned “escape routes” in your corrective action, just in case things do not go as planned. A surgeon operating on a patient knows if there are any “points of no return” in such a procedure, and stops to re-check the patient before proceeding past those points. He or she also knows how to “back out” of a surgical procedure at those points if needed. 8.02: General Troubleshooting Tips When first approaching a failed or otherwise misbehaving system, the new troubleshooter often doesn’t know where to begin. The following strategies are not exhaustive by any means, but provide the troubleshooter with a simple checklist of questions to ask in order to start isolating the problem. As for tips, these troubleshooting suggestions are not comprehensive procedures: they serve as starting points only for the troubleshooting process. An essential part of expedient troubleshooting is probability assessment, and these tips help the troubleshooter determine which possible points of failure are more or less likely than others. Final isolation of the system failure is usually determined through more specific techniques (outlined in the next section—Specific Troubleshooting Techniques). Prior occurrence If this device or process has been historically known to fail in a certain particular way, and the conditions leading to this common failure have not changed, check for this “way” first. A corollary to this troubleshooting tip is the directive to keep detailed records of failure. Ideally, a computer-based failure log is optimal, so that failures may be referenced by and correlated to a number of factors such as time, date, and environmental conditions. Example: The car’s engine is overheating. The last two times this happened, the cause was low coolant level in the radiator. What to do: Check the coolant level first. Of course, past history by no means guarantees the present symptoms are caused by the same problem, but since this is more likely, it makes sense to check this first. If, however, the cause of routine failure in a system has been corrected (i.e. the leak causing low coolant level in the past has been repaired), then this may not be a probable cause of trouble this time. Recent alterations If a system has been having problems immediately after some kind of maintenance or other change, the problems might be linked to those changes. Example: The mechanic recently tuned my car’s engine, and now I hear a rattling noise that I didn’t hear before I took the car in for repair. What to do: Check for something that may have been left loose by the mechanic after his or her tune-up work. Function vs. non-function If a system isn’t producing the desired end result, look for what it is doing correctly; in other words, identify where the problem is not, and focus your efforts elsewhere. Whatever components or subsystems necessary for the properly working parts to function are probably okay. The degree of fault can often tell you what part of it is to blame. Example: The radio works fine on the AM band, but not on the FM band. What to do: Eliminate from the list of possible causes, anything in the radio necessary for the AM band’s function. Whatever the source of the problem is, it is specific to the FM band and not to the AM band. This eliminates the audio amplifier, speakers, fuse, power supply, and almost all external wiring. Being able to eliminate sections of the system as possible failures reduces the scope of the problem and makes the rest of the troubleshooting procedure more efficient. Hypothesize Based on your knowledge of how a system works, think of various kinds of failures that would cause this problem (or these phenomena) to occur, and check for those failures (starting with the most likely based on circumstances, history, or knowledge of component weaknesses). Example: The car’s engine is overheating. What to do: Consider possible causes for overheating, based on what you know of engine operation. Either the engine is generating too much heat, or not getting rid of the heat well enough (most likely the latter). Brainstorm some possible causes: a loose fan belt, clogged radiator, bad water pump, low coolant level, etc. Investigate each one of those possibilities before investigating alternatives.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/08%3A_Troubleshooting_--_Theory_And_Practice/8.03%3A_Specific_Troubleshooting_Techniques.txt	princeton-nlp/TextbookChapters	After applying some of the general troubleshooting tips to narrow the scope of a problem’s location, there are techniques useful in further isolating it. Here are a few: Swap identical components In a system with identical or parallel subsystems, swap components between those subsystems and see whether or not the problem moves with the swapped component. If it does, you’ve just swapped the faulty component; if it doesn’t, keep searching! This is a powerful troubleshooting method, because it gives you both a positive and a negative indication of the swapped component’s fault: when the bad part is exchanged between identical systems, the formerly broken subsystem will start working again and the formerly good subsystem will fail. I was once able to troubleshoot an elusive problem with an automotive engine ignition system using this method: I happened to have a friend with an automobile sharing the exact same model of ignition system. We swapped parts between the engines (distributor, spark plug wires, ignition coil—one at a time) until the problem moved to the other vehicle. The problem happened to be a “weak” ignition coil, and it only manifested itself under heavy load (a condition that could not be simulated in my garage). Normally, this type of problem could only be pinpointed using an ignition system analyzer (or oscilloscope) and a dynamometer to simulate loaded driving conditions. This technique, however, confirmed the source of the problem with 100% accuracy, using no diagnostic equipment whatsoever. Occasionally you may swap a component and find that the problem still exists, but has changed in some way. This tells you that the components you just swapped are somehow different (different calibration, different function), and nothing more. However, don’t dismiss this information just because it doesn’t lead you straight to the problem—look for other changes in the system as a whole as a result of the swap, and try to figure out what these changes tell you about the source of the problem. An important caveat to this technique is the possibility of causing further damage. Suppose a component has failed because of another, less conspicuous failure in the system. Swapping the failed component with a good component will cause the good component to fail as well. For example, suppose that a circuit develops a short, which “blows” the protective fuse for that circuit. The blown fuse is not evident by inspection, and you don’t have a meter to electrically test the fuse, so you decide to swap the suspect fuse with one of the same rating from a working circuit. As a result of this, the good fuse that you move to the shorted circuit blows as well, leaving you with two blown fuses and two non-working circuits. At least you know for certain that the original fuse was blown, because the circuit it was moved to stopped working after the swap, but this knowledge was gained only through the loss of a good fuse and the additional “down time” of the second circuit. Another example to illustrate this caveat is the ignition system problem previously mentioned. Suppose that the “weak” ignition coil had caused the engine to backfire, damaging the muffler. If swapping ignition system components with another vehicle causes the problem to move to the other vehicle, damage may be done to the other vehicle’s muffler as well. As a general rule, the technique of swapping identical components should be used only when there is minimal chance of causing additional damage. It is an excellent technique for isolating non-destructive problems. Example 1: You’re working on a CNC machine tool with X, Y, and Z-axis drives. The Y axis is not working, but the X and Z axes are working. All three axes share identical components (feedback encoders, servo motor drives, servo motors). What to do: Exchange these identical components, one at a time, Y axis and either one of the working axes (X or Z), and see after each swap whether or not the problem has moved with the swap. Example 2: A stereo system produces no sound on the left speaker, but the right speaker works just fine. What to do: Try swapping respective components between the two channels and see if the problem changes sides, from left to right. When it does, you’ve found the defective component. For instance, you could swap the speakers between channels: if the problem moves to the other side (i.e. the same speaker that was dead before is still dead, now that its connected to the right channel cable) then you know that speaker is bad. If the problem stays on the same side (i.e. the speaker formerly silent is now producing sound after having been moved to the other side of the room and connected to the other cable), then you know the speakers are fine, and the problem must lie somewhere else (perhaps in the cable connecting the silent speaker to the amplifier, or in the amplifier itself). If the speakers have been verified as good, then you could check the cables using the same method. Swap the cables so that each one now connects to the other channel of the amplifier and to the other speaker. Again, if the problem changes sides (i.e. now the right speaker is now “dead” and the left speaker now produces sound), then the cable now connected to the right speaker must be defective. If neither swap (the speakers nor the cables) causes the problem to change sides from left to right, then the problem must lie within the amplifier (i.e. the left channel output must be “dead”). Remove parallel components If a system is composed of several parallel or redundant components which can be removed without crippling the whole system, start removing these components (one at a time) and see if things start to work again. Example 1: A “star” topology communications network between several computers has failed. None of the computers are able to communicate with each other. What to do: Try unplugging the computers, one at a time from the network, and see if the network starts working again after one of them is unplugged. If it does, then that last unplugged computer may be the one at fault (it may have been “jamming” the network by constantly outputting data or noise). Example 2: A household fuse keeps blowing (or the breaker keeps tripping open) after a short amount of time. What to do: Unplug appliances from that circuit until the fuse or breaker quits interrupting the circuit. If you can eliminate the problem by unplugging a single appliance, then that appliance might be defective. If you find that unplugging almost any appliance solves the problem, then the circuit may simply be overloaded by too many appliances, neither of them defective. Divide system into sections and test those sections In a system with multiple sections or stages, carefully measure the variables going in and out of each stage until you find a stage where things don’t look right. Example 1: A radio is not working (producing no sound at the speaker)) What to do: Divide the circuitry into stages: tuning stage, mixing stages, amplifier stage, all the way through to the speaker(s). Measure signals at test points between these stages and tell whether or not a stage is working properly. Example 2: An analog summer circuit is not functioning properly. What to do: I would test the passive averager network (the three resistors at the lower-left corner of the schematic) to see that the proper (averaged) voltage was seen at the noninverting input of the op-amp. I would then measure the voltage at the inverting input to see if it was the same as at the noninverting input (or, alternatively, measure the voltage difference between the two inputs of the op-amp, as it should be zero). Continue testing sections of the circuit (or just test points within the circuit) to see if you measure the expected voltages and currents. Simplify and rebuild Closely related to the strategy of dividing a system into sections, this is actually a design and fabrication technique useful for new circuits, machines, or systems. It’s always easier begin the design and construction process in little steps, leading to larger and larger steps, rather than to build the whole thing at once and try to troubleshoot it as a whole. Suppose that someone were building a custom automobile. He or she would be foolish to bolt all the parts together without checking and testing components and subsystems as they went along, expecting everything to work perfectly after its all assembled. Ideally, the builder would check the proper operation of components along the way through the construction process: start and tune the engine before its connected to the drivetrain, check for wiring problems before all the cover panels are put in place, check the brake system in the driveway before taking it out on the road, etc. Countless times I’ve witnessed students build a complex experimental circuit and have trouble getting it to work because they didn’t stop to check things along the way: test all resistors before plugging them into place, make sure the power supply is regulating voltage adequately before trying to power anything with it, etc. It is human nature to rush to completion of a project, thinking that such checks are a waste of valuable time. However, more time will be wasted in troubleshooting a malfunctioning circuit than would be spent checking the operation of subsystems throughout the process of construction. Take the example of the analog summer circuit in the previous section for example: what if it wasn’t working properly? How would you simplify it and test it in stages? Well, you could reconnect the op-amp as a basic comparator and see if its responsive to differential input voltages, and/or connect it as a voltage follower (buffer) and see if it outputs the same analog voltage as what is input. If it doesn’t perform these simple functions, it will never perform its function in the summer circuit! By stripping away the complexity of the summer circuit, paring it down to an (almost) bare op-amp, you can test that component’s functionality and then build from there (add resistor feedback and check for voltage amplification, then add input resistors and check for voltage summing), checking for expected results along the way. Trap a signal Set up instrumentation (such as a datalogger, chart recorder, or multimeter set on “record” mode) to monitor a signal over a period of time. This is especially helpful when tracking down intermittent problems, which have a way of showing up the moment you’ve turned your back and walked away. This may be essential for proving what happens first in a fast-acting system. Many fast systems (especially shutdown “trip” systems) have a “first out” monitoring capability to provide this kind of data. Example #1: A turbine control system shuts automatically in response to an abnormal condition. By the time a technician arrives at the scene to survey the turbine’s condition, however, everything is in a “down” state and its impossible to tell what signal or condition was responsible for the initial shutdown, as all operating parameters are now “abnormal.” What to do: One technician I knew used a video camera to record the turbine control panel, so he could see what happened (by indications on the gauges) first in an automatic-shutdown event. Simply by looking at the panel after the fact, there was no way to tell which signal shut the turbine down, but the videotape playback would show what happened in sequence, down to a frame-by-frame time resolution. Example #2: An alarm system is falsely triggering, and you suspect it may be due to a specific wire connection going bad. Unfortunately, the problem never manifests itself while you’re watching it! What to do: Many modern digital multimeters are equipped with “record” settings, whereby they can monitor a voltage, current, or resistance over time and note whether that measurement deviates substantially from a regular value. This is an invaluable tool for use in “intermittent” electronic system failures.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/08%3A_Troubleshooting_--_Theory_And_Practice/8.04%3A_Likely_Failures_in_Proven_Systems.txt	princeton-nlp/TextbookChapters	The following problems are arranged in order from most likely to least likely, top to bottom. This order has been determined largely from personal experience troubleshooting electrical and electronic problems in automotive, industrial, and home applications. This order also assumes a circuit or system that has been proven to function as designed and has failed after substantial operation time. Problems experienced in newly assembled circuits and systems do not necessarily exhibit the same probabilities of occurrence. Operator error A frequent cause of system failure is error on the part of those human beings operating it. This cause of trouble is placed at the top of the list, but of course, the actual likelihood depends largely on the particular individuals responsible for operation. When operator error is the cause of a failure, it is unlikely that it will be admitted prior to investigation. I do not mean to suggest that operators are incompetent and irresponsible—quite the contrary: these people are often your best teachers for learning system function and obtaining a history of failure—but the reality of human error cannot be overlooked. A positive attitude coupled with good interpersonal skills on the part of the troubleshooter goes a long way in troubleshooting when human error is the root cause of failure. Bad wire connections As incredible as this may sound to the new student of electronics, a high percentage of electrical and electronic system problems are caused by a very simple source of trouble: poor (i.e. open or shorted) wire connections. This is especially true when the environment is hostile, including such factors as high vibration and/or a corrosive atmosphere. Connection points found in any variety of plug-and-socket connector, terminal strip, or splice are at the greatest risk for failure. The category of “connections” also includes mechanical switch contacts, which can be thought of as a high-cycle connector. Improper wire termination lugs (such as a compression-style connector crimped on the end of a solid wire—a definite faux pas) can cause high-resistance connections after a period of trouble-free service. It should be noted that connections in low-voltage systems tend to be far more troublesome than connections in high-voltage systems. The main reason for this is the effect of arcing across a discontinuity (circuit break) in higher-voltage systems tends to blast away insulating layers of dirt and corrosion, and may even weld the two ends together if sustained long enough. Low-voltage systems tend not to generate such vigorous arcing across the gap of a circuit break, and also tend to be more sensitive to additional resistance in the circuit. Mechanical switch contacts used in low-voltage systems benefit from having the recommended minimum wetting current conducted through them to promote a healthy amount of arcing upon opening, even if this level of current is not necessary for the operation of other circuit components. Although open failures tend to more common than shorted failures, “shorts” still constitute a substantial percentage of wiring failure modes. Many shorts are caused by degradation of wire insulation. This, again, is especially true when the environment is hostile, including such factors as high vibration, high heat, high humidity, or high voltage. It is rare to find a mechanical switch contact that is failed shorted, except in the case of high-current contacts where contact “welding” may occur in over current conditions. Shorts may also be caused by conductive build up across terminal strip sections or the backs of printed circuit boards. A common case of shorted wiring is the ground fault, where a conductor accidentally makes contact with either earth or chassis ground. This may change the voltage(s) present between other conductors in the circuit and ground, thereby causing bizarre system malfunctions and/or personnel hazard. Power supply problems These generally consist of tripped overcurrent protection devices or damage due to overheating. Although power supply circuitry is usually less complex than the circuitry being powered and therefore should figure to be less prone to failure on that basis alone, it generally handles more power than any other portion of the system and therefore must deal with greater voltages and/or currents. Also, because of its relative design simplicity, a system’s power supply may not receive the engineering attention it deserves, most of the engineering focus devoted to more glamorous parts of the system. Active components Active components (amplification devices) tend to fail with greater regularity than passive (non-amplifying) devices, due to their greater complexity and tendency to amplify overvoltage/overcurrent conditions. Semiconductor devices are notoriously prone to failure due to electrical transient (voltage/current surge) overloading and thermal (heat) overloading. Electron tube devices are far more resistant to both of these failure modes but are generally more prone to mechanical failures due to their fragile construction. Passive components Non-amplifying components are the most rugged of all, their relative simplicity granting them a statistical advantage over active devices. The following list gives an approximate relation of failure probabilities (again, top being the most likely and bottom being the least likely): • Capacitors (shorted), especially electrolytic capacitors. The paste electrolyte tends to lose moisture with age, leading to failure. Thin dielectric layers may be punctured by overvoltage transients. • Diodes open (rectifying diodes) or shorted (Zener diodes). • Inductor and transformer windings open or shorted to conductive core. Failures related to overheating (insulation breakdown) are easily detected by smell. • Resistors open, almost never shorted. Usually, this is due to overcurrent heating, although it is less frequently caused by overvoltage transient (arc-over) or physical damage (vibration or impact). Resistors may also change resistance value if overheated!
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/08%3A_Troubleshooting_--_Theory_And_Practice/8.05%3A_Likely_Failures_in_Unproven_Systems.txt	princeton-nlp/TextbookChapters	“All men are liable to error;” —John Locke Whereas the last section deals with component failures in systems that have been successfully operating for some time, this section concentrates on the problems plaguing brand-new systems. In this case, failure modes are generally not of the aging kind but are related to mistakes in design and assembly caused by human beings. Wiring problems In this case, bad connections are usually due to assembly error, such as connection to the wrong point or poor connector fabrication. Shorted failures are also seen, but usually, involve misconnections (conductors inadvertently attached to grounding points) or wires pinched under box covers. Another wiring-related problem seen in new systems is that of electrostatic or electromagnetic interference between different circuits by way of close wiring proximity. This kind of problem is easily created by routing sets of wires too close to each other (especially routing signal cables close to power conductors) and tends to be very difficult to identify and locate with test equipment. Power supply problems Blown fuses and tripped circuit breakers are likely sources of trouble, especially if the project in question is an addition to an already-functioning system. Loads may be larger than expected, resulting in overloading and subsequent failure of power supplies. Defective components In the case of a newly-assembled system, component fault probabilities are not as predictable as in the case of an operating system that fails with age. Any type of component—active or passive—may be found defective or of imprecise value “out of the box” with roughly equal probability, barring any specific sensitivities in shipping (i.e fragile vacuum tubes or electrostatically sensitive semiconductor components). Moreover, these types of failures are not always as easy to identify by sight or smell as an age- or transient-induced failure. Improper system configuration Increasingly seen in large systems using microprocessor-based components, “programming” issues can still plague non-microprocessor systems in the form of incorrect time-delay relay settings, limit switch calibrations, and drum switch sequences. Complex components having configuration “jumpers” or switches to control behavior may not be “programmed” properly. Components may be used in a new system outside of their tolerable ranges. Resistors, for example, with too low of power ratings, of too great of tolerance, may have been installed. Sensors, instruments, and controlling mechanisms may be uncalibrated, or calibrated to the wrong ranges. Design error Perhaps the most difficult to pinpoint and the slowest to be recognized (especially by the chief designer) is the problem of design error, where the system fails to function simply because it cannot function as designed. This may be as trivial as the designer specifying the wrong components in a system, or as fundamental as a system not working due to the designer’s improper knowledge of physics. I once saw a turbine control system installed that used a low-pressure switch on the lubrication oil tubing to shut down the turbine if oil pressure dropped to an insufficient level. The oil pressure for lubrication was supplied by an oil pump turned by the turbine. When installed, the turbine refused to start. Why? Because when it was stopped, the oil pump was not turning, thus there was no oil pressure to lubricate the turbine. The low-oil-pressure switch detected this condition and the control system maintained the turbine in shutdown mode, preventing it from starting. This is a classic example of a design flaw, and it could only be corrected by a change in the system logic. While most design flaws manifest themselves early in the operational life of the system, some remain hidden until just the right conditions exist to trigger the fault. These types of flaws are the most difficult to uncover, as the troubleshooter usually overlooks the possibility of design error due to the fact that the system is assumed to be “proven.” The example of the turbine lubrication system was a design flaw impossible to ignore on start-up. An example of a “hidden” design flaw might be a faulty emergency coolant system for a machine, designed to remain inactive until certain abnormal conditions are reached—conditions which might never be experienced in the life of the system.
textbooks/workforce/Electronics_Technology/Book%3A_Electric_Circuits_V_-_References_(Kuphaldt)/08%3A_Troubleshooting_--_Theory_And_Practice/8.06%3A_Potential_Pitfalls.txt	princeton-nlp/TextbookChapters	Fallacious reasoning and poor interpersonal relations account for more failed or belabored troubleshooting efforts than any other impediments. With this in mind, the aspiring troubleshooter needs to be familiar with a few common troubleshooting mistakes. Trusting that a brand-new component will always be good. While it is generally true that a new component will be in good condition, it is not always true. It is also possible that a component has been mislabeled and may have the wrong value (usually this mislabeling is a mistake made at the point of distribution or warehousing and not at the manufacturer, but again, not always!). Not periodically checking your test equipment. This is especially true with battery-powered meters, as weak batteries may give spurious readings. When using meters to safety-check for dangerous voltage, remember to test the meter on a known source of voltage both before and after checking the circuit to be serviced, to make sure the meter is in proper operating condition. Assuming there is only one failure to account for the problem. Single-failure system problems are ideal for troubleshooting, but sometimes failures come in multiple numbers. In some instances, the failure of one component may lead to a system condition that damages other components. Sometimes a component in marginal condition goes undetected for a long time, then when another component fails the system suffers from problems with both components. Mistaking coincidence for causality. Just because two events occurred at nearly the same time does not necessarily mean one event caused the other! They may be both consequences of a common cause, or they may be totally unrelated! If possible, try to duplicate the same condition suspected to be the cause and see if the event suspected to be the coincidence happens again. If not, then there is either no causal relationship as assumed. This may mean there is no causal relationship between the two events whatsoever, or that there is a causal relationship, but just not the one you expected. Self-induced blindness. After a long effort at troubleshooting a difficult problem, you may become tired and begin to overlook crucial clues to the problem. Take a break and let someone else look at it for a while. You will be amazed at what a difference this can make. On the other hand, it is generally a bad idea to solicit help at the start of the troubleshooting process. Effective troubleshooting involves complex, multi-level thinking, which is not easily communicated with others. More often than not, “team troubleshooting” takes more time and causes more frustration than doing it yourself. An exception to this rule is when the knowledge of the troubleshooters is complementary: for example, a technician who knows electronics but not machine operation teamed with an operator who knows machine function but not electronics. Failing to question the troubleshooting work of others on the same job. This may sound rather cynical and misanthropic, but it is sound scientific practice. Because it is easy to overlook important details, troubleshooting data received from another troubleshooter should be personally verified before proceeding. This is a common situation when troubleshooters “change shifts” and a technician takes over for another technician who is leaving before the job is done. It is important to exchange information, but do not assume the prior technician checked everything they said they did or checked it perfectly. I’ve been hindered in my troubleshooting efforts on many occasions by failing to verify what someone else told me they checked. Being pressured to “hurry up.” When an important system fails, there will be pressure from other people to fix the problem as quickly as possible. As they say in business, “time is money.” Having been on the receiving end of this pressure many times, I can understand the need for expedience. However, in many cases, there is a higher priority: caution. If the system in question harbors great danger to life and limb, the pressure to “hurry up” may result in injury or death. At the very least, hasty repairs may result in further damage when the system is restarted. Most failures can be recovered or at least temporarily repaired in short time if approached intelligently. Improper “fixes” resulting in haste often lead to damage that cannot be recovered in short time, if ever. If the potential for greater harm is present, the troubleshooter needs to politely address the pressure received from others, and maintain their perspective in the midst of chaos. Interpersonal skills are just as important in this realm as technical ability! Finger-pointing. It is all too easy to blame a problem on someone else, for reasons of ignorance, pride, laziness, or some other unfortunate facet of human nature. When the responsibility for system maintenance is divided into departments or work crews, troubleshooting efforts are often hindered by blame cast between groups. “It’s a mechanical problem . . . it’s an electrical problem . . . it’s an instrument problem . . .” ad infinitum, ad nauseum, is all too common in the workplace. I have found that a positive attitude does more to quench the fires of the blame than anything else. On one particular job, I was summoned to fix a problem in a hydraulic system assumed to be related to the electronic metering and controls. My troubleshooting isolated the source of trouble to a faulty control valve, which was the domain of the millwright (mechanical) crew. I knew that the millwright on shift was a contentious person, so I expected trouble if I simply passed the problem on to his department. Instead, I politely explained to him and his supervisor the nature of the problem as well as a brief synopsis of my reasoning, then proceeded to help him replace the faulty valve, even though it wasn’t “my” responsibility to do so. As a result, the problem was fixed very quickly, and I gained the respect of the millwright. 9.01: Wires and Connections Older electrical schematics showed connecting wires crossing, while non-connecting wires “jumped” over each other with little half-circle marks. Newer electrical schematics show connecting wires joining with a dot, while non-connecting wires cross with no dot. However, some people still use the older convention of connecting wires crossing with no dot, which may create confusion. For this reason, I opt to use a hybrid convention, with connecting wires unambiguously connected by a dot, and non-connecting wires unambiguously “jumping” over one another with a half-circle mark. While this may be frowned upon by some, it leaves no room for interpretational error: in each case, the intent is clear and unmistakable: 9.08: Switches Process Actuated It is very important to keep in mind that the “normal” contact status of a process-actuated switch refers to its status when the process is absent and/or inactive, not “normal” in the sense of process conditions as expected during routine operation. For instance, a normally-closed low-flow detection switch installed on a coolant pipe will be maintained in the actuated state (open) when there is regular coolant flow through the pipe. If the coolant flow stops, the flow switch will go to its “normal” (un-actuated) status of closed. A limit switch is one actuated by contact with a moving machine part. An electronic limit switch senses mechanical motion but does so using light, magnetic fields, or other non-contact means. 10.01: Table (landscape view) Periodic table of chemical elements. 10.02: Table (portrait view) Periodic table of chemical elements.
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/01%3A_Basic_Principles_of_Electricity/01%3A_Fundamentals_of_Electricity/1.01%3A_Basic_principles.txt	princeton-nlp/TextbookChapters	Over the centuries scientists have discovered that electricity is predictable and measurable. Being familiar with the fundamentals of electricity will help you to understand how and why electrical circuits work. 01: Fundamentals of Electricity Learning Task 1 Explain fundamentals of electricity Over the centuries scientists have discovered that electricity is predictable and measurable. Being familiar with the fundamentals of electricity will help you to understand how and why electrical circuits work. Basic principles Electricity is a form of energy. To understand electricity, it is important that you first understand the structure of matter. Anything that occupies space and has weight is called matter. All liquids, gases, and solids are examples of matter in different forms. Matter is made of smaller units called atoms. Atoms can be grouped together in compounds to form molecules. Atomic theory Atoms are the most basic part of matter and differ in atomic structure from each other. The structure of the atom can be described in much the same way as the solar system. Instead of the Sun at the centre, there is a nucleus. This nucleus is made of two basic particles: protons and neutrons. Neutrons make up the mass (or weight equivalency) of the atom, have no electrical charge, and are considered to be neutral. Protons are particles that have a positive (+) electrical charge and cannot be separated from the nucleus. Surrounding the nucleus in orbits are electrons. These are tiny particles with a negative (–) electrical charge. Figure 1 shows a model of a carbon atom. 1. Carbon atom 2. Hydrogen and copper atoms 3. Electrical attraction 4. Transmission of impulse Sources of electrical force You have just learned that if there is a surplus of electrons at one end of a conductor and a deficiency at the other end, a current flows in the conductor. There are devices that create this difference in charge so that a current will flow. These devices are referred to as sources of electromotive force. These sources include: • chemical • electromagnetic induction • friction • heat • pressure • light Chemical A battery is a source of electrical force due to the chemical reaction that takes place between plates and an electrolyte. This reaction causes a buildup of positive ions on one plate and negative ions on the other plate. This electrical difference between the plates is also known as potential difference. Electromagnetic induction Electric force can be generated by using a magnetic field. This is the method by which most of the electrical energy we use is produced. An example is an alternator or generator. Friction Friction can cause free electrons to move from one body to another and be stored there temporarily. When you walk across a carpet, electrons are transferred to the atoms in your body and you return them to other atoms when you touch a metallic object. Heat If two unlike metals are placed together and heated, they will produce electrical force. An example is the thermocouple in a furnace. Pressure Certain crystals will produce electricity if they are squeezed under extreme pressure. An example is a barbecue starter (also called piezoelectric generator). Light Some crystals and semiconductors will produce electrical force when they are exposed to light. An example is the photocell in a calculator. All six of these sources of EMF achieve the same thing. They separate charge by: • imparting energy to the electrons • pushing them against an electrostatic field • causing a surplus of electrons (negative charge) at one terminal of the source and a deficiency of electrons (positive charge) at the other terminal In a sense, the process can be likened to compressing a spring. The energy stored in the compressed spring can be used later to do useful work. The same is true of the separated charges: they store energy that can be used to do useful work. Electrical energy always comes from some other form of energy. The source of EMF is simply the device that makes the conversion from some other form of energy to electrical energy.
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/01%3A_Basic_Principles_of_Electricity/01%3A_Fundamentals_of_Electricity/1.02%3A_Electrical_circuits_and_units_of_me.txt	princeton-nlp/TextbookChapters	Electrical circuits and units of measurement The term circuit refers to a circular journey or loop. In the case of an electrical circuit, it is the closed path or loop travelled by the electrons. The movement or flow of electrons (current) is predictable and measurable, depending on a number of variables within the circuit. Polarity Electrical polarity (positive and negative) is present in every electrical circuit. Electrons flow from the negative pole to the positive pole. In a direct current (DC) circuit, one pole is always negative, the other pole is always positive, and the electrons flow in one direction only. In an alternating current (AC) circuit, the two poles alternate between negative and positive, and the direction of the electron flow reverses. Circuit components A closed circuit provides a complete path for the flow of electrons through conductors. Included in this circuit there must be a resistance (or load), which will do the work and some form of control. For a circuit to be operational it must contain some basic components (Figure 5). These include: • power source • conductors • controls • load • protection Power source In equipment, the power source is the battery when the engine is off and the generator when the engine is running. In most buildings, it is the power supplied by the local service provider. Conductors Conductors are wires or cables wrapped in insulation that carry the current in the circuit. A common ground circuit conductor could be the frame or body of the equipment or the frame on a vehicle. Controls Switches are used to turn the current on and off or to regulate the flow of electricity. Switches can be operated mechanically by vacuum, pressure, or electricity. Load The load converts electrical energy to work, such as with electric motors, bulbs, heater coils, or horns. Protection Fuses, circuit breakers, or fusible links must be used to prevent damage to the source, load, and conductors. 1. Basic circuit 2. Ohm’s law circuit aid 3. Power circuit aid Try to solve the following questions for power, using Ohm’s law calculations. 1. How many amps will flow through a 96 W headlight bulb in a 12 V system? The formula is I = P ÷ E. Therefore I = 96 W ÷ 12 V. The result is I = 8 A. This could be an important consideration in selecting the correct circuit protection device. A fuse with a rating of more than 8 A would have to be chosen in this situation. 2. How much power will a soldering gun produce if it uses 6 A in a 120 V electrical system? The formula is P = E × I. Therefore P = 120 V × 6 A. The result is P = 720 W. Soldering guns are rated in watts. The higher the wattage rating of the gun, the more heat it will produce. Now complete the Learning Task Self-Test. 1.E: Self-Test 1 Self-Test 1 1. What are the tiny particles that matter is made of called? 1. Compounds 2. Atoms 3. Ions 4. Protons and neutrons 2. What are elements called that have atoms with electrons that are easily freed? 1. Ions 2. Conductors 3. Insulators 4. Elements 3. Which of the following best describes copper? 1. Conductor 2. Insulator 3. Semiconductor 4. Valence electron 4. Why are insulators useful? 1. They transport an electrical charge. 2. They do not transport an electrical charge. 3. They readily release valence electrons. 4. They will ionize easily when subjected to voltage. 5. In what units is current measured? 1. Volts 2. Amperes 3. Ohms 4. EMF 6. A source of electromotive force can be from a chemical reaction. 1. True 2. False 1. In a DC circuit the poles alternate from positive to negative. 1. True 2. False 2. What is the device called that is used to turn a circuit on and off? 1. A control 2. A conductor 3. A load 4. A protector 3. Which of the following best describes an electric motor? 1. A control 2. A load 3. A fuse 4. A conductor Use Ohm’s law for the following questions. E = I × R, where: • Volts (V) is represented by “E” for electromotive force. • Amperes (A) is represented by “I” for intensity of current. • Ohms (Ω) is represented by “R” for resistance. 1. If resistance in a circuit is 6 Ω and the pressure is 24 V, what is the current flow? 1. 2 A 2. 4 A 3. 6 A 4. 8 A 2. If a circuit had a current flow of 8 A and the resistance is 20 Ω, what is the pressure in volts? 1. 120 V 2. 160 V 3. 2.5 V 4. 25 V 1. If a circuit has a current flow of 5 A and a pressure of 120 V, what is the resistance? 1. 24 Ω 2. 12 Ω 3. 6 Ω 4. 3 Ω Use the power formula for the following questions. watts = volts × amps or P = E × I 1. How much power will a heater produce if it uses 15 A in a 120 V electrical system? 1. 1800 W 2. 1500 W 3. 900 W 4. 1200 W 2. How many amps will flow through a 60 W headlight bulb in a 24 V system? 1. 6 A 2. 2.5 A 3. 25 A 4. 8 A 3. Use Ohm’s law to complete the following chart. voltage current resistance 500 mA 240 12 1000 12 8 A 5 20 000 120 10 0.15 A 80 3 0.0002 A 4. Use the power formula to complete the following chart. power voltage current 1500 W 12.5 A 40 W 12 V 12 V 300 mA 200 W 10 A 96 W 12 V 12 V 40 A
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/01%3A_Basic_Principles_of_Electricity/02%3A_Basic_Circuit_Concepts/2.01%3A_Basic_Electrical_Circuits.txt	princeton-nlp/TextbookChapters	Learning Task 2 Describe basic circuit concepts You must understand how basic circuits function to properly diagnose and repair electrical problems. Now that you understand a simple circuit and how the basic components are connected, you can assemble more complex circuits and observe their characteristics. Basic electrical circuits A circuit must provide a complete path for current flow from the power source. The current must flow through a control device into an electrical load and back to the power source through a wire or through a vehicle chassis. In equipment, wire is normally used only on the insulated side of the circuit, since the return circuit is the chassis. Some components may require a ground wire from the component to the frame This type of circuit is called the single wire system (Figure 1). 1. Single wire circuit 2. Two wire circuit There are three types of basic electrical circuits: • series circuits • parallel circuits • series-parallel (combination) circuits 2.02: Series Circuits Series circuits The electrical term in series refers to a circuit in which two or more components are connected one after another in order that the current can only flow through one path. The switch that controls the circuit is always in series with the loads. If more than one switch is used, both must be closed for the circuit to function. Circuit protectors (such as fuses) will also be in series. If any one of the components in a series circuit opens, the circuit will not function (Figure 3). 1. Series circuit 2. Series circuit Perform the following calculations: 1. Total resistance or RT will equal the sum of the individual resistances. RT = R1 + R2 + R3 RT = 2 Ω + 4 Ω + 6 Ω RT = 12 Ω 2. Now apply Ohm’s law and calculate the current flow in the circuit. I = E ÷ R I = 12 V ÷ 12 Ω I = 1 A 3. Current flow is the same throughout the circuit. By using Ohm’s law you can determine how much voltage will be used by each of the loads. The 2 ohm resistor will require: E = I × R E = 1 A × 2 Ω E = 2 V The 4 ohm resistor will require: E = I × R E = 1 A × 4 Ω E = 4 V The 6 ohm resistor will require: E = I × R E = 1 A × 6 Ω E = 6 V Add the individual voltages together and you will notice that they equal the original source voltage of 12 V. ET = 2 V + 4 V + 6 V ET = 12 V The voltage that is used up in the circuit by the load is called voltage drop. This voltage drop is valuable in diagnosis as a measure of the resistance of a circuit. Some voltage may be lost in a circuit because of poor connections. If the voltage drop in connections (caused by high resistance) becomes too great, the load may not function properly or may not even work. 2.03: Parallel Circuits The parallel circuit (Figure $1$) has completely different characteristics. In a parallel circuit, two or more loads are connected side by side and are controlled by one or more switches. The different loads can each have their own switch, but the major difference is that each of the loads has access to the same amount of voltage and can operate independently of the others. There is more than one path through which the current can flow. saf $\begin{array}{l}{\mathrm{I}_{1}=\frac{\mathrm{E}_{1}}{\mathrm{R}_{1}}=\frac{120}{40}=3 \mathrm{amps}} \ {\mathrm{I}_{2}=\frac{\mathrm{E}_{2}}{\mathrm{R}_{2}}=\frac{120}{10}=12 \mathrm{amps}} \ {\mathrm{I}_{3}=\frac{\mathrm{E}_{3}}{\mathrm{R}_{3}}=\frac{120}{240}=0.5 \mathrm{amp}}\end{array}$ $R_{T}=\frac{E_{T}}{I_{T}}=\frac{120}{15.5}=7.7 \text { ohms }$ $R_{T}=\frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \ldots}$ \begin{aligned} R_{T}=& \frac{1}{\frac{1}{40}+\frac{1}{10}+\frac{1}{240}}=7.7 \text { ohms } \ R_{T}=& \frac{1}{\frac{6}{240}+\frac{24}{240}+\frac{1}{240}} \ R_{T}=& \frac{\frac{240}{240}}{31} \ R_{T}=& 7.7 \text { ohms } \end{aligned} 2.04: Series-parallel Circuits Series-parallel circuits The series-parallel circuit combines the two previously described types of circuits into one operating system with some distinct advantages. By introducing a load or resistor in series with a parallel circuit, the current flow through the circuit can be controlled (Figure 9). 1. Series-parallel circuit Using Ohm’s law you can calculate total current flow. I = E ÷ R I = 12 V ÷ 2.3 Ω I = 5.15 mA 2.05: Polarity and direction of current flow Polarity and direction of current flow Earlier you learned about the term polarity, referring to the charge at one point with respect to another. When working with electrical circuits, we often refer to the polarity between different points in the circuit. Understanding polarity is important for connecting the leads of polarity-dependent devices such as some meters and motors. Polarity is also important for determining the direction of current flow. In Figure 10 the current leaves the source at the negative terminal, travels around the circuit in a clockwise direction, and re-enters the source at the positive terminal. 1. Polarity It is important to notice that current flows through loads from negative to positive, and current flows through sources from positive to negative. A more precise way of stating this is that outside the source, current flows from negative to positive, but inside the source current flows from positive to negative. Now complete the Learning Task Self-Test. 2.E: Self-Test 2 Self-Test 2 1. What takes the place of a ground return wire in a single wire system? 1. Fuse 2. Case ground 3. Circuit breaker 4. Chassis 2. How many paths does a series circuit have for current flow? 1. 1 2. 2 3. 3 4. 4 3. What is a circuit called that has more than one path for current flow? 1. Series circuit 2. Complex circuit 3. Compound circuit 4. Parallel circuit 4. What must the total voltage drop in a circuit be equal to? 1. The source voltage 2. The first voltage drop 3. Half the source voltage 4. Twice the source voltage 5. A 12 V circuit with a 4 ohm resistor will have a current of 6 A. 1. True 2. False 6. A 120 V circuit with a current of 10 A will have a load with what resistance? 1. 12 Ω 2. 24 Ω 3. 6 Ω 4. 10 Ω 1. If one load fails in a parallel circuit, all other loads will fail. 1. True 2. False 2. What is the total resistance in a series circuit with four resistors rated at 2 Ω each? 1. 2 Ω 2. 4 Ω 3. 6 Ω 4. 8 Ω 3. A 120 V parallel circuit has three resistors: 20 Ω, 12 Ω, and 24 Ω. What is the current? 1. 6 A 2. 18 A 3. 21 A 4. 24 A 4. What is the total resistance for a 120 V circuit with three resistors of 20 Ω, 12 Ω, and 24 Ω in parallel? 1. 6 Ω 2. 8 Ω 3. 12 Ω 4. 24 Ω
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/01%3A_Basic_Principles_of_Electricity/03%3A_Electromagnetism/3.01%3A_Magnetic_Fields.txt	princeton-nlp/TextbookChapters	A magnet attracts ferrous metals and some alloys. Magnets can take three forms: • natural • artificial • electric Natural magnets (i.e., magnetite) are very weak. Artificial magnets are made from magnetic materials (such as iron, nickel, and cobalt) and are given a strong magnetic force during construction. These are permanent magnets and have some limited use. Electromagnets can be easily turned on and off and are in common use because they are not permanent. They are called temporary magnets. 03: Electromagnetism If a magnet is suspended in the air, it will always turn and align with Earth's north and south poles. The two ends, called the magnetic poles, are where the force is strongest. A magnetic field of force is set up between the two poles. You can think of it as invisible lines of force traveling from one pole to the other. The magnetic lines (flux lines) are continuous and always form loops. These invisible lines can be seen if you sprinkle iron filings on a piece of paper placed over a bar magnet (Figure $1$). Characteristics of magnetic lines of force Magnets have some specific rules governing their operation. Magnetic lines of force possess direction These lines are continuous and extend from the north pole to the south pole of the magnet (Figure $2$). Magnetic lines of force always form complete loops The lines do not begin and end at the poles but rather pass through the magnet to form complete loops. If you were to cut a magnet in half, you could observe the magnetic field between the two pieces of the magnet (Figure $3$). Magnetic lines of force always form tight loops This rule explains the idea of attraction. The flux lines attempt to pull in as close to the magnet as possible, just like rubber bands. They also try to concentrate at each pole. If you place two unlike poles together, they try to become one big magnet and shorten the lines of force (Figure $4$). Magnetic lines of force repel each other If magnetic lines of force act like rubber bands, why don’t they collapse into the center? The reason is that they repel each other. Look back at Figure 3; notice that the lines tend to diverge as they move away from the poles, rather than converge or even remain parallel. This results from their mutual repulsion. Magnetic lines of force never cross, but must always form individual loops The mutual repulsion of each magnetic line accounts for this effect. This explains why like poles repel each other. If the lines cannot cross each other, then they must exert a force against each other. If you could see the lines of force, they would look like the diagram in (Figure $5$). Magnetic lines of force can pass more easily through material that can be magnetized The magnetic lines of force will distort to include a piece of iron in the field. This will have the effect of turning the iron into a temporary magnet. Then the opposite poles of the two magnets will attract each other and try to shorten the flux lines. This accounts for the attraction of unmagnetized ferromagnetic objects (Figure $6$). There is no insulation against magnetic lines of force All magnetic field lines must terminate on the opposite pole, which means there is no way to stop them. Nature must find a way to return the magnetic field lines back to an opposite pole. However, magnetic fields can be rerouted around objects. This is a form of magnetic shielding. By surrounding an object with a material that can “conduct” magnetic flux better than the materials around it, the magnetic field will tend to flow along this material and avoid the objects inside. This allows the field lines to terminate on the opposite poles, but just gives them a different route to follow (Figure $7$). Alignment of the atoms If you took a permanent magnet and cut it in half, you would have two permanent magnets, each with a north and south pole. If you continued cutting each in half, you would have more magnets. This suggests that if you could cut right down to the atom, it would also be a perfect permanent magnet. This theory can be extended to non-magnetic material as well. Each of the atoms is a magnet, but they are all pointing in different directions. If you can get enough atoms pointing in the same direction, you will have a magnet. All you have to do is expose the piece of metal to flux lines, and the atoms will align. These atoms tend to form in groups called domains. When the domain becomes large enough, the entire piece of metal becomes the domain and exerts force. When all of the atoms become aligned, the piece has become saturated and cannot get any stronger.
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/01%3A_Basic_Principles_of_Electricity/03%3A_Electromagnetism/3.02%3A_Electricity_and_Magnetism.txt	princeton-nlp/TextbookChapters	Electricity and magnetism There is a direct relationship between electricity and magnetism. If there is current flow in a conductor there will be lines of force created around the conductor. If you could look at the magnetic field formed around a current-carrying conductor, it would look like Figure $1$. Note that the lines of force circle the conductor in rings and have direction. The direction of the lines of force depends on the direction of electron flow. If you know the direction of electron flow, you can determine the direction of the lines of force by using your left hand. The “left-hand rule” says that if you hold the conductor in your left hand with your thumb pointing in the direction of the electron current flow, your fingers will curl in the direction of the lines of force. You will sometimes find this referenced as the “right-hand rule” from those using convention flow notation. Interaction of fields Magnetic fields around a current-carrying conductor act in the same way as the fields around a permanent magnet. In Figure $2$, two conductors have been moved close together. The current is going in opposite directions, as indicated by the symbol in the end of the conductor. An X indicates electron flow in; a dot indicates electron flow out. The magnetic lines of force try to push the two conductors apart because they are in opposite directions. The arrows indicate the direction of the magnetic force. If one of the conductors has the current reversed, then the magnetic lines of force travel in the same directions. When this occurs the lines of force try to contract and pull tight, just as they did with a permanent magnet. The resulting force will try to pull the two conductors together (Figure $3$). Conductors in loops If a conductor carrying a current is formed into a loop, the magnetic field will be arranged differently. It will form looped lines of force with a north pole on one side of the loop and a south pole on the other. The magnetic flux lines add to each other and produce a much denser magnetic field in the center of the coil (Figure $4$). Electromagnets If a piece of soft iron is placed in the coil and a current is passed through the coil in one direction, the magnetic field of the coil causes the domains to align in the iron. This causes poles to form in the iron and creates an electromagnet, as shown in $5$. The strength of the electromagnet varies with the number of loops formed, the strength of the electric current, and the type of core in the winding. Because the iron core has a low magnetic retention, the magnetic field collapses when the current stops flowing. The iron core is no longer magnetized and will release whatever it was being used to hold or pull inward. Electric motors and generators Electromagnets are probably most commonly used in motors and generators. We have seen that magnetism can be caused by electricity. Electric motors use the force of electromagnets to produce rotation. On the other hand, electricity can be produced by magnetism. When a conductor is moved through a magnetic field or a magnet is moved past a conductor, the movement will induce a voltage in the conductor. Most electricity is generated in this way. To generate a voltage, three elements must be combined (Figure $6$: 1. a conductor 2. a magnetic field 3. movement by either the conductor or the magnetic field The amount of voltage produced will depend on the strength of the magnetic field and the speed at which the conductor or the field moves. A conductor that moves through a magnetic field quickly will generate a higher voltage than one that moves more slowly. A conductor that moves through a strong magnetic field will generate a higher voltage than one moved through a weak magnetic field. Alternating current Electric current that flows in one direction for a split second then changes direction in another split second is called alternating current (AC). In an alternating voltage, the polarity reverses direction periodically. The spinning mechanical motion of an electric generator produces AC voltage and current. AC waveform and hertz Hertz is the unit used to describe the frequency of AC direction change. Figure $7$ is a graphic illustration using a curved line with arrows to indicate a change of direction in AC electron flow. Starting at point A, the current flows in one direction, and then at 120 volts it changes direction, drops to 0 volts, and continues to 120 volts, where it changes direction again back to point B at 0 volts. If it takes one second to complete the cycle from A to B, we would say the frequency is 1 hertz. Household utility AC current is supplied to the customer at 60 hertz, meaning 60 cycles per second. Single-phase power supply Single-phase electric power refers to the distribution of alternating current electric power using a system in which all the voltages of the supply vary in unison. Single-phase distribution is used when loads are mostly lighting and heating, and with a few large electric motors. Single-phase power typically comprises one voltage that is carried between two separate conductors. The two hot lines are called Line 1 and Line 2. In some systems, a grounded neutral, often labeled N, is provided that reduces the referenced voltage in half. These systems are typically found in residential and small commercial applications. Three-phase AC power supply Three-phase electrical power refers to a type of electrical power distribution in which three or more energized electrical conductors are carrying alternating currents. Examples of three-phase power systems are industrial applications and power transmission. Three-phase power supplies are used to power large motors and other heavy loads. A three-phase system is generally more economical than equivalent single-phase or two-phase (an uncommon power supply) systems at the same voltage. Three-phase power comprises three independent voltages that are carried on three separate conductors. The three hot lines are called Line 1, Line 2, and Line 3. Three-phase power is typically found in commercial and industrial buildings. Now complete the Learning Task Self-Test. 3.E: Self-Test 3 Self-Test 3 1. There are three types of magnets: natural, artificial, and electric. 1. True 2. False 2. Natural magnets have the strongest force. 1. True 2. False 3. If the south poles of two magnets are brought together, what they will do? 1. Conduct 2. Relate 3. Saturate 4. Repel 4. Changing which of the following will also change the strength of an electromagnet? 1. Direction of current flow 2. Size of wires 3. The length of the core 4. Amount of current flow 5. What is the core of an electromagnet usually made from? 1. Air 2. Soft iron 3. Aluminum 4. Copper 6. What two elements must be combined with a conductor to generate a voltage? 1. Magnetic field and a current 2. Current and movement 3. Coil and a magnet 4. Magnetic field and movement 7. Magnetic lines of force never cross. 1. True 2. False 04: Answer Key Answer Key Self-Test 1 1. b. Atoms 2. b. Conductors 3. a. Conductor 4. b. They do not transport an electrical charge. 5. b. Amperes 6. a. True 7. b. False 8. a. A control 9. d. A load 10. b. 4 A 11. b. 160 V 12. a. 24 Ω 13. a. 1800 W 14. b. 2.5 A 15. voltage current resistance 120 500 mA 240 12 0.012 A 1000 12 8 A 1.5 5 0.00025 A 20 000 120 10 12 12 0.15 A 80 3 0.0002 A 15 000 16. power voltage current 1500 W 120 V 12.5 A 40 W 12 V 4 A 3.6 W 12 V 300 mA 200 W 20 V 10 A 96 W 12 V 8 A 480 W 12 V 40 A Self-Test 2 1. d. Chassis 2. a. 1 3. d. Parallel circuit 4. a. The source voltage 5. b. False 6. a. 12 Ω 7. b. False 8. d. 8 Ω 9. c. 21 A 10. a. 6 Ω Self-Test 3 1. a. True 2. b. False 3. d. Repel 4. d. Amount of current flow 5. b. Soft iron 6. d. Magnetic field and movement 7. a. True
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/02%3A_Unit_II-_Common_Circuit_Components_and_Their_Symbols/05%3A_Circuit_Components_and_their_Schematic_Symbols/5.0.txt	princeton-nlp/TextbookChapters	All electrical components are rated with different current, voltage, and other values, depending on their use. Replacing an electrical component with one of a different value could present a serious safety hazard to the person using the equipment. Should you have to replace an electrical component at any time, always be sure that the current, voltage, and other electrical ratings of the replacement match those of the original. In addition, to ensure public safety from electrical and fire hazards, the Canadian Standards Association (CSA) approves electrical components. Each component is tested before it can be sold on the Canadian market. Always use only CSA-approved equipment. The CSA approval should be clearly visible on the component or the package. You may have to assemble devices in a circuit from plans or drawings in which symbols are used to represent basic electrical devices and components. Although some plans use pictures of the devices instead of symbols, you should be familiar with the symbols so that you can identify each individual device. Not all electrical symbols are standard, but most symbols can be easily recognized. 05: Circuit Components and their Schematic Symbols Electrical systems An electrical system has two main conditions: it is closed or it is open. Closed means the circuit is complete and conducting. Open means the circuit is incomplete and no current flows. There are different electrical systems, identified by voltage. The term low voltage is relative and its definition varies by context. The Canadian Electrical Code defines low voltage as from 31 V to 750 V and systems operating at 30 volts or less. Automotive systems normally use direct current and are rated up to 24 volts. Residential alternating current voltage may be 120 or 240 volts. Lighting and small appliances normally use 120 volts. Clothes dryers, stoves, and ovens use 240 volts. Shop equipment also uses either 120 or 240 volts. Most hand-held electric tools and many shop tools use 120 volts or battery power. Some equipment, such as electric welders, use 240 volts. 5.1 Light-emitting diodes (LEDs) produce light from electricity using semiconductor materials. They operate from a low DC voltage and produce little heat because there is no incandescent filament. They are available in a range of colours, with red, green, and yellow being the most common. The seven-segment number display (Figure $2$) uses one LED for each section to create different numbers from 0 to 9. 5.E Self-Test 1 1. Match the device on the left with its purpose on the right. 1. Circuit breaker 1. Protects circuits 2. Relay 2. Electric switch 3. Solenoid 3. Variable control 4. Rheostat 4. Movable core 2. What best describes tapped or stepped resistors? 1. They have two or more fixed values. 2. They have only one unchangeable rating. 3. They have a variable range of resistance. 4. They are used to control charging systems. 3. How is a fuse different from a circuit breaker? 1. A fuse acts like a diode. 2. A circuit breaker doesn’t need a ground. 3. A fuse can be reset and a circuit breaker cannot. 4. A circuit breaker can be reset and a fuse cannot. 4. 6 gauge wire is smaller than 18 gauge. 1. True 2. False 5. What are conductors normally made from? 1. Steel 2. Copper 3. Soft iron 4. Aluminum 6. Receptacles are one-half of a two-piece multi-contact connector. 1. True 2. False 1. What are circuit breakers, fuses, and thermal limiters all examples of? 1. Relays 2. Switches 3. Receptacles 4. Protection devices 2. How many gauges of difference must there be between a fusible link and a conductor? 1. 2 2. 4 3. 6 4. 8 3. Relays require a power circuit and a control circuit. 1. True 2. False 4. What are transformers used for? 1. To act like a relay 2. To increase amperage 3. To increase or decrease voltage 4. To change the current from DC to AC 5. Who is responsible for testing all electrical components? 1. ITA 2. NSA 3. CSA 4. DNA 6. Closed means the circuit is complete and conducting. 1. True 2. False 7. What voltage other than 120 V does a residential system use? 1. 180 V 2. 200 V 3. 240 V 4. 280 V
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/02%3A_Unit_II-_Common_Circuit_Components_and_Their_Symbols/06%3A_Wiring_Diagrams/6.01%3A_Symbols_Used_in_Schematic_.txt	princeton-nlp/TextbookChapters	The ability to read and understand a wiring diagram is important for any tradesperson. You may need to repair a power tool, install a heat pump, or try to find a fuse in a car. Any of these situations requires an ability to read and understand a wiring diagram. 06: Wiring Diagrams Electrical symbols may be different for each manufacturer, but in most cases they are standard. Every manufacturer’s diagram should have a symbol identification chart or “key” located in the wiring book. Some examples of electrical symbols are shown in Figure $1\. 6.02: Types of Electrical Diagra There are four basic types of electrical diagrams: • schematic • wiring • block • pictorial Schematic Diagrams The schematic diagram (Figure \(1$), often called a ladder diagram, is intended to be the simplest form of an electrical circuit. This diagram shows the circuit components on horizontal lines without regard to their physical location. It is used for troubleshooting because it is easy to understand the operation of the circuit. The loads are located on the far right of the diagram, and the controls for each load are located to the left. To understand the sequence of operation, the drawing is read from the upper left corner and then from left to right, and from top to bottom. Wiring diagrams The wiring diagram (Figure $2$) shows the relative layout of the circuit components using the appropriate symbols and the wire connections. Although a wiring diagram is the easiest to use for wiring an installation, it is sometimes difficult to understand circuit operation and is not as applicable for troubleshooting. Block diagrams The block diagram (Figure $3$), also called a functional block diagram, is used to describe the sequence of circuit operations. This diagram indicates by functional descriptions, showing which components must operate first in order to get a final outcome. They do not refer to specifics like device symbols or related wire connections. Pictorial diagrams A pictorial diagram (Figure $4$) shows the circuit components in more detail, as they really look, and indicates how the wiring is attached. These diagrams can be used to locate components in a complex system. Now complete the Learning Task Self-Test. 6.E: Self Test 2 Self-Test 2 1. A schematic diagram is often called a ladder diagram. 1. True 2. False 2. What is the fourth type of wiring diagram, in addition to schematic, wiring, and block diagrams? 1. Line 2. Oblique 3. Pictorial 4. Isometric 3. A schematic diagram shows all physical locations of components. 1. True 2. False 4. For which operations is a wiring diagram best suited? 1. Diagnosing 2. Sequencing 3. Installation 4. Troubleshooting 5. A pictorial diagram is used to locate components in complex systems. 1. True 2. False 6. A block diagram includes symbols. 1. True 2. False 7.01: Series Circ Electrical components can be connected in different configurations to form circuits for different power outputs and applications. • 7.1: Series Circuits A series circuit is constructed by connecting all of the circuit components in line with one another. • 7.2: Parallel Circuits The parallel circuit is probably the most common type of circuit you will encounter. Loads in power distribution systems are usually connected in parallel with each other in one way or another. A parallel circuit is constructed by connecting the terminals of all the individual load devices so that the same value of voltage appears across each component. • 7.3: Voltage Source Circuits Multiple power sources can be connected in series or parallel in order to meet the different voltage or current output requirements for various applications: (1) Power sources are connected in series to increase the voltage output and (2) Power sources are connected in parallel to increase the current capacity • 7.4: Three-wire Power Supply System • 7.E: Self-Test 3 07: Common Circuit Characteristics A series circuit is constructed by connecting all of the circuit components in line with one another. The schematic diagram in Figure $1$ is an example of a simple series circuit. In this case, a battery (source) is connected through a switch to three resistors (load devices), all of which are in line with one another. When the switch is closed, there is only one path for current flow. Any circuit that provides only one path for current flow is categorized as a series circuit. If any part of a series circuit is opened, the current cannot flow and none of the components will operate. The circuit may be opened by the switch or by the failure of a component in the circuit. For example, some decorative lights have clusters within the string that are connected as a series circuit. If one lamp burns out (or opens), all the other lamps go out. You then have to test each lamp individually to find the failed bulb, and this gets very challenging if two bulbs happen to be damaged. Application of series circuits Electrical components or devices are generally connected in series whenever it is necessary to: • control the amount of current flow in a circuit • divide the total voltage of a supply For example: • Switches are connected in series with loads so that you can energize or de-energize different loads. • Protective devices such as fuses and overload relays are connected in series with line conductors. • By connecting equal values of resistance in series, the same voltage drop can be obtained across each resistance. Twenty Christmas tree lights connected in series to a 120 V supply would have a voltage rating of 6 V per light. Disadvantages of series circuits When designing a series circuit, consider these points: • An open in any one device will also interrupt current flow to all remaining devices. • A short in one device will cause an increase in current through all the devices. • Changing the resistance value of one device will change the current, voltage, and power values of all remaining devices.
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/02%3A_Unit_II-_Common_Circuit_Components_and_Their_Symbols/07%3A_Common_Circuit_Characteristics/7.02%3A_Parallel_Ci.txt	princeton-nlp/TextbookChapters	The parallel circuit is probably the most common type of circuit you will encounter. Loads in power distribution systems are usually connected in parallel with each other in one way or another. A parallel circuit is constructed by connecting the terminals of all the individual load devices so that the same value of voltage appears across each component. In Figure $1$, you can see that each of the three resistors receives the same voltage from the source. Figure $2$ shows the more traditional schematic of the same circuit. Notice that: • The total supply voltage appears across each of the three resistors. • There are three separate paths (or branches) for current flow, each leaving the negative terminal of the supply and returning to the positive terminal. The two fundamental characteristics of any parallel circuit are that: • The voltage across each branch is the same. • There is more than one path for the current to flow through. In contrast to a series circuit, current still flows to the remaining devices in the circuit if any one branch or component in a parallel circuit is opened. 7.03: Voltage Sou Multiple power sources can be connected in series or parallel in order to meet the different voltage or current output requirements for various applications: • Power sources are connected in series to increase the voltage output. • Power sources are connected in parallel to increase the current capacity Series Sources Voltage sources are sometimes connected in series to produce a higher voltage value. This is common in devices such as flashlights and portable transistor radios, in which 1.5 V battery cells are used. To obtain a higher voltage output from series-connected sources, you must observe correct polarity. In Figure $1$, a net voltage of 6 V is obtained if the individual 1.5 V cells are acting in the same direction. This is called series aiding. For the voltages to accumulate, the negative terminal of one source connects in series with the positive terminal of the next source, and so on. When voltage sources are connected in series opposing, the net voltage value is derived by subtraction. This is illustrated in Figure $2$. • Three of the cells are connected series aiding to produce 4.5 V. • One cell is connected with opposite polarity of 1.5 V. • The net voltage is 4.5 V – 1.5 V = 3 V. • Overall polarity acts in the direction of the largest cell. Parallel sources Voltage sources are connected in parallel whenever it is necessary to deliver a current output greater than the current output that a single source of supply can provide, without increasing voltage across a load. An advantage of parallel-connected power sources is that one source can be removed for maintenance or repairs while reduced power to the load is maintained. This is common in RVs that have dual batteries. For parallel batteries, current capacity is equal to that of one battery multiplied by the number of parallel batteries. If a 6 V battery has a maximum current output of 1 amp, and if it is necessary to supply a load requiring 2 amps, then you can connect a second 6 V battery in parallel with the first, as shown in Figure $3$. Whenever batteries or other power sources such as transformers or generators are to be connected in parallel, it is very important that the power sources have the following: • The same terminal voltages A lower voltage source connected to a higher one acts as a load itself, rather than helping share the real load current with the other sources of supply. • Properly connected polarity. Like terminals of the power sources must be connected together; that is, positive-to-positive and negative-to-negative.
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/02%3A_Unit_II-_Common_Circuit_Components_and_Their_Symbols/07%3A_Common_Circuit_Characteristics/7.04%3A_Three-wire_.txt	princeton-nlp/TextbookChapters	Electrical energy to most individual and small commercial buildings in North America is distributed through a 120 V/240 V AC, single-phase, three-wire system. Several advantages are gained by using this method of distribution: • Copper conductor current requirements can be reduced. • Two different voltages (120 V and 240 V) are available. • Improved safety is established through grounding the neutral. Source connections A three-wire circuit is accomplished by connecting two 120 V sources in a series-aiding configuration. The conductor taken from the common point between the two sources is called the neutral conductor. Conductors taken from the two outer points are called the line or hot conductors. As shown in Figure $1$: • Voltage measured line-to-line is 240 V. • Voltage measured from either line to neutral is 120 V. This allows connection to either 120 V loads (such as lighting) or 240 V loads (such as ranges or clothes dryers). See Figure $2$. Note that polarities shown in Figure $1$ change every 120th of a second for a 60 hertz AC power supply. For safety reasons, it is important that circuit conductors are identified by colour: • Insulation on the two-line conductors is usually black (or sometimes one is black and one is red). • The neutral always has white insulation. The neutral is also grounded (directly connected to earth) at the source of supply. Grounding the neutral conductor Earth is a conductor of electricity. Therefore, to reduce the hazards of electrical shock and improve safety, electrical distribution systems usually have one of the circuit conductors connected to Earth, or as we say, grounded. In most electrical systems, the neutral conductor is grounded at the supply by directly connecting it to Earth by another conductor (called the system grounding conductor) or by an electrode. Although grounding electrical distribution systems is an elaborate topic, consider the following simplified example. Example The fundamental purpose of grounding is to guard against electrical shocks and fire hazards. But what makes a grounded electrical system safer? Consider an ungrounded 120 V/240 V wiring system with a fault, as shown in Figure $3$. Theoretically, if an insulation fault occurs at a piece of equipment (so that a line conductor makes accidental contact with the metal frame), nothing should happen. However, if an accidental ground should occur and a person comes in contact with the faulty equipment and ground, that person will experience a shock of 240 V (the line-to-line voltage). Now look at the same wiring system with the neutral purposely grounded, as shown in Figure $4$. With the neutral grounded and the same equipment fault as previously described, the person coming in contact with both the metal frame of the equipment and the Earth would experience a shock of only 120 V (which is the line-to-neutral voltage). The shock voltage has been reduced by 50%. To further minimize shock hazard, not only is the wiring system grounded but also all metallic, non-current-carrying parts of the equipment are grounded by using a bonding conductor. This is an important step if maximum safety is to be achieved. As shown in Figure $5$, if the equipment is also grounded intentionally, then a line-to-frame fault condition offers a low-resistance path for current flow back to the system neutral. Essentially this is a line-to-neutral short circuit, which causes the circuit overcurrent device to trip, thus eliminating the shock hazard from the system. Although properly grounded wiring systems do not eliminate shock hazard, they certainly lower the odds of being shocked! Now complete the Learning Task Self-Test. 7.E: Self-Test 3 Self-Test 3 1. Typical house wiring is an example of a series circuit. 1. True 2. False 2. If one load fails in a series circuit, what happens to the other loads? 1. They will all fail. 2. A fuse will blow. 3. Nothing happens. 4. The rest remain working. 3. As more resistors are added in series, what increases? 1. Power 2. Voltage 3. Current 4. Resistance 4. A series circuit allows the control of current flow. 1. True 2. False 5. Which of the following is true about a parallel circuit? 1. Voltage will be different at each load. 2. Voltage will be the same at each load. 3. Current will be the same at each load. 4. Resistance will be the same at each load. 6. The three-wire circuit is an example of which of the following? 1. Hot jumping 2. Series aiding 3. Parallel aiding 4. Backpacking circuit 1. For what purpose is a circuit grounded? 1. Safety 2. Series aiding 3. Circuit protection 4. Easier installation 2. What is the result of connecting three 6 V batteries in series? 1. 12 volts are produced. 2. 18 volts are produced. 3. 24 volts are produced. 4. The voltage doesn’t change. 3. Which of the following must apply to power sources connected in parallel? 1. Unlike terminals must be connected. 2. They must be connected with a fuse. 3. Like terminals must be connected. 4. They must have a transformer between them. 4. For voltages to accumulate in series aiding, what must occur? 1. Correct polarity 2. Circuit protection 3. Similar amperages 4. Dissimilar amperage 5. If two 12 V batteries are connected in parallel, what will the voltage be across any load? 1. 6 V 2. 12 V 3. 24 V 4. 48 V 08: Answer Key Answer Key Self-Test 1 1. Match the device on the left with its purpose on the right. 1. Circuit breaker (1. Protects circuits) 2. Rheostat (3. Variable control) 3. Relay (2. Electric switch) 4. Solenoid (4. Movable core) 2. a. They have two or more fixed values. 3. d. A circuit breaker can be reset and a fuse cannot. 4. b. False 5. b. Copper 6. a. True 7. d. Protection devices 8. b. 4 9. a. True 10. c. To increase or decrease voltage 11. c. CSA 12. a. True 13. c. 240 V Self-Test 2 1. a. True 2. c. Pictorial 3. b. False 4. c. Installations 5. a. True 6. b. False Self-Test 3 1. b. False 2. a. They will all fail. 3. d. Resistance 4. a. True 5. b. Voltage will be the same at each load. 6. b. Series aiding 7. a. Safety 8. b. 18 volts are produced. 9. c. Like terminals must be connected. 10. a. Correct polarity 11. b. 12 V
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/03%3A_Unit_III-_Wiring_Connections/09%3A_Wiring_Connections/9.01%3A_Conductors.txt	princeton-nlp/TextbookChapters	Learning Objectives When you have completed the Learning Tasks in this Competency, you will be able to: • define the terms used and explain the principles of soldering • describe the methods for making properly soldered connections • maintain soldering equipment • use wireless connectors It is important for you to be familiar with techniques for soldering electrical connections and how to use wireless connectors. For example, the ends of the finely stranded wires used for power supply cords on most portable power tools are soldered to permit a long-lasting, trouble-free connection. Solder also produces secure, durable electrical connections for switches, plugs, and tools. Wireless connectors are commonly used in many electrical applications because they are quick and easy to use. Making tight electrical connections is critical to a safe wiring job. If wires come loose, you could get arcing and overheating, which could lead to a fire. The right connector is determined by a number of variables. 09: Wiring Connections A material that allows energy to flow with relative ease is known as a conductor. The most common form of electrical conductor used is the wire. Most electrical wires are made from copper or aluminum and are in one of two forms: solid or stranded. The term electrical cable usually refers to multiple insulated wires grouped in a common sheathing (Figure $1$). Stranded conductors Stranded wire is a collection of solid wires twisted or braided together, commonly around a central core (Figure $2$). The current carrying capacity of a stranded wire is close to the current carrying ability of a single strand. Stranded wires act as a single conductor and carry a single electrical current. Stranded conductors are normally used in a thin wire that requires flexibility, such as speaker wire. Ordinarily, a stranded conductor has wires all the same size. The size of the strands used depends on the flexibility required. For example, #00 gauge cable may be made up of seven strands of #7 gauge wire, or 19 strands of #12 gauge, or 37 strands of #24 gauge, the last one being rated “extra flexible.” Solid conductors Solid wire consists of one strand of copper metal wire, bare or surrounded by an insulator. Solid wire is normally found in smaller sizes only. Solid wire is cheaper to manufacture than stranded wire and is used where there is little need for flexibility in the wire. Insulating materials The purpose of conductor insulation is to prevent unwanted flow of electrical current, such as ground faults, short circuits, or electric shock. There are various methods used to insulate conductors to satisfy the many conditions encountered in electrical installations, such as temperature, moisture, and different voltage ratings. Insulating materials include: • enamel coating • rubber • thermoplastics • minerals Stripping insulation To make any type of electrical connection, you will need to expose the base wire from the insulated covering. You can do this with wire strippers (Figure $3$). With wire strippers, you can strip the amount of wire required for the type of connection being made. It is important to avoid damaging the copper wire by nicking the copper or cutting into it. Nicked wires can lead to overheating and eventually could cause an electrical fire. Colour coding Most electrical wiring circuits look complicated because several wires are found at any one point in the circuit. To make it easier to know exactly which is which, wires are identified by colour or labeled. For building construction, the Canadian Electrical Code reserves two colours for specific applications: When this system of colour coding is followed, at any point in any circuit, a white wire always indicates a neutral conductor. A green wire always indicates an equipment grounding conductor. Any other colour wires, such as red, black, or blue, can be assumed to be live or hot, meaning that they will have a voltage on the conductor and are therefore dangerous. Wire size Wires are manufactured in sizes according to the American Wire Gauge (AWG) system. The cross-sectional area of each gauge is an important factor for determining the current carrying capacity of a wire (ampacity). Increasing gauge numbers denote decreasing wire diameters, ranging from the largest 0000 (4/0) to the smallest, 44. • White or natural grey covering is reserved for insulated, identified conductors, identified common conductors, and identified neutral conductors. • Green covering is reserved for the equipment grounding conductor. 9.02: Soldered Connections A variety of joints are used to prepare wires for soldering. These include: • Western Union splice • tap joint • twist joint Western Union splice This splice joins the ends of two wires inline (compared to the twist joint below). Strip the wires for a length of 2.5 to 8 cm (1" to 3"), as shown in Figure $1$. Clean the wire, then twist the ends of the wire tightly together as shown. Tap joint The tap joint (Figure $2$) connects a stranded wire to an intermediate point along the length of a second wire. Wrap the wire at least six times. Twist joint The twist joint (Figure $3$) is used to join parallel wires, whereas the Western Union splice is used to connect wires that are in line. Strip the insulation, clean the wires, and twist them together tightly for a length of 2.5 cm (1 in.). Tinning stranded wire In a general sense, tinning is the process of applying a thin layer of solder to something and will be discussed in more detail in Learning Task 2. In the case of stranded wire, you should tin the stripped ends of the wire to prevent the strands from separating while bending or connecting. Use only enough solder to make the stripped portion of the wire solid. The strands of the wire should be visible through the solder. Avoid solder from wicking in a wire underneath the insulation because it will make the wire solid and cause it to break more easily.
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/03%3A_Unit_III-_Wiring_Connections/09%3A_Wiring_Connections/9.03%3A_Solderless_connectors.txt	princeton-nlp/TextbookChapters	Soldering is the recommended way to splice, tap, or join wires to make a rigid, permanent, weather-resistant connection. The process of soldering can be time-consuming, awkward, restrictive, and expensive. In many applications, soldering has been replaced by special connecting devices that simplify wire joining procedures. Solderless connectors are used on both wire and cable connections. Types of solderless connectors include: • looped-end • twist-on • set-screw • crimp-on Looped-end connectors The most common solderless connection has the looped end of a wire (Figure $1$) held in place by a set-screw at an electrical terminal (Figure 9). Note that the direction of the loop is the same as the direction the screw is turned when it is tightened (clockwise). The screw and washer should be made of corrosion-resistant materials such as copper or brass. Twist-on connectors The twist-on connector is a one-piece connecting device designed to splice aluminum or copper wires. Twist-on connectors are also known as wire nuts, wire connectors, cone connectors, thimble connectors, or Marrettes. Inside the blunt, bullet-like cover of the twist-on connector is a cone-shaped spring insert that threads itself onto conductors when the connector is twisted. When the connector is twisted onto the stripped ends of wires, the wires are drawn, twisted, and squeezed into the connector’s metal insert. Electrical continuity is maintained both by the direct twisted wire-to-wire contact and by contact with the metal insert. Wing-like extensions (Figure $5$) are molded into some makes of connectors to reduce operator muscle fatigue when installing a large number of the connectors. The shell of the twist-on connector provides sufficient insulation to allow these connectors to be used in circuits carrying up to 600 V. Twist-on wire connectors are commonly colour-coded to indicate the connector size and, hence, their capacity (Figure $6$). They are commonly used as an alternative to soldering conductors since they are quicker to install and allow easy removal for future modifications, unlike soldered connections. Twist-on connectors are not often used on wire gauges thicker than AWG #10 (5.26 mm²) because such solid wires are too stiff to be reliably connected with this method. Instead, set screw connectors, clamps, or crimp connectors are used. Set-screw connectors Set-screw connectors (Figure 13) consist of two parts: • a brass connector body into which wires are inserted • an insulated cone-shaped cap that is screwed onto the brass connector The set-screw connector is most often used as a splice inside a protected electrical box and lighting fixtures. Although set-screws are more time-consuming to install and are more expensive than twist-ons, they may offer a more secure connection than twist-on connectors. Crimp-on connectors A crimp-on connector is used for a permanent tight splice. The crimp-on connector (compression connection) can have one or two parts. The two-part connector (Figure $8$) has a conductor retaining sleeve that is compressed by using special crimping pliers and an insulated screw cap into which the crimped retainer is inserted. The sleeve is composed of copper or zinc-plated steel, while the cap is a high dielectric substance. The zinc-plated steel retaining sleeve should not be used with aluminum conductors, as electrolysis can occur between the metals. These devices are available in many sizes. As with other solderless connectors, each application must carefully select the correct size two-piece crimp-on connector. The one-part crimp-on connector (Figure $9$) is commonly used as a terminal lug. Both the fork and the ring-type greatly simplify connecting stranded conductors to terminal screws. The crimp-on connector sometimes has a soft, hose-like tube that is molded to the connector. The connector and the insulation are crimped together. After crimping, the insulation returns to its original form. Now complete the Learning Task Self-Test. 9.E: Self-Test 1 Self-Test 1 1. Which term best describes a material that allows electrical energy to pass through it? 1. Resister 2. Insulator 3. Conductor 4. Connector 2. Which of the following best describes the term electrical cable? 1. Any wire 2. Any insulated wire 3. Multiple wires grouped together in a common insulation 4. Multiple insulated wires grouped together in a common sheathing 3. What is the primary purpose of insulation on wires? 1. To protect the wire 2. To make installation easier 3. To prevent unwanted current flow 4. So the wire can be colour coded 4. When is stranded wire used? 1. On short wires 2. When cost is a factor 3. On straight runs of wire 4. When flexibility is needed 5. Wire is sized by gauge: the higher the number, the larger the wire. 1. True 2. False 6. What should be done to stranded wire prior to bending? 1. It should be curled. 2. It should be tinned. 3. It should be wound. 4. It should be twisted. 1. Solderless connections are more costly than soldering. 1. True 2. False 2. What is one advantage to a twist-on connector? 1. It is permanent. 2. One size fits all. 3. It will not come apart. 4. It can be removed easily. 3. It doesn’t matter what material the conductor is made from when making a connection. 1. True 2. False 4. What type of connector should be used to create a permanent splice? 1. Twist 2. Winged 3. Crimp-on 4. Set screw
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/03%3A_Unit_III-_Wiring_Connections/10%3A_Soldering_Techniques/10.01%3A_Solder_Bonding.txt	princeton-nlp/TextbookChapters	Most components are fitted with leads, pins, lugs, or some other means of interconnecting them electrically. Most soldering involves bonding these leads to other leads, circuit wires, copper pads, or other circuit parts. The primary purpose of soldering an electrical connection is to ensure an efficient flow of current between the joined parts. Soldering properly is an important skill. Correct operation of electric circuitry depends on correct soldering. Poor soldering will often lead to poor operation of the circuit. Safety Your safety must always be a concern while you are soldering. There is a risk of inhaling fumes from soldering operations that can irritate the nose, throat, and lungs. Studies show that prolonged exposure to certain fumes may result in occupational asthma and contribute to chronic lung disease. In addition, fumes that you breathe may contain invisible particles, such as lead and zinc, that could cause poisoning. Always complete soldering operations in well-ventilated spaces. You should also carefully wash your hands before eating, drinking, or smoking. You should wear safety glasses with side shields to protect yourself from splashing solder. 10: Soldering Techniques The soldering process depends on molten solder flowing into all the microscopic surface imperfections of the metals to be soldered and even penetrating very slightly below their surface. In this process, a chemical reaction occurs in which the solder actually melts some of the metals and alloys with them. Upon cooling, this combination of penetration and alloying results in a very strong bond between the solder and metal. When two pieces of metal are soldered together, a thin layer of solder adheres between them and completes the connection. The process of surface penetration and alloying is known as wetting of the host metals (Figure 1). Some metals are very receptive to wetting and can readily be soldered, while others are non-receptive and cannot be soldered at all. Copper is very receptive to wetting by tin/lead solders. Tin also wets readily, as do silver and gold, but to a lesser extent. Solder wetting is displayed by a smooth, shiny flow of solder onto the metal surface. The process is often called tinning. Metals such as aluminum and iron will not wet properly. The solder forms stubborn flecks and balls and fails to penetrate or adhere. Effective solder bonding of these metals is not possible. 1. Wetting action Solder flux Solder wetting of metal is severely curtailed by the presence of surface oxides. This is one of the reasons aluminum cannot be tinned and soldered. Its surface is oxidized almost instantly by the presence of atmospheric oxygen. A clean, oxide-free surface cannot be obtained for soldering. Oxidization also restricts wetting of copper, so any copper parts to be soldered should be as clean as possible. Fortunately, copper oxidizes rather slowly, so surfaces cleaned by scraping or sanding will remain pure copper for some time before a tarnishing film of copper oxide reforms. Unfortunately, oxidization is hastened by heat. Application of a heated soldering iron or molten solder will start surface oxidation, even on a freshly cleaned surface. For this reason, it is very hard to solder even clean copper without applying a soldering flux. The primary function of a soldering flux is to eliminate oxidation during the soldering process. Flux melts and flows when heated, effectively sealing the surfaces against the entry of oxygen. Flux also lowers the surface tension of the molten solder, allowing it to flow and spread more easily. Flux contains a small quantity of an active antioxidant material, which serves as a mild cleaner to remove any surface tarnish. Historically, soldering flux has been caustic liquids or pastes containing acids. This is because part of their function has been to scour and roughen the surfaces. The problem with acid flux is that it never completely vaporizes during heating and continues to corrode the metal surfaces indefinitely. The flux most commonly used in electric soldering is rosin. Rosin is an organic material derived from certain tree saps. It is non-corrosive, reasonably non-toxic, and readily liquefied by heat. Its residues are also easily removed after soldering. Rosin flux is usually a continuous single or multiple core inside the wire solder (Figure 2). Because it melts at a much lower temperature than solder, rosin is readily dispersed onto the job both before and during the melting of the solder. Low-odour solder and solders without flux are available. 2. Flux-cored solder wire Rosin core solder is the only kind you should use in electric work. Never use acid core or other solder containing corrosive flux. Never use any form of paste or liquid flux containing acid. Not only will the ongoing corrosion eventually cause mechanical deterioration, it will rapidly destroy the connection’s ability to conduct current. Composition of solder Solder is an alloy of different metals, commonly tin and lead, that have a lower melting point than the base metal. Both metals are reasonably good electrical conductors. The ratio of tin to lead has a great deal to do with the melting point and hardness of solder and also with its conductivity. Tin melts at about 327°C (620°F) and lead at about 232°C (450°F). When these metals are combined, the melting point of the mixture goes down. The melting point varies with the ratio of tin to lead, with the lowest occurring at about 183°C (360°F) for a 63/37 tin-lead mixture. This lowest melting temperature is called the eutectic point. It marks the temperature at which the solder changes directly from solid to liquid with no semi-liquid or plastic state in between. Since a narrow plastic state is desirable in soldering operations, a 60/40 mix is very common. This raises the melting point slightly to about 188°C (370°F) and gives a temperature range for plasticity of about 4°C to 6°C (40°F to 43°F). It also produces optimum conduction characteristics and hardness for electronics soldering. Note that the ratios for solder composition always state the tin content first. 60/40 solder is composed of 60% tin and 40% lead (by weight). Wire solder is available in a variety of diameters. Which to use depends on the sizes of the component leads and terminals to be soldered. Diameters of 0.75 mm (1/16ø) and 0.38 mm (1/32ø) are the most commonly used sizes. 10.02: Soldering Tools Soldering tools Historically, heating the host metals and melting the solder was done by firing in a forge or by pouring molten solder onto the metals and wiping it into place with leather pads. Later, heat was applied by means of an iron bit that was heated in the forge. The name soldering iron has carried forward to this day. Today, heat is applied by various electrically heated soldering tools called irons or pencils or guns. Figure 3 shows two examples. The majority of electronic soldering done during electronic repair, for example, is completed with a low-wattage soldering pencil. 1. Some common soldering tools 2. Soldering tip shapes Regardless of the shape, size, or design of the iron, the tip must be tinned. Tinning the tip is the process of applying a thin layer of solder to the tip to keep atmospheric oxygen and other contaminants off the soldering surface and help with the flow of the solder. A poorly tinned tip will make it virtually impossible to achieve a sound solder joint. Soldering iron manufacturers specify an operating temperature range for each type of tip. This requires mating the heating capability of iron and tip. Insufficient iron capability will result in tip temperatures that are lower than needed for quality solder work or in rapid drop in tip temperature during soldering. Excessive heat will quickly deteriorate the tip and may possibly damage the components and printed circuit board being soldered. You can estimate tip temperature by following this two-step process: • Apply a small amount of solder to the flat surface of the tip and immediately wipe the tip with a damp cellulose sponge or paper towel. • Observe tip colour immediately after wiping. • If the color of the surface is silver, the temperature is between 315°C and 370°C (600°F and 698°F). • If the tip shows gold streaks, the temperature is approaching 425°C (797°F). The copper tips of irons and pencils are progressively dissolved by solder, and they soon become pitted and corroded. This is particularly true of the continuous-heat types. It is virtually impossible to do quality soldering with a corroded tip. Corroding can be slowed down by keeping the tip clean and well tinned. Clean the tip by wiping it frequently with a damp cloth or cellulose sponge. The damp wipe will shock the built-up burned flux from the tip. Immediately re-tin the tip and leave a thin coating to keep atmospheric oxygen off the soldering surface. Wipe the excess solder off the tip before the next use. Reclean and recoat with solder when you finish each soldering task. When pitting becomes significant, you should dress the tip and reshape it to clean metal with a fine file. This can be done with the tip hot so that the refreshed tip can immediately be re-tinned. Excess solder should be wiped away after re-tinning. Steel-clad tips suffer much less corrosion and should never be dressed with a file. Like copper tips, however, they should be cleaned frequently when hot.
textbooks/workforce/Electronics_Technology/Book%3A_Electrical_Fundamentals_Competency_(Industry_Training_Authority_of_BC)/03%3A_Unit_III-_Wiring_Connections/10%3A_Soldering_Techniques/10.03%3A_Soldering_techniques.txt	princeton-nlp/TextbookChapters	Soldering techniques To avoid soldering problems, it is extremely important to work with clean materials and the correct amount of heat. Soldering problems can normally be avoided by bringing the metals to soldering temperature quickly and completing the solder application in a short period of time. You know you have the proper heat when a joint can be completed in about two seconds. The heat will transfer most effectively to the work if a clean tip is lightly tinned with a film of solder. The film of solder will create a bridge between the iron and soldering surfaces by flowing into all gaps. Sometimes a small amount of solder must be added to help form this bridge by applying a small drop to the iron’s tip before applying it to the work surfaces. Although learning the theories of good soldering is important in developing soldering skills, good soldering is primarily learned through practice. Holding the iron and applying it and the solder to the work surface must be done using techniques that are comfortable and natural to each individual. How you do the job is unimportant as long as the end result is a quality soldered joint with no damage to the surrounding components and materials. At every opportunity, you should experiment with different techniques, always making certain that your soldering meets the requirements of effective soldering listed earlier. Procedures To solder effectively, follow these procedures: 1. Follow safety precautions. Always wear safety glasses with side shields when soldering. Ensure adequate ventilation or use solder fume extraction hoods to prevent accumulation of solder fumes. Wear closed-toed shoes and clothing made of natural fibres, with long sleeves and long trouser legs to protect against burns from solder splashes. Avoid touching the solder pencil tip or freshly soldered joints. Use an iron holder and allow the iron to cool completely before putting it away. Never solder on equipment that has power supplied to it. Before eating, drinking, or smoking, always wash your hands to avoid accidentally ingesting lead. 2. Clean and tin host materials. The materials to be soldered (leads, pads, terminals, etc.) must be clean and tinned. Inspect all host metals and clean them to remove contaminants such as oxides, machine oil, hand lotion, and skin oils. Avoid touching cleaned surfaces. Most component leads and hookup wires are factory tinned. Copper parts and solder pads that are untinned should be cleaned and tinned separately. To tin a surface, clean it and then heat the surface with a soldering tip. Apply the solder to the surface and allow a thin coating to form on the surface. Allow the surface to cool. When tinning stranded insulated wires, strip the wire to the appropriate length for the joint being made. Tin the wire, using only enough solder to make the stripped wire solid. The strands of wire should be visible through the solder. Avoid solder from wicking in the wire underneath the insulation. When tinning and soldering, make a solder bridge to increase the linkage area and speed heating of the surface or joint (Figure 5). 1. Cross-section view of iron tip on a round lead - “X” shows point of contact 1. Form a mechanical joint between the host metals. 2. Needle-nose pliers used as a heat sink 1. Allow the connection to cool undisturbed. 3. Steps to solder conductors to turret terminals 4. Soldering procedures for cup terminals 5. Correctly soldered connection Soldering defects The following characteristics are unacceptable in a solder joint: • charred, burned, or melted insulation or parts • excessive solder, including peaks, icicles, and bridging • flux residue, solder splatter, or other foreign materials on circuitry of adjacent areas • insufficient solder • pits, holes, or voids or exposed base metal in the soldered connection • fractured or cracked solder connection or evidence of grain change • cut, nicked, gouged, or scraped conductors • improper conductor length During the soldering process, you must be very careful to avoid defects in the solder joint itself. Soldering defects primarily reduce the efficiency of the electrical connection between the metals to be joined. Cold solder joint A cold solder joint occurs when the component leads have not been heated sufficiently. A lack of heat in the metals to be joined will reduce or eliminate proper wetting of the surfaces, as described earlier. Insufficient wetting will cause the solder to pile up on the joint surface rather than flow smoothly through the joint. An efficient electrical connection between the metals to be joined will not be made, resulting in resistance to current flow through the joint. Cold joints commonly result from applying solder to the soldering iron’s tip rather than to the joint to be soldered. When the solder is touched to the iron rather than to the joint, the solder will melt before the joint has heated sufficiently. The melted solder will flow over the joint, but will not properly wet it. Unless heat is maintained well after the solder flows over the joint, a cold solder joint will usually occur. The major indicator of a cold solder joint is a frosty appearance to the surface of the solder. In some instances, reheating the joint adequately will correct a cold joint. If the surface stays frosty, the used solder must be removed and the joint resoldered using correct procedures. Fractured joint A fractured joint occurs during the cooling process when the soldered joint is moved while the solder is in its plastic state. Movement during the plastic state will have a crystallizing effect on the solder and a very rough, inefficient joint will result. The usual cause of a fractured joint is a poor mechanical connection of the metals before soldering begins. Components must be mounted firmly before soldering begins. Reheating usually cures a fractured joint, but the addition of a small amount of fresh solder may be needed to reflux the exposed metals. Rosin joint A rosin joint occurs when part of the joint has been heated enough to melt the flux and coat the metals, but not enough to cause the solder to flow. The covering of flux acts as an insulator and consequently provides a very poor electrical connection or no connection at all. Reheating and applying a small drop of fresh solder will often cure a rosin joint. Now complete the Learning Task Self-Test. 10.E: Self-Test 2 Self-Test 2 1. Safety factors such as toxic fumes and splashing flux should always be addressed when soldering. 1. True 2. False 2. Which of the following best describes the process of surface penetration? 1. Bonding 2. Wetting 3. Soldering 4. Prepping 3. Which of the following should apply when tinning stranded wire? 1. The strands should be thickly coated. 2. The strands should be visible under the solder. 3. The solder should wick up underneath the insulation. 4. A large blob of solder should form at the end of the wire. 4. Metals like aluminum and iron wet easily. 1. True 2. False 5. What is the purpose of flux? 1. To remove oxides 2. To clean the metal 3. To assist with heating 4. To remove the solder 6. What is the most common alloy used for solder? 1. Tin-lead 2. Lead-silver 3. Tin-copper 4. Lead-copper 1. Soldering pencils are used for heavy-duty applications. 1. True 2. False 2. What must be done to a soldering tip prior to soldering? 1. Tin it. 2. Wash it. 3. Wire brush it. 4. Heat it red hot. 3. What should be done to an overly corroded soldering tip? 1. Nothing. 2. Re-tin it. 3. Throw it away. 4. Dress it with a fine file. 4. What is the purpose of a heatsink? 1. To protect the solder 2. To pull flux to the joint 3. To pull heat to the area for soldering 4. To pull heat away from certain components 5. What would cause a solder joint to be piled up and lumpy in appearance? 1. Insufficient heat 2. Lack of flux 3. Poor tinning 4. A corroded tip 11: Answer Key Answer Key Self-Test 1 1. c. Conductor 2. d. Multiple insulated wires grouped together in a common sheathing 3. c. To prevent unwanted current flow 4. d. When flexibility is needed 5. b. False 6. b. It should be tinned. 7. b. False 8. d. It can be removed easily. 9. b. False 10. c. Crimp-on Self-Test 2 1. a. True 2. b. Wetting 3. b. The strands should be visible under the solder. 4. b. False 5. a. To remove oxides 6. a. Tin-lead 7. b. False 8. a. Tin it. 9. d. Dress it with a fine file. 10. d. To pull heat away from certain components 11. a. Insufficient heat 14: Answer Key Answer Key Self-Test 1 1. c. Resistance 2. b. False 3. b. 2.2 V 4. b. False 5. c. A negative voltage would be read. 6. c. Using the one-hand technique 7. b. False 8. b. False 9. a. Series 10. c. After checking resistance 11. a. 0 12. c. 2125 Ω 13. c. Continuity test Self-Test 2 1. c. 50 mA 2. a. Open 3. d. The load has failed. 4. c. The wiring has failed. 5. a. The load has failed. 6. d. Turn the circuit power off. 7. b. Continuity test 8. a. Voltage
textbooks/workforce/Electronics_Technology/Book%3A_Trigonometry_and_Single_Phase_AC_Generation_for_Electricians_(Flinn)/01%3A_Trigonometry/1.01%3A_Angles.txt	princeton-nlp/TextbookChapters	To have a good grasp of electrical theory it is important to have a grasp of trigonometry. Whether we are talking about single phase or polyphase power, trigonometry is a key concept. The first part of this textbook will look at one of the most basic parts of trigonometry: the triangle. • 1.1: Angles Before we even get into trigonometry, we need to discuss angles. • 1.2: Triangles Learning about electrical theory necessitates the study of triangles. More specifically: right triangles. Before we dig too much into the right triangle, let’s go over two key points about triangles: All triangles have three sides and All triangles contain 180 degrees. • 1.3: Pythagoras The Pythagorean theorem, also known as Pythagoras’ theorem, is a relation in Euclidean geometry among the three sides of a right triangle. ‘It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. • 1.4: Naming Right Triangle Sides Trigonometry is the study of the relationship that exists between the sides and the angles of a triangle. • 1.5: Trigonometry Functions When determining the designate angle we can use different ratios of sides: (1) We can use a ratio of the opposite to the hypotenuse. (2) We can use a ratio of the adjacent to the hypotenuse. (3) We can use a ration of the opposite to the adjacent. • 1.6: Power and Impedance Triangles When dealing with DC circuits the only thing that opposes current is the resistance in the circuit. As we will learn in later units, AC adds a component that opposes current as well. This is called reactance and it runs 90 degrees to the circuit resistance. This means it is not possible to add them together arithmetically; it has to be done using the Pythagoras’ theorem. When you add these two together, you get a total opposition to current flow called impedance. 01: Trigonometry What’s the deal with angles anyway? Before we even get into trigonometry, we need to discuss angles. Don’t worry. Things are not going to get too crazy. I promise. Let’s go over the basics first. Degree. One-three-hundred-and-sixtieth of the circumference of a circle. It is also the unit by which we measure angles. Figure 1. Degrees Angle. This is the space between two intersecting lines. Figure 2. Angle Complementary angles. These are two angles whose sum equals 90 degrees. Figure 3. Complementary angle Supplementary angles. These are two angles whose sum equals 180 degrees. Figure 4. Supplementary angle Acute angle. An angle that is less than 90 degrees. Figure 5. Acute angle Obtuse angle. An angle that is greater than 90 degrees. Figure 6. Obtuse angle Similar angles. It is possible for triangles to each have different sized sides but share the same sized angles. These are called similar angles. Figure 7. Similar angles Right angle. This is an angle that is 90 degrees. Figure 8. Right angle There is a ton of information about angles that we don’t need to get into. Remember: Try not to overcomplicate things. Just focus on the basics and you’ll be fine. 1.02: Triangles Why triangles are important Learning about electrical theory necessitates the study of triangles. More specifically: right triangles. Before we dig too much into the right triangle, let’s go over two key points about triangles. • All triangles have three sides. (File this fact under the “thank you Captain Obvious” category.) • All triangles contain 180 degrees. Figure 9. Triangle Different triangles The right triangle is the most common triangle that will be used in electrical theory. It is a good idea to have a basic understanding of other triangles as well. Here are some common triangles you will come across in trigonometry. Isosceles triangle. This triangle has two sides that are equal, and two angles that are equal. Figure 10. Isosceles triangle Equilateral triangle. All three sides of this triangle are equal, and all three of its angles are equal too. Figure 11. Equilateral triangle Similar triangles. These triangles each have different sized sides, but they share the same sized angles. Figure 12. Similar triangles So what about these right triangles you were talking about? A right triangle is a triangle that has one right angle (equal to 90 degrees). This means that the other two angles are complementary, that is, they must add to 90 degrees. Figure 13. Complementary angles. Ok, so what does a right triangle have to do with electrical? Quite a bit actually. In the world of electrical theory, we will have to add up values. We call these units vectors (more on the concept of vectors in a later chapter). These vectors each head in a different direction. In fact, they are 90 degrees to each other. When we add them, the sum of these two vectors ends up being the point between the two sides. Figure 14. Vector triangle Because they are not heading in the same direction (they are heading in directions that are 90 degrees to each other) we can’t add them up normally. They have to be added vectorially. How do you do this? I’m glad you asked.
textbooks/workforce/Electronics_Technology/Book%3A_Trigonometry_and_Single_Phase_AC_Generation_for_Electricians_(Flinn)/01%3A_Trigonometry/1.03%3A_Pythagoras.txt	princeton-nlp/TextbookChapters	Who is this Pythagoras and why does he matter? Pythagoras was a Greek philosopher who lived around 500 BC. He is credited as being a philosopher and mathematician. Much of what we know of Pythagoras is from writings that were copied down hundreds of years after his death, so the validity of what we do know is questionable. He is credited with Pythagoras’ theorem when actually it has been proven that Babylonians and Indians were using variations of it for hundreds of years before he even came along. More can be found about him in this article. Thanks for the history lesson, but get on with it! The Pythagorean theorem, also known as Pythagoras’ theorem, is a relation in Euclidean geometry among the three sides of a right triangle. ‘It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It’s not as bad as it seems. Basically, the Pythagoras’ theorem says that you can figure out any side of a right triangle as long as you have the other two sides, using the equation: \[A^2 + B^2 = C^2\] When we look at the formula, there is one important thing to remember: $C$ is always the longest side. $A$ and $B$ can be swapped around, but when using this formula, $C$ is always the longest side (which is also the side opposite the 90-degree angle). Figure 15. Longest side triangle Video! This video walks through how to apply Pythagoras’ theorem on a right triangle. 1.04: Naming Right Triangle Sides What is this big fancy word, trigonometry? Trigonometry is the study of the relationship that exists between the sides and the angles of a triangle. That sounds complicated and scary. It can be, but lucky for us we are only dealing with right triangles. This makes it very simple and almost fun. (Nerd alert!) First steps We have already learned how to determine the sides of a triangle using the Pythagoras’ theorem. Next up is using those sides to determine the angles. Lucky for us we know that in a right triangle we already have one 90-degree angle. We also know that if we can solve any of the other two angles, the third one is easy. (All triangles have 180 degrees.) Our next step is to name the sides of the triangle. The names of these sides are dependent on something called the designate angle or theta. Theta is an angle that you determine or is determined for you. Figure 16. Theta 1 Figure 17. Theta 2 Now once you have figured out which angle is your theta, we can get to business naming the sides. Adjacent. This is the side that sits adjacent to the designate angle. Opposite. This is the side that sits opposite to the designate angle. Hypotenuse. This is the side that sits opposite the 90-degree angle. The hypotenuse is always the longest side of the triangle and doesn’t care where the designate angle is. It only cares that it is opposite the 90-degree angle. Figure 18. Hypotenuse And if we switch the designate angle, the names of the sides change as in Figure 19. Figure 19. Adjacent and Opposite sides switch places The next chapter tells us what to do with these names.
textbooks/workforce/Electronics_Technology/Book%3A_Trigonometry_and_Single_Phase_AC_Generation_for_Electricians_(Flinn)/01%3A_Trigonometry/1.05%3A_Trigonometry_Functions.txt	princeton-nlp/TextbookChapters	When determining the designate angle we can use different ratios of sides. • We can use a ratio of the opposite to the hypotenuse. • We can use a ratio of the adjacent to the hypotenuse. • We can use a ration of the opposite to the adjacent. Each ratio has a trigonometric function that helps turn the ratio into an angle. They are: • sin θ = opposite/hypotenuse • cos θ = adjacent/hypotenuse • tan θ = opposite/adjacent One way of remembering the ratios are these mnemonics: • SOH – Sine is opposite/ hypotenuse • CAH – Cosine is adjacent/hypotenuse • TOA – Tangent is opposite/ adjacent By the way, • sin is short for sine • cos is short for cosine • tan is short for tangent Video! This video walks through how to determine the angle of a right triangle when you have two sides. A YouTube element has been excluded from this version of the text. You can view it online here: https://pressbooks.bccampus.ca/trigf...tricians/?p=34 1.06: Power and Impedance Triangles What is going on here? This is the point where I am going to ask you to take my hand and to trust me. Okay, you don’t have to take my hand, but you do have to trust me. We are going to start using some terms before totally going into the theory behind them. I promise that we will get more in-depth into these concepts in future lessons. Impedance triangles When dealing with DC circuits the only thing that opposes current is the resistance in the circuit. Figure 20. DC resistive circuit As we will learn in later units, AC adds a component that opposes current as well. This is called reactance and it runs 90 degrees to the circuit resistance. This means it is not possible to add them together arithmetically; it has to be done using the Pythagoras’ theorem. When you add these two together, you get a total opposition to current flow called impedance. Figure 21. DC inductive circuit The triangle that is created when adding the resistance to the reactance is known as an impedance triangle. Figure 22. Impedance triangle In an impedance triangle, the resistance (r) is always on the bottom of the triangle, the reactance (x) always goes on the side and the hypotenuse is always the impedance (z). Power triangles When dealing with a purely resistive circuit, the power being dissipated is in the form of heat or light and is measured in watts and is known as true or active power. It is a product of I2R. Figure 23. Resistive power circuit In an AC circuit with inductance, watts are still present. There is also a reactive power present as current passes across the reactance. This power is called reactive power and is also called wattless or quadrature power. Its unit is the Vars. Figure 24. Inductive power circuit Much like the impedance triangle, we can not just add the two powers together to get overall power. They must be added using the Pythagoras’ theorem. Their sum is equal to the apparent power (VA). Figure 25. Power triangle When calculating for reactive power, we are still able to use the power formulas. We just have to use them with reactance instead of resistance. • I2X = Vars • E2 (inductor voltage) /X = Vars • I x E (inductor voltage) = Vars Remember When building an impedance or power triangle, the resistive component always goes on the bottom of the triangle and the reactive component always goes on the side.
textbooks/workforce/Electronics_Technology/Book%3A_Trigonometry_and_Single_Phase_AC_Generation_for_Electricians_(Flinn)/02%3A_Vectors/2.01%3A_A_Vector_Primer.txt	princeton-nlp/TextbookChapters	• 2.1: A Vector Primer A vector is a quantity that possesses magnitude and direction. As an example, let’s say I roundhouse kicked you in the head. The magnitude of the force and the angle at which I kicked you would be a vector. • 2.2: Quadrants A quadrant is a circle cut into four parts. • 2.3: Polar vs. Rectangular Form When dealing with vectors, there are two ways of expressing them. Up to this point, we have used a magnitude and a direction such as 30 V @ 67°. This is what is known as the polar form. It is more often the form that we like to express vectors in. • 2.4: Vector Addition When adding vectors, we have to find some common ground. This is why we focus on the X and Y coordinates. Each vector can be broken down into X and Y coordinates. This allows us to find some common ground as the X coordinates are heading in the same direction and the Y coordinates are heading in the same direction. Thumbnail: Vector in a Cartesian coordinate system. (CC BY-SA 4.0 unported; Acdx). 02: Vectors What is a vector? A vector is a quantity that possesses magnitude and direction. As an example, let’s say I roundhouse kicked you in the head. The magnitude of the force and the angle at which I kicked you would be a vector. I know what you’re thinking: “This electrical stuff sounds cool.” And you’d be right. Image retrieved from pixabay.com. Used under Creative Commons CC0 license. Aside from helping me become a fighting machine, how do vectors have anything to do with electricity? AC values are constantly changing magnitude and direction. We will talk about this more in-depth in the AC generation portion of the course. Eventually, we will be required to add these values together. The sum of the vectors is called the resultant. This is all well and good when vectors are heading in the same direction… Figure 26. Vectors in the same direction … because you can just add them together. Figure 27. Vectors in the opposite direction It isn’t even bad if they are heading in the opposite direction. You can just subtract them. The only thing when adding them in opposite directions is that you have to pay attention to which vector has the greatest value. This will become the new direction of the sum of the vectors. The problem arises when they are heading in completely different directions. Figure 28. Vectors moving in different direction How did you do that? Trust me, it is not difficult. In order to figure out how to add vectors, we first have to talk about the quadrant system. 2.02: Quadrants Like a Star Trek quadrant? First off: Nerd alert! Secondly, yes, a quadrant is a circle cut into four parts. What does this have to do with electricity? Voltage and currents are constantly changing magnitude and direction. When changing direction, they actually rotate in a counterclockwise direction. They are tethered to a point of origin. Figure 29. Quadrant point of origin Each quadrant contains certain directions. • Quadrant 1 has 0 to 90 degrees. • Quadrant 2 has 90 to 180 degrees. • Quadrant 3 has 180 to 270 degrees. • Quadrant 4 has 270 to 360 degrees. This is very important as it helps us to determine which vectors belong in which quadrant. Polarity It is also important to understand polarity when dealing with quadrants. A quadrant system is basically an X-Y graph. We use the point of origin as a reference point. On the X axis, anything to the right of the point of origin is positive and anything to the left is negative. On the Y axis, anything above the point of origin is positive and anything underneath it is negative. This means each quadrant has its own polarity, as shown in Figure 30. Figure 30. Quadrant polarity This too is extremely important when it comes to adding vectors. Are you getting excited yet? This is all going to come together in one magical dance. Video! This video goes into greater detail about the specifics of all four quadrants.
textbooks/workforce/Electronics_Technology/Book%3A_Trigonometry_and_Single_Phase_AC_Generation_for_Electricians_(Flinn)/02%3A_Vectors/2.03%3A_Polar_vs._Rectangular_Form.txt	princeton-nlp/TextbookChapters	Polar form When dealing with vectors, there are two ways of expressing them. Up to this point, we have used a magnitude and a direction such as 30 V @ 67°. This is what is known as the polar form. It is more often the form that we like to express vectors in. Rectangular form Rectangular form breaks a vector down into X and Y coordinates. In the example below, we have a vector that, when expressed as polar, is 50 V @ 55 degrees. The first step to finding this expression is using the 50 V as the hypotenuse and the direction as the angle. Next, we draw a line straight down from the arrowhead to the X axis. What does this look like to you? If you said right triangle, give yourself a pat on the back. We then can use the angle and the hypotenuse to determine the X axis with these equations: • cos 55°×50 = 28.7 for the X axis • sin 55°×50 = 41 for the Y axis This is accomplished just by transposing the ratios from what we learned previously in trigonometry. Figure 31. Quadrant 1 We then can express the same vector as 28.7, j 41. Where did that j come from? The letter j is put in front of the y component to indicate the difference between the X and the Y. The reason j is used is this. As a way of telling the difference between X and Y, it was decided that a letter should be put in front of the Y. The X and Y components don’t really exist, and are referred to as imaginary numbers. Because each is an imaginary number, the letter i was suggested. However, the letter i is also used as a symbol for current, so it was decided to go with the letter j instead. Why polarity is important Let’s look at another example. The polar form is 60 V @ 140 degrees. This puts the vector in the second quadrant. In the second quadrant, X is – (negative) and Y is + (positive). The angle of 140° is used from the 0° point. To use trigonometry, we need to determine what the angle is in reference to the X axis. In this example, it is 40° (the supplement of 140°). After that, we can use trigonometry to determine the X and Y components. • cos 40°×60 = 46 for the X axis • sin 40°×60 = 39 for the Y axis Figure 32. Quadrant 2 If we are going to express it in rectangular form, use -46, j39. Remember that the X component is negative and the Y component is positive as they are in the second quadrant. Video! This video walks through how to convert from polar form to rectangular form. 2.04: Vector Addition A quick recap There was a fair bit to wrap our heads around before we finally got into vector addition. Here are some of the key points: • Vectors contain magnitude (resultant) and direction (angle). • Each vector can be broken into X and Y coordinates. • We must use a quadrant system to chart the X and Y coordinates. • Pay attention to the polarity (what quadrant is it in?). • Vectors can be expressed in the polar form (resultant and angle) or rectangular form (X and Y coordinates). • Base your angle off of the X axis. • When converting from rectangular to polar, it is extremely important to pay attention to what quadrant you are in. • Quadrant 1 is the angle you calculate. • Quadrant 2 is 180 minus the angle you calculate. • Quadrant 3 is 180 plus the angle you calculate. • Quadrant 4 is either 360 minus the angle you calculate, or, put a negative in front of the angle you calculate. Okay, let’s learn how to add vectors. Adding vectors When adding vectors, we have to find some common ground. This is why we focus on the X and Y coordinates. Each vector can be broken down into X and Y coordinates. This allows us to find some common ground as the X coordinates are heading in the same direction and the Y coordinates are heading in the same direction. Let’s look at the example in Figure 39. In this example, we have one vector that is 38 V @ 20 degrees and another that is 100 V @ 135 degrees. Figure 39. Adding vectors The first step is to draw in the X and Y axes. (See Figure 40.) This will help provide us with a reference when determining our X and Y coordinates. Figure 40. Adding vectors draw quadrant Next we will work out the X and the Y for each vector, in Figure 41. Figure 41. Adding vectors determining X and Y Next add an X-Y chart and enter the coordinates (Figure 42). Figure 42. Adding vectors X and Y chart Add up your X coordinates and your Y coordinates and you have your answer in rectangular form (Figure 43). Figure 43. Adding vectors for rectangular form Take your rectangular form and chart it on its own (Figure 44). Figure 44. Adding vectors for polar form Take the resultant and the angle, and convert it to polar form: 90.6 @ (180°−68°)90.6 @ 112°. There you have it. If you have more vectors, you just keep adding other rows to your X-Y chart. Video! This video walks through how to add vectors heading in completely different directions.
textbooks/workforce/Electronics_Technology/Book%3A_Trigonometry_and_Single_Phase_AC_Generation_for_Electricians_(Flinn)/03%3A_AC_Generation/3.01%3A_Electromagnetic_Induction.txt	princeton-nlp/TextbookChapters	• 3.1: Electromagnetic Induction Electromagnetic induction is when a voltage is created by passing a conductor through a magnetic field. • 3.2: The Alternator We have established that if we have a conductor pass through a field or a field through a conductor a voltage is established. This means that voltage is only established when there is constant motion. Instead of having someone passing a conductor through a field rapidly, it was discovered that the conductor could be formed into a loop and rotated through the field to maintain a voltage. This would be an example of what is known as a simple alternator. • 3.3: How a Waveform Is Generated Any time you pass a conductor through a magnetic field, you induce a voltage. If we take that conductor and turn it into a loop and spin it continually through that magnetic field, we have created an alternator. This means that a voltage will constantly be induced. However, this is not a flat line voltage like direct current. It creates an oscillating voltage that rises and falls. • 3.4: AC Waveform Analysis Well, it turns out that there is an awful lot going on in that waveform. Most of it is actually useful as well. • 3.5: Frequency and Alternators In the last chapter, we learned the term cycle means from the point in a waveform to where the waveform starts to repeat itself. When we discuss the term frequency, we are referring to how many cycles can occur in one second. Frequency is measured in hertz or CPS (cycles per second). Two factors affect the frequency in an alternator: rotation speed and the number of poles. Thumbnail: Simple Alternator 03: AC Generation What is this electromagnetic induction of which you speak? Electromagnetic induction is when a voltage is created by passing a conductor through a magnetic field. Figure 45. Magnetic poles and induction The size of the voltage can be varied by three factors: 1. The size of the magnetic field. The more flux lines there are, the more flux lines there are for the conductor to cut. The strength of flux is directly proportional to the induced voltage. 2. The active length of the conductor. Active length meaning the part of the conductor that actually passes through the field. The active length is directly proportional to the induced voltage. 3. The speed at which the conductor passes through the field. The faster the conductor passed through the field, the greater the voltage induced. The speed is directly proportional to the induced voltage. These relationships to voltage can be broken into this formula: \[e = βlv.\] Where: • $e$ = peak voltage induced in the inductor (volts) • $B$ = field strength between the poles (Tesla) • $l$ = active length of conductor (meters) • $v$ = velocity of the conductor through the field (m/sec) Example $1$: A conductor that has an active length of 4 meters passes through a field of 5 Tesla at a speed of 15 meters per second. Determine the peak voltage induced on this conductor. Solution (4 m)(5 T)(15 m/sec) = 300 volts peak That’s crazy! Who discovered that? The discovery of electromagnetic induction is attributed to Michael Faraday who discovered that when he passed a magnetic field through a conductor a current would flow. As long as there was motion between the field and the conductor, a voltage could be induced. This could mean the conductor passes through a field or a field passed through a conductor.
textbooks/workforce/Electronics_Technology/Book%3A_Trigonometry_and_Single_Phase_AC_Generation_for_Electricians_(Flinn)/03%3A_AC_Generation/3.02%3A_The_Alternator.txt	princeton-nlp/TextbookChapters	How do we keep the voltage coming? We have established that if we have a conductor pass through a field or a field through a conductor a voltage is established. This means that voltage is only established when there is constant motion. Instead of having someone passing a conductor through a field rapidly, it was discovered that the conductor could be formed into a loop and rotated through the field to maintain a voltage. This would be an example of what is known as a simple alternator. A simple alternator has two magnetic poles that establish a magnetic field. The conductor (armature) rotates through this field to establish a voltage. Figure 46. Simple alternator A practical alternator has a stationary conductor and the field rotates. Figure 47. Practical alternator What are the parts of the alternator? Figure 48. Simple alternator parts Figure 49. Practical alternator parts Armature. This part is what the voltage is induced on to. It can be rotating (simple alternator) or stationary (practical alternator). Slip rings. Made of brass, they rotate and either bring current to the load (simple alternator) or excitation to the field (practical alternator). Brushes. Made of graphite carbon, they are stationary and either pass current to the load (simple alternator) or current to the field (practical alternator). Field poles. They are either stationary (simple alternator) or rotating (practical alternator). Prime mover. This part spins the armature (simple) or the field (practical). Examples include: • combustion engine • hydro dam • hand crank • windmill Which is better the simple or the practical? If you guessed the practical, you would be right. The brushes of a simple alternator have to be sized for the load. If you have a large load that draws a lot of current, then your brushes would have to be sized accordingly. Whereas, with the practical alternator the brushes bring current to the field and can be small yet still allow enough current to adjust the field. With either alternator, the easiest way to adjust the voltage is by varying the field strength. It is possible to vary the speed on the alternator to adjust the voltage, but this will also change the frequency. 3.03: How a Waveform Is Generated AC generation with an alternator If Faraday has taught us anything it is this: Any time you pass a conductor through a magnetic field, you induce a voltage. If we take that conductor and turn it into a loop and spin it continually through that magnetic field, we have created an alternator. Figure 50. Alternator picture This means that a voltage will constantly be induced. However, this is not a flat line voltage like direct current. It creates an oscillating voltage that rises and falls. Is this what you mean by sine wave generation? Yup, this is exactly what I mean. As the conductor spins through the field, there will be times that it does not cut any lines of flux. There will be times when it cuts some of the lines of flux, and there will be times that it is cutting the maximum amount of flux lines that it can. This means that at some point during the sine wave generation there will be no voltage generated. Then there will be some voltage generated, and then there will be a maximum voltage generated. This creates this thing of beauty. A sine wave. Figure 51. Sine wave Oh yeah, I think I have seen that before This wave pattern occurs often in nature, including ocean waves, sound waves and light waves. In fact, if you take the hours of daylight in a day and graph it out with the months of the year, guess what? A sine wave is generated. If you’d like to read an interesting article on the seasons and sine wave generation, read Calculus of the seasons. Isn’t nature cool? But I digress. This sine wave is extremely important when it comes to electrical generation. Future postings will discuss its importance and go into in-depth analysis of the waveform. Video! This video explains how a sine wave is generated in an alternator.
textbooks/workforce/Electronics_Technology/Book%3A_Trigonometry_and_Single_Phase_AC_Generation_for_Electricians_(Flinn)/03%3A_AC_Generation/3.04%3A_AC_Waveform_Analysis.txt	princeton-nlp/TextbookChapters	What fun can we have with that waveform? Well, it turns out that there is an awful lot going on in that waveform. Most of it is actually useful as well. Video! This video shows all that is happening in the sine wave. To Recap • Average (1 alternation) = .639 × peak • Instantaneous = sin θ × peak • Effective (RMS) = .707 × peak 3.05: Frequency and Alternators In the last chapter, we learned the term cycle means from the point in a waveform to where the waveform starts to repeat itself. When we discuss the term frequency, we are referring to how many cycles can occur in one second. Frequency is measured in hertz (shout out to Heinrich Hertz) or CPS (cycles per second). Two factors affect the frequency in an alternator: rotation speed and the number of poles. Figure 52. Sine wave cycle Rotation speed As the armature rotates through the field, it starts to create a waveform (as we saw in the last chapter). One full mechanical rotation of the armature creates one full sine wave on a two-pole alternator. If the two-pole alternator spins three complete revolutions in one second, it will create three full sine waves in that one second. We would say that the frequency is at three cycles per second or three hertz (as the cool kids say). A machine’s rotational speed is measured in rotations per minute or RPM. However, we are not concerned with minutes, but rather, with seconds when dealing with frequency. Therefore, RPM must be converted to rotations per second (RPS). As there are 60 seconds in a minute, all we have to do is to divide the RPM by 60 to convert it to RPS. For example, if the armature is spinning at a rate of 1800 RPM on a two-pole alternator, we can say that it is spinning at 30 rotations per second. If this alternator has two poles, then in one second it will generate 30 cycles of voltage. It then could be said to have a frequency of 30 cycles per second or 30 Hertz. The frequency of an alternator is directly proportional to the rotational speed of the alternator. Number of Poles If we add poles to the alternator, we can change the frequency. In a two-pole alternator, Side A of the armature (Figure 53) passes from north to south, and then south to north, to create one complete sine wave. I f we add two more poles, as in Figure 54, then Side A of the armature will move past two north poles and two south poles in one full mechanical revolution. Figure 53. Two pole alternator Two full sine waves are created in one complete mechanical revolution. If a two-pole alternator creates one cycle of voltage in one second (or one hertz of frequency), a four pole alternator will create two cycles of voltage in one second (or two hertz). The frequency of an alternator is directly proportional to the number of poles in the alternator. Figure 54. Four pole alternator Formula time! Knowing that rotation speed is directly proportional to frequency and that the number of poles is directly proportional to frequency, we can use a formula. The formula looks like this: $f= \dfrac{P}{2} \times \dfrac{N}{60} \tag{Frequency formula}$ where… • $f$ = frequency in hertz • $P$ = number of poles • $N$ = rotational speed in RPM We divide the number of poles by two because there will always be a set of two poles. You can’t have a north pole without a south. We divide the RPM by 60 because we are concerned with rotations per second, not rotations per minute. The formula in Figure 56 can be combined to look like this: $f = \dfrac{PN}{120} \tag{Combined frequency formula}$ Video! This video will walk you through how frequency is related to the RPM and the number of poles of an alternator. A YouTube element has been excluded from this version of the text. You can view it online here: https://pressbooks.bccampus.ca/trigf...ricians/?p=278
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/01%3A_Lesson_1/1.01%3A_Safety.txt	princeton-nlp/TextbookChapters	Nothing should be more important to you than your own safety. Think about Charlie Morecraft. A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=25 He had an industrial accident that left him in the hospital for about five years. Think about that. A shortcut in safety procedures left him in the hospital for five. Long. Years.Charlie had to open a valve on a petroleum line. It was a routine task he’d done “a thousand times” before. It was messy and difficult. The valves leaked and were sticky, but management had planned to replace the valves, and they put a safe procedure in place to ensure the valves could be operated without danger to the operator. Spoiler alert: Charlie didn’t follow the procedure. Charlie worked on the valve without his safety glasses, and the valve leaked. Charlie didn’t bother trying to control the petroleum leak (“this will just take a minute”), and it got worse. When Charlie completely actuated the valve, it sprayed material into his face and soaked his clothes. Now blinded, he ran past his truck toward a nearby safety shower. Unfortunately, Charlie left the truck running (against procedure), and it ignited the vapors, engulfing Charlie in a ball of fire. When you think about taking shortcuts at work, remember Charlie. The work we do is dangerous, and while I can never watch Mehdi Sadaghar (an electrical engineer who does unsafe things with electricity) without laughing, we have to remember that electricity can be fatal, and you never want to be involved in an arc flash incident. A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=25 Shock Current Path As we’ve already learned, electricity requires a complete path (circuit) to continuously flow. This is why the shock received from static electricity is only a momentary jolt: the flow of electrons is necessarily brief when static charges are equalized between two objects. Shocks of self-limited duration like this are rarely hazardous. Without two contact points on the body for current to enter and exit, respectively, there is no hazard of shock. This is why birds can safely rest on high-voltage power lines without getting shocked: they make contact with the circuit at only one point. In order for electrons to flow through a conductor, there must be a voltage present to motivate them. Voltage, as you should recall, is always relative between two points. There is no such thing as voltage “on” or “at” a single point in the circuit, and so the bird contacting a single point in the above circuit has no voltage applied across its body to establish a current through it. Yes, even though they rest on two feet, both feet are touching the same wire, making them electrically common. Electrically speaking, both of the bird’s feet touch the same point, hence there is no voltage between them to motivate current through the bird’s body. This might lend one to believe that its impossible to be shocked by electricity by only touching a single wire. Like the birds, if we’re sure to touch only one wire at a time, we’ll be safe, right? Unfortunately, this is not correct. Unlike birds, people are usually standing on the ground when they contact a “live” wire. Many times, one side of a power system will be intentionally connected to earth ground, and so the person touching a single wire is actually making contact between two points in the circuit (the wire and earth ground): The ground symbol is that set of three horizontal bars of decreasing width located at the lower-left of the circuit shown, and also at the foot of the person being shocked. In real life the power system ground consists of some kind of metallic conductor buried deep in the ground for making maximum contact with the earth. That conductor is electrically connected to an appropriate connection point on the circuit with thick wire. The victim’s ground connection is through their feet, which are touching the earth. A few questions usually arise at this point in the mind of the student: • If the presence of a ground point in the circuit provides an easy point of contact for someone to get shocked, why have it in the circuit at all? Wouldn’t a ground-less circuit be safer? • The person getting shocked probably isn’t bare-footed. If rubber and fabric are insulating materials, then why aren’t their shoes protecting them by preventing a circuit from forming? • How good of a conductor can dirt be? If you can get shocked by current through the earth, why not use the earth as a conductor in our power circuits? In answer to the first question, the presence of an intentional “grounding” point in an electric circuit is intended to ensure that one side of it is safe to come in contact with. Note that if our victim in the above diagram were to touch the bottom side of the resistor, nothing would happen even though their feet would still be contacting ground: Because the bottom side of the circuit is firmly connected to ground through the grounding point on the lower-left of the circuit, the lower conductor of the circuit is made electrically common with earth ground. Since there can be no voltage between electrically common points, there will be no voltage applied across the person contacting the lower wire, and they will not receive a shock. For the same reason, the wire connecting the circuit to the grounding rod/plates is usually left bare (no insulation), so that any metal object it brushes up against will similarly be electrically common with the earth. Circuit grounding ensures that at least one point in the circuit will be safe to touch. But what about leaving a circuit completely ungrounded? Wouldn’t that make any person touching just a single wire as safe as the bird sitting on just one? Ideally, yes. Practically, no. Observe what happens with no ground at all: Despite the fact that the person’s feet are still contacting ground, any single point in the circuit should be safe to touch. Since there is no complete path (circuit) formed through the person’s body from the bottom side of the voltage source to the top, there is no way for a current to be established through the person. However, this could all change with an accidental ground, such as a tree branch touching a power line and providing connection to earth ground: Such an accidental connection between a power system conductor and the earth (ground) is called a ground fault. Ground faults may be caused by many things, including dirt buildup on power line insulators (creating a dirty-water path for current from the conductor to the pole, and to the ground, when it rains), ground water infiltration in buried power line conductors, and birds landing on power lines, bridging the line to the pole with their wings. Given the many causes of ground faults, they tend to be unpredictable. In the case of trees, no one can guarantee which wire their branches might touch. If a tree were to brush up against the top wire in the circuit, it would make the top wire safe to touch and the bottom one dangerous—just the opposite of the previous scenario where the tree contacts the bottom wire: With a tree branch contacting the top wire, that wire becomes the grounded conductor in the circuit, electrically common with earth ground. Therefore, there is no voltage between that wire and ground, but full (high) voltage between the bottom wire and ground. As mentioned previously, tree branches are only one potential source of ground faults in a power system. Consider an ungrounded power system with no trees in contact, but this time with two people touching single wires: With each person standing on the ground, contacting different points in the circuit, a path for shock current is made through one person, through the earth, and through the other person. Even though each person thinks they’re safe in only touching a single point in the circuit, their combined actions create a deadly scenario. In effect, one person acts as the ground fault which makes it unsafe for the other person. This is exactly why ungrounded power systems are dangerous: the voltage between any point in the circuit and ground (earth) is unpredictable, because a ground fault could appear at any point in the circuit at any time. The only character guaranteed to be safe in these scenarios is the bird, who has no connection to earth ground at all! By firmly connecting a designated point in the circuit to earth ground (“grounding” the circuit), at least safety can be assured at that one point. This is more assurance of safety than having no ground connection at all. In answer to the second question, rubber-soled shoes do indeed provide some electrical insulation to help protect someone from conducting shock current through their feet. However, most common shoe designs are not intended to be electrically “safe,” their soles being too thin and not of the right substance. Also, any moisture, dirt, or conductive salts from body sweat on the surface of or permeated through the soles of shoes will compromise what little insulating value the shoe had to begin with. There are shoes specifically made for dangerous electrical work, as well as thick rubber mats made to stand on while working on live circuits, but these special pieces of gear must be in absolutely clean, dry condition in order to be effective. Suffice it to say, normal footwear is not enough to guarantee protection against electric shock from a power system. Research conducted on contact resistance between parts of the human body and points of contact (such as the ground) shows a wide range of figures (see end of chapter for information on the source of this data): • Hand or foot contact, insulated with rubber: 20 MΩ typical. • Foot contact through leather shoe sole (dry): 100 kΩ to 500 kΩ • Foot contact through leather shoe sole (wet): 5 kΩ to 20 kΩ As you can see, not only is rubber a far better insulating material than leather, but the presence of water in a porous substance such as leather greatly reduces electrical resistance. In answer to the third question, dirt is not a very good conductor (at least not when its dry!). It is too poor of a conductor to support continuous current for powering a load. However, as we will see in the next section, it takes very little current to injure or kill a human being, so even the poor conductivity of dirt is enough to provide a path for deadly current when there is sufficient voltage available, as there usually is in power systems. Some ground surfaces are better insulators than others. Asphalt, for instance, being oil-based, has a much greater resistance than most forms of dirt or rock. Concrete, on the other hand, tends to have fairly low resistance due to its intrinsic water and electrolyte (conductive chemical) content. Safe Practices If at all possible, shut off the power to a circuit before performing any work on it. You must secure all sources of harmful energy before a system may be considered safe to work on. In industry, securing a circuit, device, or system in this condition is commonly known as placing it in a Zero Energy State. The focus of this lesson is, of course, electrical safety. However, many of these principles apply to non-electrical systems as well. Securing something in a Zero Energy State means ridding it of any sort of potential or stored energy, including but not limited to: • Dangerous voltage • Spring pressure • Hydraulic (liquid) pressure • Pneumatic (air) pressure • Suspended weight • Chemical energy (flammable or otherwise reactive substances) • Nuclear energy (radioactive or fissile substances) Voltage by its very nature is a manifestation of potential energy. In the first chapter I even used elevated liquid as an analogy for the potential energy of voltage, having the capacity (potential) to produce current (flow), but not necessarily realizing that potential until a suitable path for flow has been established, and resistance to flow is overcome. A pair of wires with high voltage between them do not look or sound dangerous even though they harbor enough potential energy between them to push deadly amounts of current through your body. Even though that voltage isn’t presently doing anything, it has the potential to, and that potential must be neutralized before it is safe to physically contact those wires. All properly designed circuits have “disconnect” switch mechanisms for securing voltage from a circuit. Sometimes these “disconnects” serve a dual purpose of automatically opening under excessive current conditions, in which case we call them “circuit breakers.” Other times, the disconnecting switches are strictly manually-operated devices with no automatic function. In either case, they are there for your protection and must be used properly. Please note that the disconnect device should be separate from the regular switch used to turn the device on and off. It is a safety switch, to be used only for securing the system in a Zero Energy State: With the disconnect switch in the “open” position as shown (no continuity), the circuit is broken and no current will exist. There will be zero voltage across the load, and the full voltage of the source will be dropped across the open contacts of the disconnect switch. Note how there is no need for a disconnect switch in the lower conductor of the circuit. Because that side of the circuit is firmly connected to the earth (ground), it is electrically common with the earth and is best left that way. For maximum safety of personnel working on the load of this circuit, a temporary ground connection could be established on the top side of the load, to ensure that no voltage could ever be dropped across the load: With the temporary ground connection in place, both sides of the load wiring are connected to ground, securing a Zero Energy State at the load. Since a ground connection made on both sides of the load is electrically equivalent to short-circuiting across the load with a wire, that is another way of accomplishing the same goal of maximum safety: Either way, both sides of the load will be electrically common to the earth, allowing for no voltage (potential energy) between either side of the load and the ground people stand on. This technique of temporarily grounding conductors in a de-energized power system is very common in maintenance work performed on high voltage power distribution systems. A further benefit of this precaution is protection against the possibility of the disconnect switch being closed (turned “on” so that circuit continuity is established) while people are still contacting the load. The temporary wire connected across the load would create a short-circuit when the disconnect switch was closed, immediately tripping any overcurrent protection devices (circuit breakers or fuses) in the circuit, which would shut the power off again. Damage may very well be sustained by the disconnect switch if this were to happen, but the workers at the load are kept safe. It would be good to mention at this point that overcurrent devices are not intended to provide protection against electric shock. Rather, they exist solely to protect conductors from overheating due to excessive currents. The temporary shorting wires just described would indeed cause any overcurrent devices in the circuit to “trip” if the disconnect switch were to be closed, but realize that electric shock protection is not the intended function of those devices. Their primary function would merely be leveraged for the purpose of worker protection with the shorting wire in place. Since it is obviously important to be able to secure any disconnecting devices in the open (off) position and make sure they stay that way while work is being done on the circuit, there is need for a structured safety system to be put into place. Such a system is commonly used in industry and it is called Lock-out/Tag-out. A lock-out/tag-out procedure works like this: all individuals working on a secured circuit have their own personal padlock or combination lock which they set on the control lever of a disconnect device prior to working on the system. Additionally, they must fill out and sign a tag which they hang from their lock describing the nature and duration of the work they intend to perform on the system. If there are multiple sources of energy to be “locked out” (multiple disconnects, both electrical and mechanical energy sources to be secured, etc.), the worker must use as many of his or her locks as necessary to secure power from the system before work begins. This way, the system is maintained in a Zero Energy State until every last lock is removed from all the disconnect and shutoff devices, and that means every last worker gives consent by removing their own personal locks. If the decision is made to re-energize the system and one person’s lock(s) still remain in place after everyone present removes theirs, the tag(s) will show who that person is and what it is they’re doing. Even with a good lock-out/tag-out safety program in place, there is still need for diligence and common-sense precaution. This is especially true in industrial settings where a multitude of people may be working on a device or system at once. Some of those people might not know about proper lock-out/tag-out procedure, or might know about it but are too complacent to follow it. Don’t assume that everyone has followed the safety rules! After an electrical system has been locked out and tagged with your own personal lock, you must then double-check to see if the voltage really has been secured in a zero state. One way to check is to see if the machine (or whatever it is that’s being worked on) will start up if the Start switch or button is actuated. If it starts, then you know you haven’t successfully secured the electrical power from it. Additionally, you should always check for the presence of dangerous voltage with a measuring device before actually touching any conductors in the circuit. To be safest, you should follow this procedure of checking, using, and then checking your meter: • Check to see that your meter indicates properly on a known source of voltage. • Use your meter to test the locked-out circuit for any dangerous voltage. • Check your meter once more on a known source of voltage to see that it still indicates as it should. While this may seem excessive or even paranoid, it is a proven technique for preventing electrical shock. I once had a meter fail to indicate voltage when it should have while checking a circuit to see if it was “dead.” Had I not used other means to check for the presence of voltage, I might not be alive today to write this. There’s always the chance that your voltage meter will be defective just when you need it to check for a dangerous condition. Following these steps will help ensure that you’re never misled into a deadly situation by a broken meter. Finally, the electrical worker will arrive at a point in the safety check procedure where it is deemed safe to actually touch the conductor(s). Bear in mind that after all of the precautionary steps have taken, it is still possible (although very unlikely) that a dangerous voltage may be present. One final precautionary measure to take at this point is to make momentary contact with the conductor(s) with the back of the hand before grasping it or a metal tool in contact with it. Why? If, for some reason there is still voltage present between that conductor and earth ground, finger motion from the shock reaction (clenching into a fist) will break contact with the conductor. Please note that this is absolutely the last step that any electrical worker should ever take before beginning work on a power system, and should never be used as an alternative method of checking for dangerous voltage. If you ever have reason to doubt the trustworthiness of your meter, use another meter to obtain a “second opinion.” This chapter is an adaptation of Lessons in Electric Circuits by Tony R. Kuphaldt (on allaboutcircuits.com), and is used under a Design Science License.
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/01%3A_Lesson_1/1.02%3A_Electrical_Fundamentals.txt	princeton-nlp/TextbookChapters	Hopefully by the time you’re considering wiring up motors and their controls, you already have a knowledge of electricity and how it behaves. The following is just a brief refresher, but any technician considering the wiring of three-phase motors should have a solid understanding of electrical fundamentals. If you do not have this understanding, please use your favorite education resource to complete training. Electrons moving around in a never-ended loop is considered a circuit. Circuits that are closed allow for electron flow. Circuits that are open (broken) do not allow for electron flow. Electricity has three main components. Voltage is the amount of potential electrical energy between two points, and it is usually represented by the letter E (for electromotive force) and is measured in volts, abbreviated with V. Current is the flow of electrons from negatively-charge atoms toward atoms with a positive charge. We measure current in Amperes or Amps (abbreviated A), and the symbol for current is I. Current that travels in only one direction we call direct current (DC). Current that changes direction at regular intervals we call alternating current (AC). The final component is resistance. Resistance (abbreviated R) is the opposition to current flow, and it is measured in ohms (abbreviated with the Greek letter Omega, Ω). These three terms are related to one another in the following way: E = I * R. Knowing this, if we ever know any two of these variables in a circuit, we can always calculate the third. Two other ways to express the same equation are: I = E / R and R = E / I. In electricity, we often use scientific notation and prefixes with the units we measure. If you’re unfamiliar with these concepts, you may want to study them a bit more. With electricity, some multiples and prefixes are used more often than others. These are in bold in the table below. Abbreviations and Prefixes When building electrical circuits, components can be connected in two basic ways: either in series with one another or in parallel. Series When there is only one path for current flow, the components are said to be in series. Look at this example of a series circuit. Series circuit with three resistors The circuit has three resistors (labeled R1, R2, and R3), and these resistors are in series with each other. Notice too that the push button (labeled PB) is also in series with the resistors, as is the 9-volt battery. There is only one path for electrons to take, and all electrons must follow the same path through the circuit when the push button is pushed. Because the electrons only have one path, the current flow is the same throughout the entire circuit, and all resistances are cumulative. Let’s say that R1 has a resistance of 10Ω, R2 has a resistance of 20Ω, and R3 has a resistance of 30Ω. Because all resistances are cumulative and current is the same through, voltage at any particular component is determined by that component’s resistance. The formula look like this: Series RTotal = R1 + R2 + R3 + … ITotal = I1 = I2 = I3 = … ETotal = ER1 + ER2 + ER3 + … In our example, total resistance is 60 ohms (10Ω + 20Ω + 30Ω). Since the total resistance is 60Ω in a 12-volt system, the total current must be 0.2A, or 200mA (12V/60Ω). Now that total current is known, voltage at each load can be calculated. For instance, the voltage at R1 (E=IR) is going to be 0.2A * 10Ω, or 2V. Voltage at R2 is 4V and voltage at R3 is 6V. Notice that all of our voltages (2V, 4V, 6V) add up to the source voltage of 12V. This rule applies to all series circuits. Parallel In parallel circuits, current flow has more than one path. This changes the behavior of the electrons in the circuit. First, the voltage across parallel components is no longer split among them. Since they are in parallel with one another (electrically common), they each get full voltage. Notice on the diagram below where the black connecting dots are located. Each of those represent two (or more) locations where voltage is going to be available equally in either direction. Parallel Circuit with Three resistors So, in this example, when the push button is pushed, 12 volts becomes available to every resistor in the circuit, since they are each parallel with each other (the push button, however, is still in series with all resistors). So, if every resistor has the full source voltage available, how much current will be flowing through the circuit? This depends on the resistance of each “branch” or “rung” of our circuit. We simply calculate the current through each resistor, then add them together to get the total current (see below). Parallel ETotal = E R1 = E R2 = E R3 = … I Total = I 1 + I 2 + I 3 + … RTotal = 1 / (1/R1 + 1/R2 + 1/R3 + …] Total resistance, however, is now a little more difficult, because as resistors are added in parallel to our circuit, we’re providing more paths for electrons to flow. Each new path that’s added decreases the total resistance of the whole circuit. In fact, the total resistance of our parallel circuit MUST be lower than the resistance of the lowest resistor. Let’s use the same resistance values as the series circuit (R1 has a resistance of 10Ω, R2 is 20Ω, and R3 is 30Ω). Knowing that our total resistance is now going to be less than 10Ω, let’s do the math. RTotal = 1 / (1/10 + 1/20 + 1/30) RTotal = 1 / (0.1 + 0.05 + 0.0333) RTotal = 1 / 0.1833 RTotal = 5.45Ω Clever technicians always look for ways to verify results. In this case, we could calculate current for our circuit at each resistor. IR1 = 12/10 IR2 = 12/20 IR3 = 12/30 IR1 = 1.2A IR2 = 0.6A IR3 = 0.4A ITotal = 1.2A + 0.6A + 0.4A = 2.2A of total current Using Ohm’s Law, our total resistance should be equal to total voltage divided by total current, and indeed, if we divide 12V by 2.2A, we get a total resistance of 5.45Ω. matching our previous result. Nice. Testing Components Switches/Contacts Switches and contacts are designed to allow and stop the flow of current. When a switch or set of contacts are closed, the resistance should be very low (near zero), meaning that very little voltage is dropped (near zero). When a switch or set of contacts are open, the resistance should be infinite (OL on many meters), meaning that all potential voltage is available across those open contacts (assuming there aren’t other opens in series with the one being measured). Protection Devices Testing fuses, circuit breakers, or overloads is similar to testing switches, except they are designed to always allow current flow. It’s only when a protection device has experienced current higher than its specified amount that the device opens the circuit, stopping current. When testing resistance, these devices should have very low resistance. Since they are placed in series with the circuit they are designed to protect, we don’t want them using up available voltage. A protection device with infinite resistance is “blown” or in its “tripped” state. When measuring voltage across one of these devices, when good there should be very little voltage dropped. If source voltage is present, the device is “blown” or in its “tripped” state. Loads Loads are designed to use applied voltage to do the work of the circuit. This could be running a motor, lighting a bulb, or actuating a relay. Loads need to have some amount of resistance (this amount will vary by load and can be found by checking the manufacturer’s specifications or measuring similar “known good” parts). Loads that measure either no resistance or an infinite amount of resistance are not good. Because loads are designed to use the available voltage, measuring voltage at a load may not always tell you if the load is good or bad. If the load has an internal open, source voltage will be read at the load. If the load is working properly, source voltage will also be found at the load. If the load is shorted, most likely, any protection devices in the circuit (fuses, circuit breakers, overloads) will be tripped, due to the increased current. Relays Because relays operate like an electrically-controlled switch, you have two components to test. First is the coil of the relay, which acts as a load. Next are the contacts within the relay, which act as switches. The contacts of the relay are often in a different circuit than the coil, but all of these components are tested as described above. Transformers Lastly are transformers. Transformers are typically used to change AC voltage by either stepping it up or stepping it down. Transformers consist of two coils of wire wrapped around an iron core. The coils of wire behave like a typical load and can be tested similarly, as described above. Step-down Transformer 1. Test primary coil 2. Test secondary coil 3. Measure Resistance (Rs) from primary to secondary coil (should be no continuity) 4. Measure Rs from Primary coil to transformer housing (should be no continuity) 5. Measure Rs from Secondary coil to transformer housing (should be no continuity) Ladder Diagrams A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=44
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/01%3A_Lesson_1/1.03%3A_Meter_Usage.txt	princeton-nlp/TextbookChapters	Safe Meter Usage Using an electrical meter safely and efficiently is perhaps the most valuable skill an electronics technician can master, both for the sake of their own personal safety and for proficiency at their trade. It can be daunting at first to use a meter, knowing that you are connecting it to live circuits which may harbor life-threatening levels of voltage and current. This concern is not unfounded, and it is always best to proceed cautiously when using meters. Carelessness more than any other factor is what causes experienced technicians to have electrical accidents. The most common piece of electrical test equipment is a meter called the multimeter. Multimeters are so named because they have the ability to measure a multiple of variables: voltage, current, resistance, and often many others, some of which cannot be explained here due to their complexity. In the hands of a trained technician, the multimeter is both an efficient work tool and a safety device. In the hands of someone ignorant and/or careless, however, the multimeter may become a source of danger when connected to a “live” circuit. There are many different brands of multimeters, with multiple models made by each manufacturer sporting different sets of features. Most meters used in industry today have digital displays, rather than a needle style. These Digital Multimeters (DMMs) allow us to measure voltage, current and resistance. The multimeter shown here in the following illustrations is a “generic” design, not specific to any manufacturer, but general enough to teach the basic principles of use: The rotary selector switch (now set in the Off position) has five different measurement positions it can be set in: two “V” settings, two “A” settings, and one setting in the middle with a funny-looking “horseshoe” symbol on it representing “resistance.” The “horseshoe” symbol is the Greek letter “Omega” (Ω), which is the common symbol for the electrical unit of ohms. Of the two “V” settings and two “A” settings, you will notice that each pair is divided into unique markers with either a pair of horizontal lines (one solid, one dashed), or a dashed line with a squiggly curve over it. The parallel lines represent “DC” while the squiggly curve represents “AC.” The “V” of course stands for “voltage” while the “A” stands for “amperage” (current). The meter uses different techniques, internally, to measure DC than it uses to measure AC, and so it requires the user to select which type of voltage (V) or current (A) is to be measured. Although we haven’t discussed alternating current (AC) in any technical detail, this distinction in meter settings is an important one to bear in mind. There are three different sockets on the multimeter face into which we can plug our test leads. Test leads are nothing more than specially-prepared wires used to connect the meter to the circuit under test. The wires are coated in a color-coded (either black or red) flexible insulation to prevent the user’s hands from contacting the bare conductors, and the tips of the probes are sharp, stiff pieces of wire: The black test lead always plugs into the black socket on the multimeter: the one marked “COM” for “common.” The red test lead plugs into either the red socket marked for voltage and resistance, or the red socket marked for current, depending on which quantity you intend to measure with the multimeter. To see how this works, let’s look at a couple of examples showing the meter in use. First, we’ll set up the meter to measure DC voltage from a battery: Note that the two test leads are plugged into the appropriate sockets on the meter for voltage, and the selector switch has been set for DC “V”. Now, we’ll take a look at an example of using the multimeter to measure AC voltage from a household electrical power receptacle (wall socket): The only difference in the setup of the meter is the placement of the selector switch: it is now turned to AC “V”. Since we’re still measuring voltage, the test leads will remain plugged in the same sockets. In both of these examples, it is imperative that you not let the probe tips come in contact with one another while they are both in contact with their respective points on the circuit. If this happens, a short-circuit will be formed, creating a spark and perhaps even a ball of flame if the voltage source is capable of supplying enough current! The following image illustrates the potential for hazard: This is just one of the ways that a meter can become a source of hazard if used improperly. Voltage measurement is perhaps the most common function a multimeter is used for. It is certainly the primary measurement taken for safety purposes (part of the lock-out/tag-out procedure), and it should be well understood by the operator of the meter. Being that voltage is always relative between two points, the meter must be firmly connected to two points in a circuit before it will provide a reliable measurement. That usually means both probes must be grasped by the user’s hands and held against the proper contact points of a voltage source or circuit while measuring. Because a hand-to-hand shock current path is the most dangerous, holding the meter probes on two points in a high-voltage circuit in this manner is always a potential hazard. If the protective insulation on the probes is worn or cracked, it is possible for the user’s fingers to come into contact with the probe conductors during the time of test, causing a bad shock to occur. If it is possible to use only one hand to grasp the probes, that is a safer option. Sometimes it is possible to “latch” one probe tip onto the circuit test point so that it can be let go of and the other probe set in place, using only one hand. Special probe tip accessories such as spring clips can be attached to help facilitate this. Remember that meter test leads are part of the whole equipment package, and that they should be treated with the same care and respect that the meter itself is. If you need a special accessory for your test leads, such as a spring clip or other special probe tip, consult the product catalog of the meter manufacturer or other test equipment manufacturer. Do not try to be creative and make your own test probes, as you may end up placing yourself in danger the next time you use them on a live circuit. Also, it must be remembered that digital multimeters usually do a good job of discriminating between AC and DC measurements, as they are set for one or the other when checking for voltage or current. As we have seen earlier, both AC and DC voltages and currents can be deadly, so when using a multimeter as a safety check device you should always check for the presence of both AC and DC, even if you’re not expecting to find both! Also, when checking for the presence of hazardous voltage, you should be sure to check all pairs of points in question. For example, suppose that you opened up an electrical wiring cabinet to find three large conductors supplying AC power to a load. The circuit breaker feeding these wires (supposedly) has been shut off, locked, and tagged. You double-checked the absence of power by pressing the Startbutton for the load. Nothing happened, so now you move on to the third phase of your safety check: the meter test for voltage. First, you check your meter on a known source of voltage to see that its working properly. Any nearby power receptacle should provide a convenient source of AC voltage for a test. You do so and find that the meter indicates as it should. Next, you need to check for voltage among these three wires in the cabinet. But voltage is measured between two points, so where do you check? The answer is to check between all combinations of those three points. As you can see, the points are labeled “A”, “B”, and “C” in the illustration, so you would need to take your multimeter (set in the voltmeter mode) and check between points A & B, B & C, and A & C. If you find voltage between any of those pairs, the circuit is not in a Zero Energy State. But wait! Remember that a multimeter will not register DC voltage when its in the AC voltage mode and vice versa, so you need to check those three pairs of points in each mode for a total of six voltage checks in order to be complete! However, even with all that checking, we still haven’t covered all possibilities yet. Remember that hazardous voltage can appear between a single wire and ground (in this case, the metal frame of the cabinet would be a good ground reference point) in a power system. So, to be perfectly safe, we not only have to check between A & B, B & C, and A & C (in both AC and DC modes), but we also have to check between A & ground, B & ground, and C & ground (in both AC and DC modes)! This makes for a grand total of twelve voltage checks for this seemingly simple scenario of only three wires. Then, of course, after we’ve completed all these checks, we need to take our multimeter and re-test it against a known source of voltage such as a power receptacle to ensure that its still in good working order. Using a multimeter to check for resistance is a much simpler task. The test leads will be kept plugged in the same sockets as for the voltage checks, but the selector switch will need to be turned until it points to the “horseshoe” resistance symbol. Touching the probes across the device whose resistance is to be measured, the meter should properly display the resistance in ohms: One very important thing to remember about measuring resistance is that it must only be done on de-energized components! When the meter is in “resistance” mode, it uses a small internal battery to generate a tiny current through the component to be measured. By sensing how difficult it is to move this current through the component, the resistance of that component can be determined and displayed. If there is any additional source of voltage in the meter-lead-component-lead-meter loop to either aid or oppose the resistance-measuring current produced by the meter, faulty readings will result. In a worse-case situation, the meter may even be damaged by the external voltage. The “resistance” mode of a multimeter is very useful in determining wire continuity as well as making precise measurements of resistance. When there is a good, solid connection between the probe tips (simulated by touching them together), the meter shows almost zero Ω. If the test leads had no resistance in them, it would read exactly zero: If the leads are not in contact with each other, or touching opposite ends of a broken wire, the meter will indicate infinite resistance (usually by displaying dashed lines or the abbreviation “O.L.” which stands for “open loop”): By far the most hazardous and complex application of the multimeter is in the measurement of current. The reason for this is quite simple: in order for the meter to measure current, the current to be measured must be forced to go through the meter. This means that the meter must be made part of the current path of the circuit rather than just be connected off to the side somewhere as is the case when measuring voltage. In order to make the meter part of the current path of the circuit, the original circuit must be “broken” and the meter connected across the two points of the open break. To set the meter up for this, the selector switch must point to either AC or DC “A” and the red test lead must be plugged in the red socket marked “A”. The following illustration shows a meter all ready to measure current and a circuit to be tested: Now, the circuit is broken in preparation for the meter to be connected: The next step is to insert the meter in-line with the circuit by connecting the two probe tips to the broken ends of the circuit, the black probe to the negative (-) terminal of the 9-volt battery and the red probe to the loose wire end leading to the lamp: This example shows a very safe circuit to work with. 9 volts hardly constitutes a shock hazard, and so there is little to fear in breaking this circuit open (bare handed, no less!) and connecting the meter in-line with the flow of electrons. However, with higher power circuits, this could be a hazardous endeavor indeed. Even if the circuit voltage was low, the normal current could be high enough that an injurious spark would result the moment the last meter probe connection was established. Another potential hazard of using a multimeter in its current-measuring (“ammeter”) mode is failure to properly put it back into a voltage-measuring configuration before measuring voltage with it. The reasons for this are specific to ammeter design and operation. When measuring circuit current by placing the meter directly in the path of current, it is best to have the meter offer little or no resistance against the flow of electrons. Otherwise, any additional resistance offered by the meter would impede the electron flow and alter the circuits operation. Thus, the multimeter is designed to have practically zero ohms of resistance between the test probe tips when the red probe has been plugged into the red “A” (current-measuring) socket. In the voltage-measuring mode (red lead plugged into the red “V” socket), there are many mega-ohms of resistance between the test probe tips, because voltmeters are designed to have close to infinite resistance (so that they don’t draw any appreciable current from the circuit under test). When switching a multimeter from current- to voltage-measuring mode, its easy to spin the selector switch from the “A” to the “V” position and forget to correspondingly switch the position of the red test lead plug from “A” to “V”. The result—if the meter is then connected across a source of substantial voltage—will be a short-circuit through the meter! To help prevent this, most multimeters have a warning feature by which they beep if ever there’s a lead plugged in the “A” socket and the selector switch is set to “V”. As convenient as features like these are, though, they are still no substitute for clear thinking and caution when using a multimeter. All good-quality multimeters contain fuses inside that are engineered to “blow” in the event of excessive current through them, such as in the case illustrated in the last image. Like all overcurrent protection devices, these fuses are primarily designed to protect the equipment (in this case, the meter itself) from excessive damage, and only secondarily to protect the user from harm. A multimeter can be used to check its own current fuse by setting the selector switch to the resistance position and creating a connection between the two red sockets like this: A good fuse will indicate very little resistance while a blown fuse will always show “O.L.” (or whatever indication that model of multimeter uses to indicate no continuity). The actual number of ohms displayed for a good fuse is of little consequence, so long as its an arbitrarily low figure. So now that we’ve seen how to use a multimeter to measure voltage, resistance, and current, what more is there to know? Plenty! The value and capabilities of this versatile test instrument will become more evident as you gain skill and familiarity using it. There is no substitute for regular practice with complex instruments such as these, so feel free to experiment on safe, battery-powered circuits. This chapter is an adaptation of Lessons in Electric Circuits by Tony R. Kuphaldt (on allaboutcircuits.com), and is used under a Design Science License. 1.04: Homework 1 Use the following schematic for questions 1, 2 and 3. 1. Between which points would you expect to measure no voltage? 2. Between which points would you expect to measure source voltage? 3. The light bulb stops working. Using your meter, you read zero volts between points F and H and between E and J. You measure source voltage from I and B and from G and J. Where is the problem located? 4. Draw a ladder diagram of the following circuit: Wired Circuit 5. Using Ohm’s Law, fill in the missing values for the following circuit: Series Circuit R1 R2 R3 Total E 12V I R 3Ω 6Ω 4Ω 6. Using Ohm’s Law, fill in the missing values for the following circuit: Parallel circuit R1 R2 R3 Total E 12V I R 3Ω 6Ω 4Ω 7. Given the following schematic diagram with a control relay, siren and four switches, describe the behavior of this circuit in words. Speaker Circuit 8. How much current is in a 12V circuit that has 24kΩ of resistance? 9. How much voltage is present in a circuit with 30mA of current and 800Ω of resistance? 10. What resistance is present in a circuit with 120V and 80µA of current? 11. How would you write 2.4MΩ in scientific notation? 12. How would you write 2.4µA in scientific notation? 13. How might you write 3.45 x 108A? 14. How might you write 8.34 x 10-6Ω? 15. In the circuit below, draw in your meter to measure the following properties: 1. Resistance of R1 2. Voltage across R2 3. Current through R1, R2, and R3
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/02%3A_Lesson_2/2.01%3A_Combination_Series_and_Parallel_Circuits.txt	princeton-nlp/TextbookChapters	With simple series circuits, all components are connected end-to-end to form only one path for electrons to flow through the circuit: With simple parallel circuits, all components are connected between the same two sets of electrically common points, creating multiple paths for electrons to flow from one end of the battery to the other: With each of these two basic circuit configurations, we have specific sets of rules describing voltage, current, and resistance relationships. • Series Circuits: • Voltage drops add to equal total voltage. • All components share the same (equal) current. • Resistances add to equal total resistance. • Parallel Circuits: • All components share the same (equal) voltage. • Branch currents add to equal total current. • Resistances diminish to equal total resistance. However, if circuit components are series-connected in some parts and parallel in others, we won’t be able to apply a single set of rules to every part of that circuit. Instead, we will have to identify which parts of that circuit are series and which parts are parallel, then selectively apply series and parallel rules as necessary to determine what is happening. Take the following circuit, for instance: This circuit is neither simple series nor simple parallel. Rather, it contains elements of both. The current exits the bottom of the battery, splits up to travel through R3 and R4, rejoins, then splits up again to travel through R1and R2, then rejoins again to return to the top of the battery. There exists more than one path for current to travel (not series), yet there are more than two sets of electrically common points in the circuit (not parallel). Because the circuit is a combination of both series and parallel, we cannot apply the rules for voltage, current, and resistance “across the table” to begin analysis like we could when the circuits were one way or the other. For instance, if the above circuit were simple series, we could just add up R1 through R4 to arrive at a total resistance, solve for total current, and then solve for all voltage drops. Likewise, if the above circuit were simple parallel, we could just solve for branch currents, add up branch currents to figure the total current, and then calculate total resistance from total voltage and total current. However, this circuit’s solution will be more complex. The table will still help us manage the different values for series-parallel combination circuits, but we’ll have to be careful how and where we apply the different rules for series and parallel. Ohm’s Law, of course, still works just the same for determining values within a vertical column in the table. If we are able to identify which parts of the circuit are series and which parts are parallel, we can analyze it in stages, approaching each part one at a time, using the appropriate rules to determine the relationships of voltage, current, and resistance. The rest of this chapter will be devoted to showing you techniques for doing this. Process of Series-Parallel Resistor Circuit Analysis The goal of series-parallel resistor circuit analysis is to be able to determine all voltage drops, currents, and power dissipations in a circuit. The general strategy to accomplish this goal is as follows: • Step 1: Assess which resistors in a circuit are connected together in simple series or simple parallel. • Step 2: Re-draw the circuit, replacing each of those series or parallel resistor combinations identified in step 1 with a single, equivalent-value resistor. If using a table to manage variables, make a new table column for each resistance equivalent. • Step 3: Repeat steps 1 and 2 until the entire circuit is reduced to one equivalent resistor. • Step 4: Calculate total current from total voltage and total resistance (I=E/R). • Step 5: Taking total voltage and total current values, go back to last step in the circuit reduction process and insert those values where applicable. • Step 6: From known resistances and total voltage / total current values from step 5, use Ohm’s Law to calculate unknown values (voltage or current) (E=IR or I=E/R). • Step 7: Repeat steps 5 and 6 until all values for voltage and current are known in the original circuit configuration. Essentially, you will proceed step-by-step from the simplified version of the circuit back into its original, complex form, plugging in values of voltage and current where appropriate until all values of voltage and current are known. • Step 8: Calculate power dissipations from known voltage, current, and/or resistance values. This may sound like an intimidating process, but its much easier understood through example than through description. In the example circuit above, R1 and R2 are connected in a simple parallel arrangement, as are R3 and R4. Having been identified, these sections need to be converted into equivalent single resistors, and the circuit re-drawn: The double slash (//) symbols represent “parallel” to show that the equivalent resistor values were calculated using the 1/(1/R) formula. The 71.429 Ω resistor at the top of the circuit is the equivalent of R1 and R2 in parallel with each other. The 127.27 Ω resistor at the bottom is the equivalent of R3 and R4 in parallel with each other. It should be apparent now that the circuit has been reduced to a simple series configuration with only two (equivalent) resistances. The final step in reduction is to add these two resistances to come up with a total circuit resistance. When we add those two equivalent resistances, we get a resistance of 198.70 Ω. Now, we can re-draw the circuit as a single equivalent resistance and add the total resistance figure to the rightmost column of our table. Note that the “Total” column has been relabeled (R1//R2—R3//R4) to indicate how it relates electrically to the other columns of figures. The “—” symbol is used here to represent “series,” just as the “//” symbol is used to represent “parallel.” Now, total circuit current can be determined by applying Ohm’s Law (I=E/R) to the “Total” column in the table: Back to our equivalent circuit drawing, our total current value of 120.78 milliamps is shown as the only current here: Now we start to work backwards in our progression of circuit re-drawings to the original configuration. The next step is to go to the circuit where R1//R2and R3//R4 are in series: Since R1//R2 and R3//R4 are in series with each other, the current through those two sets of equivalent resistances must be the same. Furthermore, the current through them must be the same as the total current, so we can fill in our table with the appropriate current values, simply copying the current figure from the Total column to the R1//R2 and R3//R4 columns: Now, knowing the current through the equivalent resistors R1//R2 and R3//R4, we can apply Ohm’s Law (E=IR) to the two right vertical columns to find voltage drops across them: Because we know R1//R2 and R3//R4 are parallel resistor equivalents, and we know that voltage drops in parallel circuits are the same, we can transfer the respective voltage drops to the appropriate columns on the table for those individual resistors. In other words, we take another step backwards in our drawing sequence to the original configuration, and complete the table accordingly: Finally, the original section of the table (columns R1 through R4) is complete with enough values to finish. Applying Ohm’s Law to the remaining vertical columns (I=E/R), we can determine the currents through R1, R2, R3, and R4individually: Placing Voltage and Current Values into Diagrams Having found all voltage and current values for this circuit, we can show those values in the schematic diagram as such: As a final check of our work, we can see if the calculated current values add up as they should to the total. Since R1 and R2 are in parallel, their combined currents should add up to the total of 120.78 mA. Likewise, since R3 and R4 are in parallel, their combined currents should also add up to the total of 120.78 mA. You can check for yourself to verify that these figures do add up as expected. This chapter is an adaptation of Lessons in Electric Circuits by Tony R. Kuphaldt (on allaboutcircuits.com), and is used under a Design Science License.
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/02%3A_Lesson_2/2.02%3A_Redrawing_Complex_Circuits.txt	princeton-nlp/TextbookChapters	Typically, complex circuits are not arranged in nice, neat, clean schematic diagrams for us to follow. They are often drawn in such a way that makes it difficult to follow which components are in series and which are in parallelwith each other. The purpose of this section is to show you a method useful for re-drawing circuit schematics in a neat and orderly fashion. Like the stage-reduction strategy for solving series-parallel combination circuits, it is a method easier demonstrated than described. Let’s start with the following (convoluted) circuit diagram. Perhaps this diagram was originally drawn this way by a technician or engineer. Perhaps it was sketched as someone traced the wires and connections of a real circuit. In any case, here it is in all its ugliness: With electric circuits and circuit diagrams, the length and routing of wire connecting components in a circuit matters little. (Actually, in some AC circuits it becomes critical, and very long wire lengths can contribute unwanted resistance to both AC and DC circuits, but in most cases wire length is irrelevant.) What this means for us is that we can lengthen, shrink, and/or bend connecting wires without affecting the operation of our circuit. The strategy I have found easiest to apply is to start by tracing the current from one terminal of the battery around to the other terminal, following the loop of components closest to the battery and ignoring all other wires and components for the time being. While tracing the path of the loop, mark each resistor with the appropriate polarity for voltage drop. In this case, I’ll begin my tracing of this circuit at the negative terminal of the battery and finish at the positive terminal, in the same general direction as the electrons would flow. When tracing this direction, I will mark each resistor with the polarity of negative on the entering side and positive on the exiting side, for that is how the actual polarity will be as electrons (negative in charge) enter and exit a resistor: Any components encountered along this short loop are drawn vertically in order: Now, proceed to trace any loops of components connected around components that were just traced. In this case, there’s a loop around R1formed by R2, and another loop around R3 formed by R4: Tracing those loops, I draw R2 and R4 in parallel with R1 and R3(respectively) on the vertical diagram. Noting the polarity of voltage drops across R3 and R1, I mark R4 and R2 likewise: Now we have a circuit that is very easily understood and analyzed. In this case, it is identical to the four-resistor series-parallel configuration we examined earlier in the chapter. Let’s look at another example, even uglier than the one before: The first loop I’ll trace is from the negative (-) side of the battery, through R6, through R1, and back to the positive (+) end of the battery: Re-drawing vertically and keeping track of voltage drop polarities along the way, our equivalent circuit starts out looking like this: Next, we can proceed to follow the next loop around one of the traced resistors (R6), in this case, the loop formed by R5 and R7. As before, we start at the negative end of R6 and proceed to the positive end of R6, marking voltage drop polarities across R7 and R5 as we go: Now we add the R5—R7 loop to the vertical drawing. Notice how the voltage drop polarities across R7 and R5 correspond with that of R6, and how this is the same as what we found tracing R7 and R5 in the original circuit: We repeat the process again, identifying and tracing another loop around an already-traced resistor. In this case, the R3—R4 loop around R5 looks like a good loop to trace next: Adding the R3—R4 loop to the vertical drawing, marking the correct polarities as well: With only one remaining resistor left to trace, then next step is obvious: trace the loop formed by R2 around R3: Adding R2 to the vertical drawing, and we’re finished! The result is a diagram that’s very easy to understand compared to the original: This simplified layout greatly eases the task of determining where to start and how to proceed in reducing the circuit down to a single equivalent (total) resistance. Notice how the circuit has been re-drawn, all we have to do is start from the right-hand side and work our way left, reducing simple-series and simple-parallel resistor combinations one group at a time until we’re done. In this particular case, we would start with the simple parallel combination of R2 and R3, reducing it to a single resistance. Then, we would take that equivalent resistance (R2//R3) and the one in series with it (R4), reducing them to another equivalent resistance (R2//R3—R4). Next, we would proceed to calculate the parallel equivalent of that resistance (R2//R3—R4) with R5, then in series with R7, then in parallel with R6, then in series with R1 to give us a grand total resistance for the circuit as a whole. From there we could calculate total current from total voltage and total resistance (I=E/R), then “expand” the circuit back into its original form one stage at a time, distributing the appropriate values of voltage and current to the resistances as we go. This chapter is an adaptation of Lessons in Electric Circuits by Tony R. Kuphaldt (on allaboutcircuits.com), and is used under a Design Science License.
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/02%3A_Lesson_2/2.03%3A_Introduction_to_Logic.txt	princeton-nlp/TextbookChapters	Logic in Electronics While this lesson is a brief introduction to logic, understand that almost no part of our modern society can function without the touch of digital electronics. Everything from our TVs to phones, cars to gaming consoles, and computers to even the cash registers at the local grocery store would not be possible without these electronic devices. In this lesson, you’ll learn how to hard-wire these types of logical functions. Later, when you learn to use Programmable Logic Controllers (PLCs), you’ll also learn about the small electronic devices that perform the following functions. AND Logical AND In words, the logical AND sounds something like this, “If A AND B are pressed, then Y is energized.” Considering A and B as our inputs, we can determine when Y (our output) is energized. Folks sometimes use a truth table to help analyze these functions. We use binary (using only the numerals 0 and 1) to help represent the state of our circuit. Binary can be used any time something only has two states (true/false, high/low, yes/no, open/closed, etc.). If “0” is the normal state, and “1” denotes an activated or energized state, let’s look a truth table for the AND function. AND A B Y 0 0 0 0 1 0 1 0 0 1 1 1 The table is read row-by-row. In the first case, neither A or B is pressed, and Y is not activate. In the second row, A is not pressed, B is pressed, and Y is not energized. Notice that Y is only energized when both A and B are pressed. In any other case, lamp Y is not lit. OR Logical OR In words, the logical OR description might be, “If button A OR B are pressed, then Y is energized.” The truth table for OR logic looks like the following. Notice that in this case, the only time lamp Y is not lit is in the first row when neither button is pressed. In all other cases, Y is energized. OR A B Y 0 0 0 0 1 1 1 0 1 1 1 1 NOT Logical NOT Not is the simplest logical operation. It simply takes the input and inverts it. In our case, if button A is NOT pressed, then Y is energized (you could also say that if A is pressed, then Y is NOT energized). The truth table is shorter, since there’s only one input, and it looks like this: OR A Y 0 1 1 0 NOR Logical NOR In the case of NOR, Y is energized as long as neither A NOR B is pushed. Notice that the truth table is an exact inverse of OR. In the case of OR, Y was energized if either button was pressed. With NOR, Y is de-energized if either button is pushed. NOR A B Y 0 0 1 0 1 0 1 0 0 1 1 0 NAND Logical NAND With NAND, if both A and B are not pressed, then Y is energized. Notice the wording NOT AND. Looking at the truth table might confirm your suspicions. The output column for NAND is an inverse of the AND truth table. NAND A B Y 0 0 1 0 1 1 1 0 1 1 1 0 XOR Logical XOR XOR (pronounced “ex-or” or “exclusive or”) allows us to energize Y if either A or B is pressed, but not if both are pressed. So, it’s function is like OR logic, but the load is not energized if both buttons are pressed. 2.04: Homework 2 1. Calculate the resistance between points A and B for the following resistor networks: 2. From this circuit (with components attached to a “terminal strip”), draw an appropriate schematic diagram. Then explain the function of the resistor and what happens when the pushbutton is pressed (assuming it is normally open). 3. Complete the table of values for this circuit: 4. Draw a schematic for the following: 5. Considering your two inputs (A and B) in the image below, what type of logic is used to actuate the coil of CR3? Lamp 1? Lamp 2? If Lamp 2 never turns on, what components of the circuit could be causing the problem? 6. Create a truth table for the following diagram:What conditions must exist in order for the light to energize? 7. Create a simplified schematic for the following complex circuit: 8. Complete the table for the following schematic: Express all current in milliamps. R1 R2 R3 R2 // R3 Total E 48 V I R 120 Ω 120 Ω 200 Ω 9. Create a truth table for the following diagram: What conditions must exist in order for the light to energize? This chapter is an adaptation of Lessons in Electric Circuits by Tony R. Kuphaldt (on allaboutcircuits.com), and is used under a Design Science License. Media Attributions • Logic Problem • Complex Circuit • Combination Circuit • Logic Problem 2
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/03%3A_Lesson_3/3.01%3A_Motor_Controls_-_Introduction.txt	princeton-nlp/TextbookChapters	In order to understand how motors are controlled, it is first necessary to understand the basics. To help with this, we’ll be using several videos from Jim Pytel’s Big Bad Tech YouTube channel. The playlist we’ll be using is titled Electrically Controlled Systems. There are over 50 videos in this playlist, and while we won’t be using all of them, you’d be well-served to watch as many of them as you can throughout the term. The information there is clear, concise, and entertaining. Much of the hardware described in labs for this course may not match the components used in the video, but this actually helps you to learn about the many varieties of hardware you’ll find in industry. The following videos are REQUIRED for this lesson before starting Lab 3. Give yourself a couple hours to watch the videos and digest the material. Remember, this isn’t like that History of Architecture class you took in high school, wondering if you were ever going to use the information you were being tested on. If you’re taking this course, you’ve chosen a profession that requires you to know how to wire, maintain and repair systems very similar to this. Do not short-change yourself, thinking you’ll be able to skim material and still be an effective technician. You won’t. What you’ll become, if you’re ever hired into the field, is a liability to yourself, your company, and your co-workers. Taking time now will prevent potentially disastrous mistakes later. Contactors A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=152 Control Relays A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=152 Overload Relays A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=152 2- and 3-Wire Magnetic Motor Starters A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=152 3.02: Homework 3 1. Create a truth table for each of the following circuits and identify the logical function of each (what’s it take for the pilot light to energize?). 2. You’ve been given a partial ladder diagram. Finish the diagram so that an OR function is formed (the indicator lamp energizes if either button A OR B is actuated). 3. Analyze this AC motor control circuit diagram, explaining the meaning of each symbol. Also, explain the operation of this motor control circuit. What happens when someone pushes the “Run” button? What happens when they let go of the “Run” button? When does the motor stop? 4. The L-side of the contactor is often known as the _______ side, while the T-side of the contactor is often known as the _______ side. 5. What do the auxiliary contacts of a contactor do? 6. Describe, in your own words, the difference between pick-up, hold-in, and dropout voltage. 7. According to the video, how much greater is inrush current than full load current? 8. Use IEC numbering to label the following two schematics (you can re-draw these on separate paper, if necessary): 9. List 5 possible causes of overload in an industrial setting. 10. What are the two components of a motor starter? 11. What’s the difference between a manual and automatic reset on an overload relay? 12. Name three types of overloads discussed in the video. 13. Draw the NEMA schematic symbol for an overload and show how overloads are represented in a ladder diagram. 14. Draw a diagram (not one used in the video) of a 2-wire circuit. 15. Draw a diagram (not one used in the video) of a 3-wire circuit. This chapter is an adaptation of Lessons in Electric Circuits by Tony R. Kuphaldt (on allaboutcircuits.com), and is used under a Design Science License. Media Attributions • Relay Schematics
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/04%3A_Lesson_4/4.01%3A_Multiple_Push_Button_Stations.txt	princeton-nlp/TextbookChapters	In this lesson, we’ll learn how to wire and draw multiple push buttons into our motor control station. It is often convenient to be able to control industrial machinery or equipment from more than one location. In this lesson, we’ll combine videos, schematics, and lab activities to deepen our understanding of the best way of adding multiple inputs to control motors. Again, we’ll be using several videos from Jim Pytel’s Big Bad Tech YouTube channel. The following videos are REQUIRED for this lesson before starting Lab 4. Remember to give yourself ample time to watch the videos and digest the material BEFORE coming in to do the labs. HAND-OFF-AUTO Circuits A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=182 Troubleshooting HAND-OFF-AUTO Circuits A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=182 Multiple Push Button Stations A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=182 4.02: Homework 4 1. Give 3 examples of different types of automatic switches typically used in 2-wire control circuits. 2. Name 2 things that the “Hand” position allows us to do in an HOA control circuit. 3. Design, draw and describe (with words) your own HOA circuit. Make sure to label your schematic and that your description indicates how it operates. 4. Is there, or why should there be, a testing/commissioning period of all new motor control circuit installs? You should give at least 2 reasons. 5. What is a pushbutton station? 6. What is a benefit of having multiple pushbutton stations? What is a disadvantage of having multiple pushbutton stations? 7. If I wanted to add an additional stop function to a motor control station, should I wire the new stop in series or parallel with the other stop pushbuttons? 8. If I wanted to add an additional start function to a motor control station, should I wire the new start in series or parallel with the other start pushbuttons? 9. Design, draw and label a motor control circuit that uses 4 pushbutton stations and 4 E-Stops. 10. Explain why it’s best to think of all of the additional push button stations needed before the installation takes place. 5.01: Intermediate Motor Controls As our circuits get more complex and we’re able to control more systems from various inputs, we’ll need to learn ways to systematically troubleshoot our motors and controls. A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=205 Once we can troubleshoot basic 3-wire controls, we can easily see how to implement jogging and reversing motor controls. A YouTube element has been excluded from this version of the text. You can view it online here: openoregon.pressbooks.pub/motorcontrols/?p=205 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=205 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=205 A YouTube element has been excluded from this version of the text. You can view it online here: openoregon.pressbooks.pub/motorcontrols/?p=205 5.02: Homework 5 1. What is the first step in troubleshooting any system? 2. What would happen in a scenario where only the primary power to the motor is lost, while pilot-level ladder logic remains functional)? 3. Describe the difference between overloads in manual reset mode and automatic reset mode. 4. What is “jogging” or “inching” 5. When is jogging used? 6. What is in-rush current and what is its proportion compared to normal full-load current? 7. Describe the purpose of a magnetic reversing motor starter and how it functions. 8. What is an interlock and what are the three different types? 9. Why must magnetic reversing motor starters contain an interlock? 10. What types of events may cause an overload? 11. If a motor is running in reverse mode when the overloads are tripped, can the motor be run in forward mode? Also, what is required in order to start the motor in reverse mode again? 12. What happens when the electrical interlocks are removed form a circuit and the reverse button is pressed while the motor is running in the forward direction (mechanical interlocks are in place)?
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/06%3A_Lesson_6/6.01%3A_Testing_Motor_Components.txt	princeton-nlp/TextbookChapters	A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=213 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=213 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=213 Testing capacitors Warning: A good capacitor stores an electrical charge and may remain energized after power is removed. Before touching it or taking a measurement: 1. Turn all power OFF 2. Use your multimeter to confirm that power is OFF 3. Carefully discharge the capacitor by connecting a resistor across the leads. Be sure to wear appropriate personal protective equipment. To safely discharge a capacitor: After power is removed, connect a 20,000 Ω, 2-5 watt resistor across the capacitor terminals for 20 – 40 seconds. (You can use your multimeter set to volts to confirm the capacitor is fully discharged.) 1. Visually inspect the capacitor. If leaks, cracks, bulges or other signs of deterioration are evident, replace the capacitor. 2. Turn the dial to the Capacitance Measurement mode ( ). 3. For a correct measurement, the capacitor will need to be removed from the circuit and properly discharged. 4. Connect the test leads to the capacitor terminals. Keep test leads connected for a few seconds to allow the multimeter to automatically select the proper range. 5. Read the measurement displayed. Value should fall within specified range (or +/- 10% of stated value). DMM will display OL if a) the capacitance value is higher than the measurement range or b) the capacitor is faulty. Troubleshooting single-phase motors is one of the most practical uses of a digital multimeter’s Capacitance Function. A capacitor-start, single-phase motor that fails to start is a symptom of a faulty capacitor. Such motors will continue to run once operating, making troubleshooting tricky. Failure of the hard-start capacitor for HVAC compressors is a good example of this problem. The compressor motor may start, but soon overheat resulting in a breaker trip. Three-phase power factor correction capacitors are typically fuse protected. Should one or more of these capacitors fail, system inefficiencies will result, utility bills will most likely increase and inadvertent equipment trips of may occur. Should a capacitor fuse blow, the suspected faulty capacitor farad value must be measured and verified it falls within the range marked on the capacitor. Motor Nameplates There are many different types of electric motors, and they all have unique parameters, requirements and specifications. Motor nameplates contain information concerning motor performance and mounting parameters, defined by the National Electrical Manufacturers Association (NEMA). These parameters include: • Manufacturer’s type and frame designation – This can include information such as the frame mounting pattern, shaft diameter and shaft height • Horsepower – Measure of motor’s mechanical output. This is based on the motor’s full-load torque and speed. Horsepower = Motor Speed x Torque / 5250. If your application’s requirement falls between two horsepower ratings, generally pick the larger-sized motor. • RPM – Sometimes called “slip speed” (as opposed to synchronous speed). Determined by winding pattern and power frequency. • Locked-rotor Code Letter – Uses letters A to V to define the locked rotor kVA per HP. Typically, A is the lowest. B is greater than A. C is greater than B, etc. A higher code may require replacing other equipment, such as motor starters to handle greater current. • Maximum ambient temperature and time rating or duty cycle- Standard motors are rated for continuous duty (24/7) at their rated load and maximum ambient temperature. Specialized motors can be designed for “short-time” requirements where intermittent duty is all that’s needed. These motors can carry a short-time rating from 5 minutes to 60 minutes. • Voltage – 230V motor running at 208V will be less efficient, but a 480V motor works at 460V because voltage drop is assumed (if motors are designed to handle a 10% voltage difference, then a 480V motor should be able to handle any voltage from 432-528V. • Frequency – Input frequency (60 Hz in the US, 50 Hz in many other countries) • Phase – The number of AC power lines supplying the motor • Current draw – When motor is fully loaded. Unbalanced phases and under voltage can cause current deviation. • Power factor – Ratio of the active power to the apparent power (at full load). • Efficiency – Power calculation = (Output / Input) x 100 • Service factor – This will only by on the nameplate if it is higher than one. Service factor (SF) is an indication of how much overload a motor can withstand when operating normally within the correct voltage tolerances. For example, the standard SF for open drip-proof (ODP) motors is 1.15. This means that a 10-hp motor with a 1.15 SF could provide 11.5 hp when required for short-term use. n general, it’s not a good practice to size motors to operate continuously above rated load in the service factor area. • Wiring diagrams • Bearing – Drive-end (sometimes called shaft-end) and non-drive-end bearing identification. 6.02: Homework 6 1. Complete the table below R1 R2 R3 R4 R3//R4 Total E 10V I R 200Ω 300Ω 400Ω 400Ω 1. Create a truth table based upon the ladder diagram below: 1. Create a truth table based upon the ladder diagram below 1. Draw a ladder diagram of a 2-wire circuit using a temperature switch. 1. Draw a ladder diagram of a 3-wire circuit using 2 E-Stops 1. I thought that I wired up the circuit shown below. As soon as I plugged the circuit in, the motor starter coil immediately energized and pulled-in. When I push either STOP button, the coil will de-energize. Give at least two things that could be wrong. 1. I wired up another motor starter, identical to the circuit shown in problem #6. I am 100% sure that all of the wiring is correct. When I plug my circuit in, nothing happens (which is how it should be, right?), but when I press either START button, the coil will not energize. What could be causing this problem? Give at least two things that could be wrong. 1. Using the same circuit that’s shown in problem #6, what voltage should I measure across the coil when it is energized? (Zero, Ghost, or Source) 1. Using the same circuit that’s shown in problem #6, what voltage should I measure across any of the START pushbuttons when the coil is energized? (Zero, Ghost, or Source) 1. How can using a 2-wire circuit be dangerous?
textbooks/workforce/Electronics_Technology/Book%3A_Troubleshooting_Motors_and_Controls_(Dickson-Self)/07%3A_Lesson_7/7.01%3A_Timers.txt	princeton-nlp/TextbookChapters	A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=221 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=221 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=221 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=221 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=221 7.02: Homework 7 1. What is another name for an on-delay timer? 2. Draw a timing diagram for the on-delay timer (including signal/control, NO and NC contacts) 3. What’s the difference between a single-function and multi-function timer? 4. Draw the schematic symbol for both the NO and NC contacts of an on-delay timer. 5. Describe a situation in industry where you might want to use a cumulative on-delay timer. 6. Describe the example Jim uses in the first video where an on-delay timer is used to control two conveyor belts. What’s the function of the timer in this case? 7. What is another name for an off-delay timer? 8. Draw a timing diagram for the off-delay timer (including signal/control, NO and NC contacts). 9. Draw the schematic symbol for both the NO and NC contacts of an off-delay timer. 10. Describe the performance of a flash/repeat/recycle timer. 11. Describe the difference between symmetric and asymmetric timers. 12. Describe the function of a positive/rising edge triggered one-shot timer. 13. Draw the timing diagram for a negative/falling edge triggered one-shot timer. 8.01: Motor Drives A frequently-used component in any modern industry are motor drives, sometimes called variable frequency drives or VFDs. In order to understand how VFDs control the speed of a motor, you must first understand what happens inside an AC induction motor. A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=282 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=282 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=282 Below, Jim Pytel explains an example motor drive by Omron. Use this information as an introduction to the topic. There are MANY different types of motor drives, and they all have their own little idiosyncrasies. Even VFDs made by the same manufacturer may have very different programming steps. READ THE MANUAL for the drive you’re working with. As you become more familiar with these, you’ll be able to quickly find the information you need to set-up your particular drive. A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=282 A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/motorcontrols/?p=282 8.02: Homework 8 1. How can you change the direction of rotation on a three-phase AC motor? 2. The rotating part of a three-phase AC motor is called a __________. 3. The stationary part of a three-phase AC motor is called a ___________. 4. Which three-phase AC motor has a higher RPM, one with 2 poles, or one with 4 poles? 5. When the supplied frequency for a three-phase AC motor increases, does the motor RPM’s increase or decrease? 6. Name one mechanical method to step-up or step-down a motor’s output speed (note: changing the number of poles, while technically correct, is not a method typically used in an industrial environments to change the speed of rotating equipment). 7. In a motor drive, what does the rectifier portion of the drive do? 8. Name three characteristics of an inverter rated motor. 9. Name three of the broad categories that motor drives need to have programmed by the user. 10. What is the purpose of the communication port on a motor drive?
textbooks/workforce/Electronics_Technology/Hydraulics_and_Electrical_Control_of_Hydraulic_Systems_(Pytel)/1%3A_Introduction/01.1%3A_Introduction_to_Fluid_Power_Systems.txt	princeton-nlp/TextbookChapters	A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=18 Describe the purpose of a fluid power system Differentiate between fluid power systems and mechanical or electrical systems Differentiate between hydraulic and pneumatic systems with respect to the fluid medium employed, characteristics, capacity, performance, and cleanliness Describe a basic fluid power system in terms of power conversion. Describe the role of a prime mover like a motor or internal combustion engine in a fluid power system. Draw the schematic symbol for a motor and internal combustion engine. Describe the role of a pump in a fluid power system. Draw the schematic symbol for a pump and reservoir. Describe what properties pressure, flow rate, and valve position influence in a fluid power system. Describe Pascal’s Law and the formula used to relate force, pressure, and area. Describe the role of an actuator in a fluid power system. Draw the schematic symbol for a cylinder and hydraulic motor. Comment on the drawbacks of systems composed of numerous stages Comment on the advantages and disadvantages of fluid power systems Identify safety concerns associated with fluid power systems. Comment on sources of inefficiency within a fluid power system Identify five different types of pressure control valves Draw the schematic symbol for a pressure gauge, pressure switch, and pressure transducer List the devices that control flow rate Draw the schematic symbol for a flow control valve and comment on how they are employed in fluid power systems. Draw the schematic symbol for flow meters and comment on how they are employed in fluid power systems. Draw the schematic symbol for a check valve. Differentiate between free flow and blocked direction. Describe the purpose of a directional control valve in a fluid power system. Draw the schematic symbol for a 3 position, spring centered, manually actuated directional control valve with a closed center, a straight through position, and a cross connect position Discuss how the above valve’s position influences a double acting cylinder’s actuation direction when the cap end port is hooked to actuator port A and rod end port is hooked to actuator port B. Discuss how the above valve’s position influences a double acting cylinder’s actuation direction when the actuator ports are swapped (rod end port is hooked to actuator port A and cap end port is hooked to actuator port B). Discuss how a double acting cylinder’s actuation direction is influenced when one port is blocked. Describe the purpose of mechanical limit switches, magnetic proximity switches, and position transducers in a fluid power system. Differentiate between energy and power and give examples of common energy and power units. Determine the energy requirement in ftlbf to move a 500lbf object 12ft. Determine the power requirement in ftlbf/s, hp, and W to move a 500lbf object 12ft in 2.3s. Given a 72% efficient system determine the input power in W necessary to produce 5.6hp output Given a 79% efficient system determine the output power in hp if 3.2kW was input 01.2: Hydraulics Math A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=24 Given F=pA, solve for p in terms of F and A. Given F=pA, solve for A in terms of F and p. Given Q = V/t, solve for V in terms of Q and t Given Q = V/t, solve for t in terms of v and Q Comment on pressure and flow rate and how they influence the force and speed of a hydraulic actuator. List units commonly employed to measure hydraulic quantities US SI/metric length area volume pressure force flow rate time Determine equivalencies for the following values: 1 in => cm 1 lbf => N 1 l => cm3 1 gallon => in3 14.5 psi => bar=> kPa 1 gallon => l Convert a volume of 0.45 gallon to in3 Convert a volume of 40 in3 to gallons Convert 650kPa to psi and bar Convert 18 bar to psi and kPa Convert 490psi to bar and kPa Differentiate between the terms cap end, rod, and rod end with respect to area and volume. Draw a picture. Which volume must be filled to extend a cylinder, the cap end, the rod, or the rod end? Which volume must be filled to retract a cylinder, the cap end, the rod, or the rod end? Write the formula used to determine the surface area of a circle. Write the formula used to determine the surface area of a ring. Write the formula used to determine the volume of a cylinder. Write the formula used to determine the volume of a tube (a cylinder with a cylinder removed). Given cylinder X with the following dimensions calculate the desired quantities: dcap = 2 ¾ in drod = ¾ in travel length = 12 in Acap = Arod = Arod end = Vcap = Vrod = Vrod end = Given a fixed flow rate of 0.75 gpm calculate the desired quantities for cylinder X: textend (s) = tretract (s) = speedextend (in/s) = speedretract (in/s) = Given a pump with a fixed displacement of 0.4 in3/rev is rotated at 1800rpm calculate the flow rate in units of gpm. Given a motor with fixed speed describe how flow rate can be varied. Given a pump with fixed displacement describe how flow rate can be varied. Given cylinder X calculate the desired quantities given the applied load is 2300lbf. pextend = pretract = Given cylinder X calculate the desired quantities given maximum pressure is limited to 670psi. Fextend MAX = Fretract MAX =
textbooks/workforce/Electronics_Technology/Hydraulics_and_Electrical_Control_of_Hydraulic_Systems_(Pytel)/1%3A_Introduction/01.3%3A_Hydraulic_Cylinders.txt	princeton-nlp/TextbookChapters	A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=27 Define the term actuator and give examples of a rotational electrical actuator and a linear hydraulic actuator. Draw a pictorial diagram of a double acting hydraulic cylinder. Identify the barrel, piston, rod, cap end plate, rod end plate, rod wiper, cap end port, and rod end port. NOTE: the rod end is often called the “head” end and the cap end is often called the “blind” end. Draw the schematic symbol for a double acting hydraulic cylinder. Differentiate between the cap end and rod end. Which has more functional area? Describe the act of extending and retracting a double acting cylinder in terms of which volumes are filled and which volumes are emptied. Comment on observed differences between extension and retraction speeds given constant flow rate. Comment on how blocked ports affect extension and retraction of double acting hydraulic cylinders. Differentiate between static and dynamic seals. Point out static and dynamic seals in a double acting hydraulic cylinder. Comment on how a gasket is used to form a static seal. Comment on gasket composition and fluid compatibility. Comment on how O-rings, piston rings and oil form a dynamic seal. Comment on why oil is used in hydraulic systems. Describe the cross sections of other dynamic seals. Comment on the purpose of the rod wiper. Comment on storage of hydraulic equipment and the role of fabric bellows. Comment on the purpose of a stop tube. Describe a double rod cylinder and draw its schematic symbol. Describe a tandem cylinder. Describe a duplex cylinder. Draw the schematic symbols. Describe how a cushion works. Draw the schematic symbol for a cushion on extension. Draw the schematic symbol for a cushion on retraction. Draw the symbol for a variable cushion. Draw lug, flange, flush, and tie rod mounted cylinders. Describe the purpose of fixed mounting methods. Draw trunnion and clevis mounted cylinders. Describe the purpose of pivoting mounts. NOTE: Pivoting mounts are often specified by the location of the pivot point (example: head trunnion vs. center mounted barrel trunnion) Describe and draw the schematic symbol for a single acting cylinder. Describe the means a single acting cylinder uses to retract. Describe a ram. Describe how the descent of a lifted object can be controlled. Describe a telescoping cylinder. Describe how a spring can be used to apply or remove a brake in the event of pressure loss. Comment on how a spring is a source of hazardous energy. 01.4: General Industrial Safety A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=30 Comment on elements essential to emergency preparedness. Enroll in a First Aid/CPR/AED class if you are not already certified Define the purpose of a lock out and tag out program. Describe lock out devices used for plugs, switches, and valve handles. Describe how a hasp is utilized with a group of workers and their individual lock and tag. Define lock out, define tag out, and differentiate between the two terms. Describe the general procedure to conduct service on a system. Comment on the purpose of inspecting Personal Protective Equipment (PPE) prior to use. Differentiate between types and classes of hard hats. Describe the features and types of eye protection and prescription eyewear. Describe the purpose of eye wash stations and emergency showers. Differentiate between ear plugs and ear muffs. Describe how the NRR of a hearing protection device affects environmental noise. Describe the time weighted average requirement Comment on protective clothing and hand protection utilized for specialized industrial tasks (ie: electrical, abrasion resistance, chemicals, etc.). Comment on machine guards. Comment on the purpose of protective toes and oil resistant soles. Comment on when fall arrest systems must be utilized. Comment on the purpose of a harness and shock absorbing lanyard. Describe the purpose and function of a ladder climber. Describe the purpose of suspension trauma mitigation straps. Describe the purpose of a work positioning lanyard. Describe other uses of a work positioning lanyard. Describe the purpose of a rescue, retrieval and evacuation device. Describe how a pre-roped pulley assembly, additional pulleys, slings, and carabiners complement a rescue kit. Describe the purpose of an exclusion zone and tethering. Describe the 3 features of a confined space and how environmental testing, attendants, communication, and rescue equipment mitigate the problems associated with confined spaces. Describe some of the unique safety concerns associated with fluid power systems and best practices to mitigate these hazards. Describe the purpose of OSHA. Describe the purpose of ANSI. Describe the purpose of the NEC. Describe the purpose of NRTLs and give examples. Describe the purpose of the NEMA and the IEC and differentiate between them. Show up to your assigned lab period wearing long pants and closed toed shoes.
textbooks/workforce/Electronics_Technology/Hydraulics_and_Electrical_Control_of_Hydraulic_Systems_(Pytel)/2%3A_Pascal's_Law_and_Hydraulic_Components/02.1%3A_Pascal%27s_Law.txt	princeton-nlp/TextbookChapters	A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=41 Describe Pascal’s Law and the formula used to relate force, pressure, and area. Solve for F in terms of p and A. Solve for p in terms of F and A. Solve for A in terms of F and p. List common units of force, pressure, and area. Determine equivalency for psi, Pa, and bar. If area is kept constant determine how changes in pressure affect force. If pressure is kept constant determine how changes in area affect force. If area is kept constant determine how changes in force affect pressure. If force is kept constant determine how changes in area affect pressure. Given a force multiplication system with the following dimensions: d1 = 3/4 in F1 = 120 lbf h1 = 4 in d2 = 1 ¼ in Calculate A1, p, V1, A2, F2, h2, energyin, energyout Comment on the differences between the cap end and rod end of a double acting cylinder with respect to functional area. Explain why the pressure necessary to retract is greater than the pressure necessary to extend with the same force for a double acting cylinder. Explain why the force of extension is greater than the force of retraction given the same pressure limit for a double acting cylinder. Given cylinder X with the following dimensions: dcap = 2 7/8 in drod = 7/8 in Calculate pext and pret for cylinder X given the system is tasked with moving a 1350lbf object. Calculate FextMAX and FretMAX for cylinder X given the system is limited to 640psi. 02.2: Pascal's Law Examples A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=44 02.3: Pressure and Pressure Measurement A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=46 List common units of pressure. Equate psi, bar, and Pa. Convert 230psi to bar and kPa. Convert 7.3 bar to psi and kPa. Convert 440kPa to bar and psi. Determine the minimum of height of a water tower necessary to ensure at least 30 psi Describe atmospheric pressure and the sources of variance. Convert 550psi to psia Convert 900psia to psig Define a vacuum Describe the function of a pressure gauge and draw its schematic symbol. Differentiate between analog (needle) and digital pressure gauges. Differentiate between bourdon tube and spring loaded piston (Schrader) gauges and describe the basic operation and constituent parts of both. Differentiate between pressure switches and pressure sensors (transducers). Describe set, reset, and span (hysteresis) for a pressure switch. 02.4: Check Valves A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=48 Describe the basic purposes of valves in fluid power systems. Define the terms: body, ports/ways, spool, poppet, seal, springs, actuation/adjustment methods Describe the different valve mounting methods: inline, subplate, manifold, cartridge, stack Draw the schematic symbol and cutaway view of a basic poppet style check valve. Identify direction of free flow. Identify direction of blocked flow. Describe how a primitive pressure relief valve can be created with a check valve. Define cracking and full open pressure. Discuss the main disadvantage of a basic poppet style check valve in the free flow direction and how a right angle check valve overcomes this disadvantage. Draw a cutaway view of a right angle check valve. Draw the schematic symbol and cutaway view of a restriction (orifice) style check valve. Identify direction of free flow. Identify direction of restricted flow. Describe how a restriction (orifice) style check valve works. Draw the schematic symbol and cutaway view of a pilot to open check valve. Describe how a pilot to open check valve works in the absence and presence of pilot pressure. Draw the schematic symbol and cutaway view of a pilot to close check valve. Describe how a pilot to close check valve works in the absence and presence of pilot pressure. Describe how check valves are employed in the following applications: foot valves, manual pumps, filters in bidirectional systems, quick disconnects, valve bypasses, clogged filter bypasses Determine how these 4 flow control valves with check valve bypasses influence speed of extension or retraction. 02.5: Pressure Relief Valves A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=55 Describe the purpose of a pressure relief valve Describe scenarios that call for pressure relief Draw the schematic symbol for a rupture/burst disc and discuss its purpose and method of operation. Draw the schematic symbol for a pressure relief valve and describe the purpose of the individual elements. Describe how a check valve and heavy bias spring can be used to create a primitive pressure relief valve. Draw a cutaway view of a spool type direct acting pressure relief valve. Describe its operation. Describe the terms overshoot, set, reset, and span (hysteresis) Define cracking pressure and pressure override. Discuss the influence of pressure override for actuators operating near the set point. Differentiate between the terms pilot (control) and primary (power) Draw a cutaway view of a balanced piston type pilot operated pressure relief valve. Describe its operation. Describe the principle advantage of pilot operated pressure relief valves over direct acting pressure relief valves Comment on observed properties of systems with malfunctioning, improperly set, or improperly connected pressure relief valves. Comment on the efficiency of systems that actuate the pressure relief valve frequently. Comment on alternate methods to prevent overpressure events without the necessity of actuating the pressure relief valve. 02.6: Example Pilot Operated Pressure Relief Valve A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/hydraulics/?p=57

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