EET222 Worksheet #5: Regulated Power Supplies

EET222 Worksheet #5: Regulated Power Supplies This worksheet deals with regulated power supplies. In EET221 we used rectifying diodes to convert AC to DC. We then used a zener diode to create a stable DC supply. In this worksheet we will explore how op-amps can be used to create a better DC supply than a simple zener diode. Help for this worksheet may be found in Chapter 22 of the textbook. You may have to review your notes from EET112, and/or 113. This is not the only place to find help. Don t be afraid to explore. The first 16 problems pertain specifically to regulators. These problems are required to be completed when you turn in your worksheet. The remaining problems are provided as study problems for the test. These problems are not practice test problems. They are additional worksheet problems to help you review material that we covered this term. Most of the review problems are advanced problems. If you want to review basic problems, consult your worksheet on that topic. I strongly recommend that you work on the review problems. However, I will not grade them when I grade your worksheet. Educational Objectives Describe Shunt Regulators Describe Series Regulators Analyze regulators to determine operation and faults If you want additional practice you should try these problems from the book Ch22 # 1-17 and 24-34 1

Question 1 Questions Suppose you had the boring job of manually maintaining the output voltage of a DC generator constant. Your one and only control over voltage is the setting of a rheostat: Gen (You) Rheostat V Load What would you have to do to maintain the load voltage constant if the load resistance changed so as to draw more current? Being that your only control over load voltage is the adjustment of a variable resistance in series with the generator, what does this imply about the generator s output voltage (directly across the generator terminals), compared to the target load voltage? Kuphaldt file 00888 Question 2 Suppose you had the boring job of manually maintaining the output voltage of a DC generator constant. Your one and only control over voltage is the setting of a rheostat: Gen Rheostat (You) V Load What would you have to do to maintain the load voltage constant if the load resistance changed so as to draw more current? Being that your only control over load voltage is the adjustment of a variable resistance in parallel with the load, what does this imply about the generator s output voltage (directly across the generator terminals), compared to the target load voltage? Kuphaldt file 00889 2

Question 3 Describe how a zener diode is able to maintain regulated (nearly constant) voltage across the load, despite changes in load current: R Gen Load Kuphaldt file 00890 Question 4 When regulating or converting power, efficiency is very important. In terms of power regulation, how is efficiency defined? Why is this important? file ch24001 Question 5 So-called linear regulator circuits work by adjusting either a series resistance or a shunt resistance to maintain output voltage at some fractional value of input voltage: "Linear" regulator circuit types Series regulator Shunt regulator V in V out V in V out Typically, these variable resistances are provided by transistors rather than actual rheostats, which would have to be manually controlled. Explain why the series requlator is more efficient. Which type of linear regulator does the typical zener regulator circuit belong to, series or shunt? Kuphaldt file 02162c 3

Question 6 Explain why a switching regulator circuit would perform the same task as a linear regulator circuit at a much greater efficiency. What are the three basic types of switching regulators? Which switching regulator steps voltage up, which steps it down, and which produces a negative output from a positive input? file ch24004 Question 7 Explain how the operational amplifier maintains a constant current through the load: V supply R 1 V supply Load V Z A V(OL) β R 2 Write an equation solving for the regulated load current, given any relevant variables shown in the schematic diagram (R 1, V Z, V supply, A V(OL), etc.). Kuphaldt file 02512 4

Question 8 Explain how this regulator maintains a constant voltage at V: Power plug Fuse Switch T 1 D 1 D 2 D 3 D 4 C 1 R 1 D 5 Q 1 U 1 C 2 V Gnd What is the output voltage for this regulator, assume Vz=3.3V? Why is it important to know the zener voltage? What is the purpose of R1? What is the purpose of Q1? What happens to this regulator if the output is shorted out? What type of regulator is it, series or shunt? Kuphaldt file 03771c 5

Question 9 Originally we built this circuit: Power plug Fuse Switch T 1 D 1 D 2 D 3 D 4 C 1 R 1 D 5 Q 1 U 1 C 2 V Gnd But the user accidentally placed a short circuit across the load and it blew up. You were asked to redesign the circuit to prevent it from blowing up if the output shorts. Your friend came up with the following design: Power plug Fuse Switch T 1 D 1 D 2 D 3 D 4 C 1 R 1 Q 1 R 2 U 1 D 5 Q 2 R 3 V C 2 Gnd 6

Explain how this circuit protects against a short circuited output. If you want to see this in action, look at the spice simulation: Series regulator SC Protection.asc For Foldback regulation see: regulator foldback limit.asc Both of these files can be found on the class website. file ch24002 Question 10 Design a circuit around a LM317 adjustable regulator. Your input is 12V and your output is 3.3V. Additional Discussion The data sheet says that a capacitor should be placed between the input and gnd if the regulator is placed an appreciable distance from the power supply. What is the purpose of this capacitor? Afterbuildingyourcircuit, youmeasuretheoutputanditisonly1.25v,whatisthemostlikelyproblem? file ch24003 7

Question 11 A student builds the following regulated AC-DC power supply circuit, but is dissatisfied with its performance: Power plug V The voltage regulation is not as good as the student hoped. When loaded, the output voltage sags more than the student wants. When the zener diode s voltage is measured under the same conditions (unloaded output, versus loaded output), its voltage is noted to sag a bit as well. The student realizes that part of the problem here is loading of the zener diode through the transistor. In an effort to improve the voltage regulation of this circuit, the student inserts an opamp voltage follower circuit between the zener diode and the transistor: Power plug Gnd V Now the zener diode is effectively isolated from the loading effects of the transistor, and by extension 8 Gnd

from the output load as well. The opamp simply takes the zener s voltage and reproduces it at the transistor base, delivering as much current to the transistor as necessary without imposing any additional load on the zener diode. This modification does indeed improve the circuit s ability to hold a steady output voltage under changing load conditions, but there is still room for improvement. Another student looks at the modified circuit, and suggests one small change that dramatically improves the voltage regulation: Power plug Modified feedback connection V Now the output voltage holds steady at the zener diode s voltage with almost no sag under load! The second student is pleased with the success, but the first student does not understand why this version of the circuit functions any better than previous version. How would you explain this circuit s improved performance to the first student? How is an understanding of negative feedback essential to being able to comprehend the operation of this circuit? Kuphaldt file 02286 Gnd 9

Question 12 Predict how the operation of this current regulator circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults): V supply V supply R 1 V supply Load Q 1 D 1 U 1 R 2 Resistor R 1 fails open: Zener diode D 1 fails shorted: Resistor R 2 fails open: Zener diode D 1 fails open: Load fails shorted: Wire between opamp output and transistor base breaks open: For each of these conditions, explain why the resulting effects will occur. Kuphaldt file 03777 10

Question 13 This regulated power supply circuit has a problem. Instead of outputting 15 volts DC (exactly) as it should, it is outputting 0 volts DC to the load: TP1 V supply R 1 TP2 U 1 TP4 Q 1 TP3 D 1 C 1 R load You measure 0.25 volts DC between TP4 and ground, and 20 volts between TP1 and ground, using your voltmeter. From this information, determine at least two independent faults that could cause this particular problem. Kuphaldt file 03772 11

Question 14 Predict how the operation of this regulated power supply circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults): Power plug Fuse Switch T 1 D 1 D 2 D 3 D 4 C 1 R 1 D 5 Q 1 U 1 C 2 V Gnd Transformer T 1 primary winding fails open: Rectifying diode D 3 fails open: Rectifying diode D 4 fails shorted: Resistor R 1 fails open: Zener diode D 5 fails open: Operational amplifier U 1 fails with output saturated positive: Transistor Q 1 fails open (collector-to-emitter): For each of these conditions, explain why the resulting effects will occur. Kuphaldt file 03771 12

Question 15 Something is wrong with this regulated DC power supply circuit. The output is supposed to be 10.0 volts, but instead it measures only about 1 volt: Power plug 120 / 12.6 VAC transformer TP3 D 1 D 2 TP1 TP2 D 3 D 4 C 1 470 µf R 1 1 kω TP5 V Z = 10.0 V D 5 Q 1 U 1 TP7 LM741C TP6 33 µf C 2 TP4 Using your digital multimeter, you measure 15.3 volts between test points TP7 (red test lead) and TP4 (black test lead). Note that V Z shown in the schematic is a specification for the zener diode, and not an actual voltmeter measurement. From this information, identify two possible faults that could account for the problem and all measured values in this circuit, and also identify two circuit elements that could not possibly be to blame (i.e. two things that you know must be functioning properly, no matter what else may be faulted) other than the 120 volt AC power source, on/off switch, and fuse. The circuit elements you identify as either possibly faulted or properly functioning can be wires, traces, and connections as well as components. Be as specific as you can in your answers, identifying both the circuit element and the type of fault. Circuit elements that are possibly faulted 1. 2. Circuit elements that must be functioning properly (besides 120 volt AC source, switch, and fuse) 1. 2. Kuphaldt file 02660 13

Question 16 Something is wrong with this regulated DC power supply circuit. The output is supposed to be 10.0 volts, but instead it measures about 16 volts: Power plug 120 / 12.6 VAC transformer TP3 D 1 D 2 TP1 TP2 D 3 D 4 C 1 470 µf R 1 1 kω TP5 V Z = 10.0 V D 5 Q 1 U 1 TP7 LM741C TP6 33 µf C 2 TP4 Using your digital multimeter, you measure 10.0 volts between test points TP5 (red test lead) and TP4 (black test lead). From this information, identify two possible faults that could account for the problem and all measured values in this circuit, and also identify two circuit elements that could not possibly be to blame (i.e. two things that you know must be functioning properly, no matter what else may be faulted) other than the 120 volt AC power source, on/off switch, and fuse. The circuit elements you identify as either possibly faulted or properly functioning can be wires, traces, and connections as well as components. Be as specific as you can in your answers, identifying both the circuit element and the type of fault. Circuit elements that are possibly faulted 1. 2. Circuit elements that must be functioning properly (besides 120 volt AC source, switch, and fuse) 1. 2. Kuphaldt file 02661 14

Question 17 The type 555 integrated circuit is a highly versatile timer, used in a wide variety of electronic circuits for time-delay and oscillator functions. The heart of the 555 timer is a pair of comparators and an S-R latch: 555 timer Disch V Reset Thresh CLR R Trig S Q Out V Ctrl The various inputs and outputs of this circuit are labeled in the above schematic as they often appear in datasheets ( Thresh for threshold, Ctrl or Cont for control, etc.). To use the 555 timer as an astable multivibrator, simply connect it to a capacitor, a pair of resistors, and a DC power source as such: Gnd R 1 V cc Disch 555 RST Out B R 2 C 1 A Thresh Trig Gnd Ctrl If were were to measure the voltage waveforms at test points A and B with a dual-trace oscilloscope, we would see the following: 15

B A Explain what is happening in this astable circuit when the output is high, and also when it is low. Kuphaldt file 01418 Question 18 What would happen to the operation of this astable 555 timer circuit if a resistor were accidently connected between the Control terminal and ground? Explain the reason for your answer. R 1 V cc Disch 555 RST Out R 2 C 1 Thresh Trig Gnd Ctrl Kuphaldt file 01435 16

Question 19 Photovoltaic solar panels produce the most output power when facing directly into sunlight. To maintain proper positioning, tracker systems may be used to orient the panels direction as the sun moves from east to west across the sky: (Sun) Axis of rotation Solar panel Axis of rotation Onewaytodetectthesun spositionrelativetothepanelistoattachapairoflight-dependentresistors (LDR s) to the solar panel in such a way that each LDR will receive an equal amount of light only if the panel is pointed directly at the sun: (Sun) Photoresistors Two comparators are used to sense the differential resistance produced by these two LDR s, and activate a tracking motor to tilt the solar panel on its axis when the differential resistance becomes too great. An H-drive transistor switching circuit takes the comparators output signals and amplifies them to drive a permanent-magnet DC motor one way or the other: 17

12 V 12 V 12 V 12 V 100 kω 150 Ω Q 1 Q 2 LDR 1 1 kω U 1 150 Ω 150 Ω Mtr LDR 2 1 kω 100 kω U 2 150 Ω Q 3 Q 4 In this circuit, what guarantees that the two comparators never output a high (V) voltage simultaneously, thus attempting to move the tracking motor clockwise and counter-clockwise at the same time? Kuphaldt file 00881 18

Question 20 A white noise source is a special type of AC signal voltage source which outputs a broad band of frequencies ( noise ) with a constant amplitude across its rated range. Determine what the display of a spectrum analyzer would show if directly connected to a white noise source, and also if connected to a low-pass filter which is in turn connected to a white noise source: Spectrum analyzer display 0 db -20 db -40 db White noise source -60 db -80 db -100 db -120 db 1 2 3 4 5 6 7 8 9 10 Spectrum analyzer display 0 db -20 db -40 db White noise source LP filter -60 db -80 db -100 db -120 db 1 2 3 4 5 6 7 8 9 10 Kuphaldt file 03621 19

Question 21 Analog-to-digital converter circuits (ADC) are usually equipped with analog low-pass filters to precondition the signal prior to digitization. This prevents signals with frequencies greater than the sampling rate from being seen by the ADC, causing a detrimental effect called aliasing. These analog pre-filters are thus known as anti-aliasing filters. Determine which of the following Sallen-Key active filters is of the correct type to be used as an antialiasing filter: V V in C 1 R 1 R 2 C 2 R 3 ADC V V in R 1 C 1 C 2 R 2 R 3 ADC Kuphaldt file 04039 20

Question 22 A popular passive filtering network called the twin-tee is often coupled with an operational amplifier to produce an active filter circuit. Two examples are shown here: "Twin-tee" network V in V out "Twin-tee" network V in V out Identify which of these circuits is band-pass, and which is band-stop. Also, identify the type of response typically provided by the twin-tee network alone, and how that response is exploited to make two different types of active filter responses. Kuphaldt file 02573 21

Question 23 Predict how the operation of this active filter circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults): R 2 R 3 V in R 1 C 1 U 1 Load Resistor R 1 fails open: Capacitor C 1 fails open: Solder bridge (short) across resistor R 1 : Solder bridge (short) across capacitor C 1 : Resistor R 2 fails open: Resistor R 3 fails open: For each of these conditions, explain why the resulting effects will occur. Kuphaldt file 03787 Question 24 Calculate the following parameters in this circuit (be sure to specify the polarity of each voltage with respect to ground!): V 1 = 4.5 volts 5 kω 5 kω TP1 R 1 R 2 V 2 = 2 volts R 3 R 4 V out 5 kω TP2 5 kω V TP1 = V TP2 = I R3 = V out = Kuphaldt file 02740 22

Question 25 Singers who wish to practice singing to popular music find that the following vocal eliminator circuit is useful: Left channel input Output (to headphone or power amp) Right channel input The circuit works on the principle that vocal tracks are usually recorded through a single microphone at the recording studio, and thus are represented equally on each channel of a stereo sound system. This circuit effectively eliminates the vocal track from the song, leaving only the music to be heard through the headphone or speaker. Explain how the operational amplifiers accomplish this task of vocal track elimination. What role does each opamp play in this circuit? Kuphaldt file 02524 23

Question 26 The following circuit is a type of difference amplifier, similar in behavior to the instrumentation amplifier, but only using two operational amplifiers instead of three: R R R R V 1 V 2 V out Complete the table of values for this opamp circuit, calculating the output voltage for each combination of input voltages shown. From the calculated values of output voltage, determine which input of this circuit is inverting, and which is noninverting, and also how much differential voltage gain this circuit has. Express these conclusions in the form of an equation. Kuphaldt file 02539 V 1 V 2 V out 0 V 0 V 1 V 0 V 0 V 1 V 2 V 1.5 V 3.4 V 1.2 V -2 V 4 V 5 V 5 V -3 V -3 V 24

Question 27 Predict how the operation of this difference amplifier circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults): V 1 R 1 R 2 U 1 V out V 2 R 3 R 4 V out = V 2 - V 1 Resistor R 1 fails open: Resistor R 2 fails open: Solder bridge (short) across resistor R 3 : Resistor R 4 fails open: Solder bridge (short) across resistor R 4 : For each of these conditions, explain why the resulting effects will occur. Kuphaldt file 03782 Question 28 Calculate the following parameters in this circuit (be sure to specify the polarity of each voltage with respect to ground!): R 1 = 5 kω 10 kω 3 V 10 kω TP1 4 V 10 kω 1 V TP2 R f = 10 kω V out V TP1 = V TP2 = I Rf = V out = Kuphaldt file 02739 25

Question 29 Predict how the operation of this summer circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults): R 1 V 1 R 2 R 4 V 2 V 3 R 3 U 1 V out Resistor R 1 fails open: Resistor R 2 fails open: Solder bridge (short) across resistor R 3 : Resistor R 4 fails open: Solder bridge (short) across resistor R 4 : For each of these conditions, explain why the resulting effects will occur. Kuphaldt file 03781 26

Answer 1 Answers In order to increase the load voltage, you must decrease the resistance of the rheostat. In order for this scheme to work, the generator s voltage must be greater than the target load voltage. Note: this general voltage control scheme is known as series regulation, where a series resistance is varied to control voltage to a load. Answer 2 In order to increase the load voltage, you must increase the resistance of the rheostat. In order for this scheme to work, the generator s voltage must be greater than the target load voltage. Note: this general voltage control scheme is known as shunt regulation, where a parallel(shunt) resistance is varied to control voltage to a load. Follow-up question: assuming the load voltage is maintained at a constant value by an astute rheostat operator despite fluctuations in load current, how would you characterize the current through the generator s windings? Does it increase with load current, decrease with load current, or remain the same? Why? Answer 3 The zener draws more or less current as necessary from the generator (through the series resistor) to maintain voltage at a nearly constant value. Follow-up question #1: if the generator happens to output some ripple voltage (as all electromechanical DC generators do), will any of that ripple voltage appear at the load, after passing through the zener diode voltage regulator circuit? Follow-up question #2: would you classify the zener diode in this circuit as a series voltage regulator or a shunt voltage regulator? Explain your answer. Challenge question: at what point is the zener diode unable to regulate load voltage? Is there some critical load condition at which the diode ceases to regulate voltage? Answer 4 Efficiency is the ratio of output power to input power. P out P in 100% Efficiency is always less than 100%. I will leave it to you do decide why efficiency is important. Answer 5 In the shunt regulator the source is always at max power. If the load doesn t need all of this power it is used by the shunt. In the series regulator the source power varies: P source = P load P consumedbyregulator A shunt regulator would be more efficient if the supply is always operated at maximum power, but this is rarely the case. 27

Answer 6 A switching regulator usually has the current/voltage control pass transistor in series with the load. However, this transistor is only on when additional output current is needed. If output current isn t needed the transistor is turned off, thus saving power. Switching regulators can achieve 70-90% efficiency. This is much better than a linear regulator. You can research the 3 common types and what they do. Answer 7 I load = V Z R 2 Follow-up question: is the transistor sourcing current to the load, or sinking current from it? Challenge question #1: modify the given equation to more precisely predict load current, taking the β of the transistor into account. Challenge question #2: modify the location of the load in this circuit so that the given equation does precisely predict load current, rather than closely approximate load current. Answer 8 When a load is placed at V, the current drawn through the load causes V to drop, this causes the opamp to respond by increasing its output, thus increasing the current out of Q1. V=4.0V Output voltage is zener voltage plus the.7v Vbe drop of the transistor. R1 ensures that D5 is on. Without current through R1 and D5 the input to the opamp would be 0V Q1 provides the current for the load. The base of Q1, controlled by the op-amp controls how much current flows through Q1 The base of Q1 will go to the rail, and Q1 will likely burn out Series regulator Answer 9 I am only giving a hint to this one: In the short circuit condition, Q2 is turned on and it serves to turn off Q1. Challenge question: Change the short circuit protection to foldback current limiting. Why is this better, how does it work? Answer 10 You can find the solution to this on the data sheet. There are many choices for R1 and R2. You should make them not to big and not to small. Between 1kΩ and 100kΩ The capacitor is a decoupling capacitor. It serves the same purpose that caps on power rails have served in all classes. It acts as a low pass filter to remove noise on the power rail, thus producing a better DC voltage. The resistor that connects to gnd is a SC. Make sure you can explain why this is the case. 28

Answer 11 With the relocated feedback connection, the opamp now senses the load voltage at the output terminals, and is able to correct for any voltage losses in the power transistor. Follow-up question: the new, improved circuit certainly exhibits better voltage regulation, but it also introduces something that the first student finds surprising: now the output voltage is approximately 0.7 volts greater than it used to be. Explain why. Answer 12 Resistor R 1 fails open: Load current falls to zero. Zener diode D 1 fails shorted: Load current falls to zero. Resistor R 2 fails open: Load current falls to zero. Zener diode D 1 fails open: Load current increases. Load fails shorted: Load current remains the same. Wire between opamp output and transistor base breaks open: Load current falls to zero. Follow-up question: which of the two opamp power terminals (V supply or Ground) carries more current during normal operation, and why? Answer 13 Possible faults: (note that this list is not exhaustive) Opamp (U 1 ) failed with output saturated negative. Zener diode (D 1 ) failed shorted. Resistor R 1 failed open. Answer 14 Transformer T 1 primary winding fails open: Output voltage falls to zero after filter capacitors C 1 and C 2 discharge. Rectifying diode D 3 fails open: No effect seen at no load, regulation falters sooner as load gets heavier. Rectifying diode D 4 fails shorted: Fuse may blow, diode D 2 may fail due to overheating (and quickly blow the fuse if it also fails shorted). Resistor R 1 fails open: Output voltage falls to zero after filter capacitor C 2 discharges. Zener diode D 5 fails open: Output voltage rises to nearly full (unregulated) value. Operational amplifier U 1 fails with output saturated positive: Output voltage rises to nearly full (unregulated) value. Transistor Q 1 fails open (collector-to-emitter): Output voltage falls to zero after filter capacitor C 2 discharges. Answer 15 Note: the following answers are not exhaustive. There may be more circuit elements possibly at fault and more circuit elements known to be functioning properly! 29

Circuit elements that are possibly faulted 1. Transistor Q 1 failed open (base-to-emitter, collector-to-emitter, or both) 2. Broken wire/trace between V opamp terminal and Q 1 collector terminal. 3. Broken wire/trace between -V opamp terminal and - output terminal. Circuit elements that must be functioning properly (besides 120 volt AC source, switch, and fuse) 1. Transformer 2. Rectifying diodes Answer 16 Note: the following answers are not exhaustive. There may be more circuit elements possibly at fault and more circuit elements known to be functioning properly! Circuit elements that are possibly faulted 1. Transistor Q 1 failed shorted (collector-to-emitter) 2. Broken wire/trace between opamp inverting input terminal and power supply output terminal. 3. Opamp U 1 output failed high Circuit elements that must be functioning properly (besides 120 volt AC source, switch, and fuse) 1. Transformer 2. Rectifying diodes 3. Zener diode 4. Resistor R 1 Answer 17 When the output is high, the capacitor is charging through the two resistors, its voltage increasing. When the output is low, the capacitor is discharging through one resistor, current sinking through the 555 s Disch terminal. Follow-up question: algebraically manipulate the equation for this astable circuit s operating frequency, so as to solve for R 2. f = 1 (ln2)(r 1 2R 2 )C Challenge question: explain why the duty cycle of this circuit s output is always greater than 50%. Answer 18 The addition of a resistor between the Control terminal and ground would increase the frequency of the circuit, as well as decrease the peak-to-peak amplitude of the sawtooth wave signal across the timing capacitor. Follow-up question: does the addition of this resistor affect the output signal (pin 3) amplitude as well? Explain why or why not. If it amplitude is affected, does it increase or decrease with the resistor in place? Answer 19 With the potentiometers connected in series like this, the upper comparator s reference voltage will always be greater than the lower comparator s reference voltage. In order for both comparators to saturate their outputs high, the voltage from the photoresistor divider would have to be greater than the upper potentiometer s voltage and less then the lower potentiometer s voltage at the same time, which is an impossibility. This comparator configuration is commonly known as a window comparator circuit. 30

Answer 20 Spectrum analyzer display 0 db -20 db -40 db White noise source -60 db -80 db -100 db -120 db 1 2 3 4 5 6 7 8 9 10 Spectrum analyzer display 0 db -20 db -40 db White noise source LP filter -60 db -80 db -100 db -120 db 1 2 3 4 5 6 7 8 9 10 Answer 21 The low-pass Sallen-Key filter, of course! What s the matter? You re not laughing at my answer. What I m doing here is asking you to some research on Sallen-Key filters to confirm your qualitative analysis. And yes, I do expect you to be able to figure out which of the two filters is low-pass based on your knowledge of capacitors and op-amps, not just look up the answer in an op-amp reference book! Answer 22 The first filter shown is a band-stop, while the second filter shown is a band-pass. Answer 23 Resistor R 1 fails open: No signal output at all from the circuit. Capacitor C 1 fails open: Filter circuit stops filtering, passes all frequencies. Solder bridge (short) across resistor R 1 : Filter circuit stops filtering, passes all frequencies. Solder bridge (short) across capacitor C 1 : No signal output at all from the circuit. Resistor R 2 fails open: Voltage gain of circuit decreases to value of 1 (0 db). Resistor R 3 fails open: Filter circuit outputs square wave at all frequencies. 31

Answer 24 V TP1 = 1 volt I R3 = 200 µa V TP2 = 1 volt V out = -2.5 volts Answer 25 The first two opamps merely buffer the audio signal inputs so they do not become unnecessarily loaded by the resistors. The third opamp subtracts the left channel signal from the right channel signal, eliminating any sounds common to both channels. Challenge question: unfortunately, the circuit as shown tends to eliminate bass tones as well as vocals, since the acoustic properties of bass tones make them represented nearly equally on both channels. Determine how the circuit may be expanded to include opamps that re-introduce bass tones to the vocal-eliminated output. Answer 26 V 1 V 2 V out 0 V 0 V 0 V 1 V 0 V -2 V 0 V 1 V 2 V 2 V 1.5 V -1 V 3.4 V 1.2 V -4.4 V -2 V 4 V 12 V 5 V 5 V 0 V -3 V -3 V 0 V V out = 2(V 2 V 1 ) Follow-up question: explain how this circuit is at once similar and different from the popular instrumentation amplifier circuit. Answer 27 Resistor R 1 fails open: V out becomes equal to 1 2 V 2. Resistor R 2 fails open: V out saturates. Solder bridge (short) across resistor R 3 : V out becomes equal to 2V 2 V 1 instead of V 2 V 1. Resistor R 4 fails open: V out becomes equal to 2V 2 V 1 instead of V 2 V 1. Solder bridge (short) across resistor R 4 : V out becomes equal to V 1. Answer 28 V TP1 = 2.667 volts I Rf = 533.3 µa V TP2 = 2.667 volts V out = 8.0 volts 32

Answer 29 Resistor R 1 fails open: V out becomes (inverted) sum of V 2 and V 3 only. Resistor R 2 fails open: V out becomes (inverted) sum of V 1 and V 3 only. Solder bridge (short) across resistor R 3 : V out saturates in a negative direction. Resistor R 4 fails open: V out saturates in a negative direction. Solder bridge (short) across resistor R 4 : V out goes to 0 volts. Kuphaldt, Tony. Socratic Electronics. Socratic Electronics. Ibiblio.org, n.d. Web. 28 Dec. 2014. This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/, or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. The terms and conditions of this license allow for free copying, distribution, and/or modification of all licensed works by the general public. 33