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systems analysis and design

The Analysis And Design Of Linear Circuits 7th Edition Roland E Thomas, Albert J Rosa, Gregory J Toussaint - Solutions

4–5 Find the voltage gain vO/vS in Figure P4–5. Rs Rp RK Wo wo w Vs (+ VX Vy + RL VO H2VY FIGURE P4-5
4–6 Find the voltage gain vO=vS in Figure P4–6. 1+ + + Vx- 200 vx +1 > 10 vo FIGURE P4-6
4–7 Find an expression for the current gain iO=iS in Figure P4–7.(Hint: Apply KCL at node A.) Rs A ww is VS RE FIGURE P4-7 BIE Rc io
4–8 (a) Find the voltage vO in Figure P4–8.(b) Validate your answer by simulating the circuit in Multisim. 10-3x 1.5 ww + 1 kQ www kV Vx 3.3 k23 2 V 1 FIGURE P4-8 0+ vo
4–9 (a) Find an expression for the gain iO=vS in Figure P4–9 in terms of RX.(b) Select a value for RX so that the gain is −0:002.(c) Simulate the circuit in Multisim and perform a parameter sweep on RX from 10 Ω to 10MΩ and using the cursor to find the required value of RX. How does your
4–10 Find an expression for the voltage gain vO/vS in Figure P4–10. 1+ Rs ww Vx+ FIGURE P4-10 gvx Rovo
4–11 (a) Find an expression for the voltage gain vO=vS in Figure P4–11.(b) Let RS = 1kΩ, RL = 1kΩ, and μ = 200. Find the voltage gain vO=vS as a function of RF. Find the voltage gain for three values of RF: ∞, 0 Ω, and 1 kΩ.(c) Simulate the circuit in Multisim and perform a parameter
4–12 Select g in the circuit of Figure P4–12 so that the output voltage is 10 V. 1 mV (+ 1 + 1.5 vo Vx gvx FIGURE P4-12 -
4–13 In the circuit of Figure P4–13, the VCVS has a μ of 10, RS is a 10-kΩ resistor and RL is a 3.3-kΩ resistor. Find the value of the feedback resistor RF that will cause the gain K = vO=vS to go to infinity. Is there a value of RF that will yield K = 2?Determine that resistance or explain
4–14 Find the Thévenin equivalent circuit that the load RL sees in Figure P4–14. Repeat the problem with RF replaced by an open circuit. VS Rs RF Rp www ww ww Vx + RL +1 FIGURE P4-14 VT, RT
4–15 (a) Find the Thévenin equivalent circuit that the load RL sees in Figure 4–15.(b) Then if RP = r = RL = 10kΩ, RS = 1kΩ, and vS = 1 V, find the power delivered to the load resistor VS 1+ Rs Rp www w ris RL3 Thvenin circuit FIGURE P4-15
4–16 Find RIN in Figure P4–16. ist R VS +- 1+ RIN FIGURE P4-16 ris
4–17 If R = 2:2 kΩ and β = 110 in Figure P4–17, what is the effect on the input resistance RIN caused by the dependent source? is ww R Bix RIN FIGURE P4-17
4–18 Find the Norton equivalent circuit seen by the load in Figure P4–18. VS 1+ Rs ww Rx Bix FIGURE P4-18 www Ro v Load
4–19 Find the Thévenin equivalent circuit seen by the load in Figure P4–19. + is R$ R vx ww Ro gvx FIGURE P4-19 A Load
4–20 Figure P4–20 is a dependent-source model of a subtractor.Use MATLAB or node-voltage analysis to derive an exact expression for the output. Then let μ ! ∞ and compare your answer to the expression for the subtractor in Eq. (4–32) in the text. VSI +1 VC +1 R VB ww R3 + Vx R www VD www
4–21 The circuit parameters in Figure P4–21 are RB = 100 kΩ, RC = 3:3 kΩ, β = 100, Vγ = 0:7 V, and VCC = 15 V. Find iC and vCE for vS = 0:5 V. Repeat for vS = 4 V and 6 V. RB www VS RC ww ic + + VCE Vcc +1 FIGURE P4-21
4–22 The circuit parameters in Figure P4–21 are RC = 3kΩ, β = 100, Vγ = 0:7 V, and VCC = 5 V. Select a value of RB such that the transistor is in the saturation mode when vS ≥2V.
4–23 The parameters of the transistor in Figure P4–23 areβ = 100 and Vγ = 0:7 V. Find iC and vCE for vS = 0:8V.Repeat for vS =2:5V. 1+ 10 ww + 10 ww + VCE 20 k 15 V 'B FIGURE P4-23
4–24 When using a transistor as a linear amplifier, it is important to avoid driving the transistor into either cutoff or saturation. Since most signals that are amplified are time varying, the maximum excursions of the time-varying signal should be known. In this problem, the time-varying signal
4–25 An emergency indicator light uses a 10-V, 2-W incandescent lamp. It is to be ON when a digital output is high ð5 VÞ.The digital circuit does not have sufficient power to turn on the lamp directly. However, as is common practice, a transistor driver is used as a digital switch. Select RB in
4–26 Find the voltage gain of each OP AMP circuit shown in Figure P4–26. + VS 15 W 470 W (a) vo 15 470 + Vo + VS (b) FIGURE P4-26
4–27 Considering simplicity and standard 10% tolerance resistors as major constraints, design OP AMP circuits that produce the following voltage gains +-10%: − 150, + 60,+ 1, −1, −0:8, + 0:7.
4–28 Two OP AMP circuits are shown in Figure P4–28.Both claim to produce a gain of either +- 100.(a) Show that the claim is true(b) A practical source with a series resistor of 1 kΩ is connected to the input of each circuit. Does the original claim still hold? If it does not, explain why +
4–29 Suppose the output of the practical source shown in Figure P4–28 needs to be amplified by −104 and you can use only the two circuits shown. How would you connect the circuits to achieve this? Explain why.
4–30 (a) Find the voltage gain vO=vS in Figure P4–30. What is the range of the input that can be amplified without causing the OP AMP to saturate?(b) Validate your answers by simulating the circuit in Multisim. 22 ww 33 w 330 w + vo +1 47 FIGURE P4-30 Voc = 15 V
4–31 What is the range of the gain vO=vS in Figure P4–31? VS 1.5 w 100 w 100 w + Vo +1 FIGURE P4-31 Vcc = 15 V
4–32 Design a simple OP AMP circuit that has a variable gain from −100 to −5000.
4–33 Using only one OP AMP, design a circuit that realizes the following equation:vO =5v1 −3:3V
4–34 Design a circuit using only one OP AMP that realizes the following equation:vO = −10v1 −0:5v2
4–36 For the circuit in Figure P4–36:(a) Find vO in terms of vS.(b) Find iO for vS = 1 V. Repeat for vS = 3V. VS 1+ 10 w ww 150 15 22 +01 FIGURE P4-36 Voc = 24 V
4–37 For the circuit in Figure P4–37:(a) Find vO in terms of vS.(b) Find iO for vS = 1 V. Repeat for vS = 2V VS +1 10 w 150 www Vo 10 w 150 FIGURE P4-37 Vcc = 18 V
4–38 A young designer needed to amplify a 2-V signal by the factors of 1, 5, and 10. Find the problem with the design shown in Figure P4–38. Recommend a fix. 10 ww 3 90 ww , 40 ww + vo + + vs Vcc = 15 V FIGURE P4-38
4–39 Design two circuits to produce the following output:vO =2v1 −4v2.(a) In your first design, use a standard subtractor.(b) In your second design, both inputs must be into high input resistance amplifiers to avoid loading.
4–40 Design a noninverting summer for five inputs with equal gains of 10.
4–41 For the circuit in Figure P4–41:(a) Find vO in terms of the inputs v1 and v2.(b) If v1 = 1 V, what is the range of values v2 can have without saturating the OP AMP? 50 ww V 50 ww 100 ww +1 + + 50 ww 50 Voc = +15 V V2 FIGURE P4-41 Vo
4–42 The input-output relationship for a three-input inverting summer isThe resistance of the feedback resistor is 100 kΩ. Find the values of the input resistors R1, R2, and R3. vo [v+10v2 + 100v3]
4–43 Find vO in terms of the inputs v1, v2, and v3 in Figure P4–43 + I 1+ 5 ww 5 w 30 w w 2.5 V3 + ww 30 FIGURE P4-43 vo
4–44 The switch in Figure P4–44 is open. Find vO in terms of the inputs vS1 and vS2. Repeat with the switch closed. +1 15 w 60 ww VSI 15 w 60 ww +1 VS2 Switch FIGURE P4-44 vo
4–45 Design an OP AMP circuit that realizes the block diagram shown in Figure 4–45. Do not use more than two OP AMPs in your design. V2 0 +5 + + V3 0 -2 FIGURE P4-45 + Vo
4–46 Design an OP AMP circuit that realizes the block diagram shown in Figure 4–46. The OP AMPs that you must use have a maximum gain of 3000. 3 x 107 FIGURE P4-46 vo
4–47 Find vO in terms of vS1 and vS2 in Figure P4–47. R3 w R4 w VSI VS2 R www R ww FIGURE P4-47 0+ Vo
4–48 It is claimed that vO = vS when the switch is closed in Figure P4–48 and that vO = −vS when the switch is open.Prove or disprove this claim. +1 R ww R ww + R ww FIGURE P4-48 Vo
4–49 The circuit in Figure P4–49 has a diode in its feedback path and is called a “log-amp” because its output is proportional to the natural log of the input. (a) Show that vo=-Vrln (1+0) if the i-v characteristics of the diode is ip = 10 (e/VT-1). (b) Using MATLAB plot vo versus vs for Rs
4–50 (a) Use node-voltage analysis to find the input-output relationship or K of the circuit in Figure P4–50.(b) Select values for the resistors so that K = −10. R R3 www ww R ww R + Vo +5 FIGURE P4-50
4–51 Use node-voltage analysis in Figure P4–51 to show that iO = −vS=2R regardless of the load. That is, show that the circuit is a voltage-controlled current source. 2R ww +5 R + ww R2R + vo FIGURE P4-51 Load
4–52 For the circuit of Figure P4–52:(a) Find the output in terms of v1.(b) Draw a block diagram for the circuit. + V 10 100 W 10 w 100 W + + + 33 V=3V vo + FIGURE P4-52
4–53 For the circuit of Figure P4–53:(a) Find the output in terms of vS.(b) Draw a block diagram for the circuit 100 www + 50 www 50 ww FIGURE P4-53 100 200 + VO
4–54 For the block diagram of Figure P4–54:(a) Find an expression for vO in terms of v1 and v2.(b) Design a suitable circuit that realizes the block diagram using only one OP AMP. V2 5 FIGURE P4-54 vo
4–55 For the block diagram of Figure P4–55:(a) Find an expression for vO in terms of vS and the input voltage source.(b) Design a suitable circuit that realizes the block diagram using only one OP AMP and the 0:5-V source. Vs o 0.5 V 10- 8. vo FIGURE P4-55
4–56 For the circuit in Figure P4–56:(a) Find vO in terms of vS and the 1-V source.(b) Prove that the block diagram provides the same output.(c) Redesign the circuit using only one OP AMP.(d) Validate your design using Multisim 1V+ 20 1 W 10 + vo 1 Vs+ W 10 W 1 V -10 +1 VS 5 vo FIGURE P4-56
4–57 On a quiz, an instructor asked the students to draw a circuit that would realize the block diagram shown in Figure P4–57.(a) One student drew the circuit shown in Figure P4–57.(b) The instructor noted three problems with the student’s design. Find the problems and correct them. 's-2 +
4–58 On an exam, students were asked to design an efficient solution for the following relationship: v2 =3v1 + 15.Two of the designs are shown in Figure P4–58. Which, if any, of the designs are correct and what grade would you award each student? 10 10 +-W www www 10 10 www + + + 5 V 20 ww
4–59 For the circuit of Figure P4–59:(a) Find the output v2 in terms of the input v1.(b) Draw a representative block diagram for the circuit. + 10 w 10 ww + 5V 10 ww 10 ww ww 10 ww 10 FIGURE P4-59 V
4–60 For the circuit of Figure P4–60:(a) Use node-voltage analysis to find the output vO in terms of the input vS.(b) Draw a representative block diagram for the circuit.(c) Verify your answer using Multisim. 100 ww VA 50 VB w 150 VC ww vs +1 FIGURE P4-60 vp 0+vo 300 VE 50
4–61 Faced with having to construct the circuit in Figure P4–61(a), a student offers to build the circuit in Figure P4–61(b) claiming that it performs the same task.Asthe teaching assistant in the course, do you agree with the students claim? 10 20 20 20 W + + VI (a) +, + 20 W 5 10 +
4–62 Design a single OP AMP amplifier with a voltage gain of −1000 and an input resistance greater than 5 kΩ using standard 5% resistance values less than 3:3MΩ.
4–63 Design an OP AMP amplifier with a voltage gain of 4 using only 15-kΩ resistors and one OP AMP.
4–64 Using a single OP AMP, design a circuit with inputs v1 and v2 and an output vO = v2 − 5v1. The input resistance seen by each input should be greater than 1 kΩ.
4–65 Design a differential amplifier with inputs v1 and v2 and an output vO = 100ðv2 − v1Þ using only one OP AMP.All resistances must be between 10 kΩ and 1MΩ.
4–66 Using no more than two OP AMPs, design an OP AMP circuit with inputs v1, v2, and 100 mV and an output vO = −3v1 + 2v2 − 300 mV.
4–67 Design a two-input noninverting summer that will produce an output vO = 200 ðv1 + v2Þ.
4–68 Design a three-input noninverting summer that will produce an output vO = 6 ðv1 + v2 + 1VÞ.
4–69 Design a cascaded OPAMPcircuit that will produce the output vO = 5 × 107 vS + 2:5 V. The maximum gain for an OP AMP is 10,000. The input stage must have an input resistance of 1 kΩ or greater.
4–70 Design a cascaded OPAMPcircuit that will produce the following output vO = – 3:5 × 106 vS − 1:5 V. The maximum gain for an OP AMP is 10,000. The input stage must have an input resistance of 1 kΩ or greater. The only voltage source available is the 15 V used to power the OP AMPs.
4–71 Using the instrumentation amplifier shown in Figure 4–78 (Example 4–27), design a circuit that will produce the output vO = 5×105 ðv1 − v2Þ. No single OP AMP can have a gain greater than 5000.
4–72 Design the interface circuit in Figure P4–72 so that 15mW is delivered to the 100-Ω load. Repeat for a 100-kΩload. Verify your designs using Multisim. Assume that your OP AMPs have VCC = +- 15 V. 1V 50 w P2 Interface V2 1000 circuit FIGURE P4-72
4–73 Design the interface circuit in Figure P4–73 so that the output is v2 = 150v1 + 1:5V. 50 w +1 15 V Interface circuit + FIGURE P4-73 150
4–74 (a) Design a circuit that can produce vO = 2000vTR −2:6 V using two OP AMPs. The input resistance must be greater than 10 kΩ for vTR. The largest resistor you can use is 1MΩ.(b) Repeat using only one OP AMP. What concession to the specifications must be made to permit this?
4–75 A requirement exists for an OP AMP circuit with the input–output relationship vO =5vS1 −2vS2 Three proposed designs are shown in Figure P4–75. As the project engineer, you must recommend one of these circuits for production. Which of these circuits would you recommend for production
4–76 A requirement exists for an OP AMP circuit to deliver 12 Vto a 1-kΩload using a 4-V source as an input voltage.Two proposed designs are shown in Figure P4–76. Some characteristics of the OPAMPthat must be used in the design are as follows:Which of these circuits would you recommend for
4–77 A particular application requires that an instrumentation interface delivers vO = 200vTR −5V2% to a DAC. The solution currently in use requires two OP AMPs and is constantly draining the supply batteries. A young engineer designed another tentative solution using just one OP AMP shown in
4–78 The analog output of a five-bit DAC is 2:97 V when the input code is (1, 0, 0, 1, 1). What is the full-scale output of the DAC? How much does the analog output change when the input LSB changes?
4–79 The full-scale output of a six-bit DAC is 10:0 V. What is the analog output when the input code is (0, 1, 0, 1, 0, 1)?What is the resolution of this DAC?
4–80 An R-2R DAC is shown in Figure P4–80. The digital voltages v1, v2, etc., can be either 5 V for a logic 1 or 0 V for a logic 0. What is the DAC’s output when the logic input is(0, 1, 0 1)? VA 6+= 6+21 V2 2R ww 2R w 2R R R + 2R w w VB ww V3 +9 VA 2R w R 2R Vc www +10 FIGURE P4-80
4–81 A fifth bit is added to the R-2R DAC shown in Figure P4–80. What is the maximum possible magnitude of the output voltage? What is the resolution of the revised DAC?
4–82 AChromel-Constantan thermocouple (curve E) has the characteristics shown in Figure P4–82. Design an interface that will produce a −5-V to + 5-V output where −5 Vrefers to 0C and + 5 V refers to 1000C. The transducer can be modeled as a voltage source in series with a 15-Ω resistor.
4–83 A Chromel-Alumel thermocouple (curve K in Figure P4–82) is used to measure the temperature of an electric oven used in the semiconductor industry. Design an interface that will produce a 0-V to 6-V output where 0 V refers to 200C and 6 V refers to 1200C (assume a straight line out to
4–84 An analog accelerometer produces a continuous voltage that is proportional to acceleration in gravitational units or g. Figure P4–84 shows the characteristics of the accelerometer in question. The black curve is the actual characteristics;the colored curve is an acceptable linearized
4–85 A small pressure transducer has the characteristics shown in Figure P4–85. Design an interface that will operate between 10 and 30 psi. An input of 10 psi should produce 0 V and 30 psi should produce + 5 V. The transducer is modeled as a voltage source in series with a 500-Ω resistor that
4–86 Amedical grade pressure transducer has been developed for use in invasive blood pressuremonitoring. The output voltage of the transducer is vTR = ð0:06P − 0:75ÞmV, where P is pressure in mmHg. The output resistance of the transducer is 1 kΩ. The blood pressure measurement is to be an
4–87 The acid/alkaline balance of a fluid is measured by the pH scale. The scale runs from 0 (extremely acid) to 14 (extremely alkaline), with pH 7 being neutral. A pH electrode is a sensor that produces a small voltage that is directly proportional to the pH of the fluid in a test chamber.For a
4–88 A photoresistor varies from 10 Ω in bright sunlight to 500 kΩ in total darkness. Design a suitable circuit using the photoresistor so that total darkness produces 0 V, while bright sunlight produces −5 V, regardless of the load. You have a 5-V source and a 15-V source to power any OP
4–89 Your engineering firm needs an instrumentation amplifier that provides the following input-output relationship:vO =106vTR −3:5 V. The transducer is modeled as a voltage source in series with a resistor that varies with the transducer voltage from 40 Ω to 750 Ω. Avendor is offering the
4–90 Your supervisor drew Figure P4–90 on the back of an envelope to show you what he expects as an output to a signal that varies between5V. Design a suitable comparator circuit to achieve his expectation vs(f) 5 0 t -5 vo(t) 15 V 0 (a) -15 V (b) FIGURE P4-90
4–91 A rocket design team has a need to detect the temperatures in a rocket motor. The combustion chamber is that part of a thrust chamber where the combustion of the propellant takes place. The combustion temperature is much higher than the melting points of most chamber wall materials and
4–92 The OP AMP in Figure P4–92 operates as a comparator.Find the output voltage when vS = 5 V. Repeat for vS = −3 V and vS = 12V. +15 V 2R R w ww +1 FIGURE P4-92 + vo
4–93 The circuit in Figure P4–93 has VCC = + 5 V and vN = −3 V. Sketch the output voltage vO on the range 0 ≤ t ≤ 2 s for vS(t) = 4 sin(2πt) V. vs(f) 1+ 3 V FIGURE P4-93 +5 V + Vo
4–94 A five-bit flash ADC in Figure P4–94 uses a reference voltage of 5 V. Find the output code for the analog inputs vS = 3:5V, 2:3 V, and 4:9 V. If the reference voltage is changed to 8 V, which of these codes would change? VREF VS I R VNI R VN2 w R ww VN3 R VN4 R VN5 ww ww R FIGURE P4-94 +/
4–95 Bipolar Power Supply Voltages The circuit in Figure P4–95 produces bipolar power supply voltages VPOS > 0 and VNEG 0. Note that the OP AMP output is grounded and that its +VCC and −VCC terminals are connected to VPOS and VNEG, respectively.(a) Show that VPOS = +VREF=2 and VNEG =
4–96 Thermometer Design Problem There is a need to design a thermometer that can read from 30C to 300C to monitor the temperature of an Unmanned Aerial Vehicle’s (UAV) power supply. The output will feed a 0-V to 5-V ADC prior to transmission of the temperature data to the ground. A reading of
4–97 High Bias Design Problem A particular pressure sensor is designed to operate under constant pressure. The task is to detect a pressure increase and sound an alarm. The sensor produces 1mV at 100 psi, its usual operating pressure, and increases by 1 μV=psi. The design must sound an alarm if
4–98 Weathervane Azimuth Detection A weathervane turns with the wind direction. The base of the weathervane is connected to a rotary potentiometer without stops, that is, the potentiometer turns from 0 Ω to 10 kΩ linearly clockwise, but jumps to 0 Ω after the maximum resistance is reached and
4–99 Current Switching DAC The circuit in Figure P4–99 is a four-bit DAC. The DAC output is the voltage vO and the input is the binary code represented by bits b1, b2, b3, and b4. The input bits are either 0 (low) or 1 (high), and each controls one of the four switches in the figure. When bits
4–100 OP AMP Circuit Analysis and Design(a) Find the input-output relationship of the circuit in Figure P4–100.(b) Design a circuit that realizes the relationship found in part (a) using only 10-kΩ resistors and one OP AMP R 2R R www ww w V2R +W V2 ww ww R 2R FIGURE P4-100 R w + vo
4–101 Instrumentation Amplifier with Alarm Strain gauges measuring the deflection of a sintered metal column are connected to a Wheatstone bridge. The output of the bridge is balanced when there is no strain producing 0 V output.As the column is deflected, the bridge produces 150 μV=Ωchange
4–102 Resistance Temperature TransducerA resistive transducer uses a sensing element whose resistance varies with temperature. For a particular transducer, the resistance varies as RTR = 0:375T + 100 Ω, where T is temperature in C. This transducer is to be included in a circuit to measure
Show that the active filter in Figure P14–4 has a transfer function of the form TðsÞ ¼ V2ðsÞV1ðsÞ¼ 1 R1R2C1C2s2 þ R2C2s þ 1 Using C1¼C2¼C, develop a method of selecting values for C, R1, and R2. Then select values so that the filter has a cutoff frequency of 100 krad/s and a z of 0.6.
The active filter in Figure P14–6 has a transfer function of the form TðsÞ ¼ V2ðsÞV1ðsÞ¼R2=R1 R2R3C1C2s2 þ R3C2 þ R2C2ð1 þ R3=R1½ Þs þ 1 Using R1¼R2¼R3¼R, develop a method of selecting values for C1, C2 and R. Then select values so that the filter has a cutoff frequency of 150
Show that the active filter in Figure P14–7 has a transfer function of the form TðsÞ ¼ V2ðsÞV1ðsÞ¼ R1R2C1C2s2 R1R2C1C2s2 þ R1C1s þ 1 Using C1¼C2¼C, develop a method of selecting values for C, R1, and R2. Then select values so that the filter has a cutoff frequency of 1 krad/s and a z

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