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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

Find RIN in Figure P4–16. is www R Bix RIN FIGURE P4-16
Find the Norton Equivalent circuit seen by the load in Figure P4–17. VS + 1 Rs ww + Bix Ro v Load Rx FIGURE P4-17
Find the Thevenin Equivalent circuit seen by the load in Figure P4–18. is Vx gvx Ro v Load FIGURE P4-18
The circuit parameters in Figure P4–19 are RB¼100 kV, RC ¼ 3.3 kV, b¼100, Vg¼0.7 V, and VCC¼15 V. Find iC and vCE for vS¼1 V. Repeat for vS¼5 V. ic RC ww + RB B w VCE +1 VS FIGURE P4-19 + Vcc
The circuit parameters in Figure P4–19 are RC¼3 kV, b¼120, Vg¼0.7 V, and VCC¼5 V. Select a value of RB such that the transistor is in the saturation mode when vS 2 V.
The parameters of the transistor in Figure P4–21 are b¼60 and Vg¼0.7 V. Find iC and vCE for vS¼0.8 V. Repeat for vS¼2 V. 1 + VS ic 10 + 'B VCE 20 KS? FIGURE P4-21 10 ww + 15 V
An emergency indicator light uses a 10 V, 2-W incandescent lamp. It is to be ON when a digital output is high (5 V). 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 the
Find the voltage gain of each OP AMP circuit shown in Figure P4–23. + VS 133 W 330 W + Vo + (a) 33 W 330 W + VO + VS FIGURE P4-23 (b)
Considering simplicity and standard 10% tolerance resistors as major constraints, design OP AMP circuits that produce the following voltage gains 10%:100,þ200,þ1,0.5, þ0.5.
Two OPAMPcircuits are shown in Figure P4–25. 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 kV is connected to the input of each circuit. Does the original claim still hold? If it does not, explain why? + 1 www Vs VIN
(a) Find the voltage gain vO/vS in Figure P4–27.(b) Validate your answer by simulating the circuit in OrCAD. VS 1+. 22 33 w - 68 330 w + vo FIGURE P4-27 Vcc = 15 V
What is the range of the gain vO/vS in Figure P4–28? VS + | 2 w 100 www 100 w + Vo FIGURE P4-28 Voc = 15 V
Design a simple OP AMP circuit that has a variable gain from þ10 to þ100.
For the circuit in Figure P4–30:(a) Find vO in terms vS.(b) Find iO for vS¼1 V. Repeat for vS¼3 V. VS 10 + io 1+ W 150 10 10 FIGURE P4-30 + Vo Vcc = 24 V
For the circuit in Figure P4–31:(a) Find vO in terms vS.(b) Find iO for vS¼0.5 V. Repeat for vS¼2 V. VS +1 10 ww 10 W 100 FIGURE P4-31 100 www + io Vcc = 18 V
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 P4–32. Recommend a fix. 2 90 w 40 1 c www 10 www 3 + Vo + VS + Vcc = 15 V FIGURE P4-32
Design two circuits to produce the following output:vO¼2v1 3v2.(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.
For the circuit in Figure P4–34:(a) Find vO in terms of the inputs v1 and v2.(b) If v1¼1 V, what is the range of values v2 can have without saturating the OP AMP? |+ + 50 ww V1 50 www 100 www + vo 50 100 www Vcc = +15 V V2 FIGURE P4-34
The input-output relationship for a three-input inverting summer is vO ¼ v1 þ 10v2 þ 100v3 ½ The resistance of the feedback resistor is 100 kV. Find the values of the input resistors R1, R2, and R3.
Find vO in terms of the inputs v1 and v2 in Figure P4–36. +1 V1 +1 10 ww 33 w V2 10 ww 33 ww FIGURE P4-36 + Vo
The switch in Figure P4–37 is open, find vO in terms of the inputs vS1 and vS2. Repeat with the switch closed. 1 + +1 30 w 60 ww VS1 30 ww + 60 w VS2 Switch FIGURE P4-37 vo
Find vO in terms of vS1 and vS2 in Figure P4–38. R3 R4 w ww 0+ VO VS1 R1 w VS2 R ww + FIGURE P4-38
It is claimed that vO¼vS when the switch is closed in Figure P4–39 and that vO¼vS when the switch is open.Prove or disprove this claim. VS + 1 R www R w Sw FIGURE P4-39 R ww + Vo
The circuit in Figure P4–40 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 ¼ VT‘nð1 þ vS=ðRSIOÞÞ if the i-v characteristics of the diode is iD ¼ IOðevD=vT 1Þ.(b) Using MATLAB plot
(a) Use node voltage analysis to find the input-output relationship or K of the circuit in Figure P4–41.(b) Select values for the resistors so that K¼6. R www R3 www R w R + VS + Vo FIGURE P4-41
Use node voltage analysis in Figure P4–42 to show that iO¼vS/2R regardless of the load. That is, show that the circuit is a voltage-controlled current source. + 2R ww VS R www 1 + R2R + Vo FIGURE P4-42 10 w Load
For the circuit of Figure P4–43:(a) Find the output in terms of v1 and v2.(b) Draw a block diagram for the circuit. + V1 10 W + 22 10 33 W 100 + 12 FIGURE P4-43 + vo
Find vO in terms of the inputs vs1 and vs2 in Figure P4–44. VS2 + R R R2 R1 www www ww Vo + FIGURE P4-44
For the block diagram of Figure P4–45:(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. V1 5 V2 0- -1 -2 Vo FIGURE P4-45
For the block diagram of Figure P4–46:(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 -2 0.5 Vo 10 10 -2 Vo FIGURE P4-46
For the circuit in Figure P4–47(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 OrCAD. 1 10 1V+ W + vs+o 1 W 10 20 Vo W 1 Vo -10 1 VS 5 FIGURE P4-47 +
For the circuit of Figure P4–49:(a) Find the output v2 in terms of the input v1 in Figure P4–49.(b) Draw a representative block diagram for the circuit. 2 V 10 w 10 ww V1 5 w ww 10 www 10 FIGURE P4-49 10 www +
For the circuit of Figure P4–50:(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 OrCAD. 1+ VA 25 k VB ww 100 W 100 w VC + VD -o+VO 300 * FIGURE P4-50 VE 100
Faced with having to construct the circuit in Figure P4–51(a), a student offers to build the circuit in Figure P4–51(b) claiming it performs the same task. As the teaching assistant in the course, do you agree with the students claim? 10 20 20 20 V1 +5 6+ 5 (a) w 20 W 20 10 5 - 10 + Vo
Design a single OPAMP amplifier with a voltage gain of 100 and an input resistance greater than 5 kV using standard 5% resistance values less than 1 MV.
Design an OPAMP amplifier with a voltage gain of 5 using only 10-kV resistors and one OP AMP.
Using a single OPAMP, design a circuit with inputs v1 and v2 and an output vO¼v2 3v1. The input resistance seen by each input should be greater than 5 kV.
Design a difference amplifier with inputs v1 and v2 and an output vO¼30(v2 v1) using only one OP AMP. All resistances must be between 5 kV and 200 kV.
Using no more than two OP AMPs, design an OP AMP circuit with inputs v1, v2, and 50 mV and an output vO¼ 3v1 þ 2v2 250 mV.
Design a two-input non-inverting summer that will produce an output vO¼500 (v1 þ v2).
Design a four- input non-inverting summer that will produce an output vO¼6 (v1 þ v2 þ v3 þ 1V).
Design a cascaded OPAMP circuit that will produce the following output vO¼2 107 vS þ 3.5 V. The maximum gain for an OPAMP is 10,000. The input stage must have an input resistance of 1 kV or greater.
Design a cascaded OPAMP circuit that will produce the following output vO¼5 106vS þ 1.8 V. The maximum gain for an OPAMP is 10,000. The input stage must have an input resistance of 1 kV or greater. The only voltage source available is the 15 V used to power the OP AMPs.
Using the difference amplifier shown in Figure 4–53(Example 4–20), design a circuit that will produce the following output vO¼500 (v1 v2).
Design the interface circuit in Figure P4–62 so that 10 mW is delivered to the 100-V. load. Repeat for a 100-kV load. Verify your designs using OrCAD. 1 V 50 ww P2 Interface 1000 V2 circuit + 1 FIGURE P4-62
Design the interface circuit in Figure P4–63 so that the output is v2¼150v1 þ 1.5 V. 1 + 50 w V1 + 15 V Interface circuit FIGURE P4-63 12 - 50
(a) Design a circuit that can produce vO¼2000vTR 2.6Vusing twoOPAMPs.The input resistancemust be greater than 5 kV for vTR.(b) Repeat using only one OPAMP.
A requirement exists for an OPAMP circuit with the input-output relationship vO ¼ 5vS1 2vS2 Two proposed designs are shown in Figure P4–65. As the project engineer, you must recommend one of these circuits for production. Which of these circuits would you recommend for production and why? Hint:
A requirement exists for an OPAMP circuit to deliver 12Vto a 1-kVload using a 4–Vsource as an input voltage.Two proposed designs are shown in Figure P4–66. Some characteristics of the OPAMP that must be used in the design areWhich of these circuits would you recommend for production and why?
A particular application requires that an instrumentation interface deliver vO¼200vTR 5 V 2 % 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 OPAMP shown in Figure
The analog output of a five-bit DAC is 3.59 V when the input code is (1, 0, 1, 1, 1). What is the full-scale output of the DAC? How much does the analog output change when the input LSB changes?
The full-scale output of a six-bit DAC is 5.0 V.What is the analog output when the input code is (0, 1, 0, 1, 0, 0)?What is the resolution of this DAC?
An R-2RDACisshowninFigureP4–70.Thedigitalvoltages 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 (1, 1, 0 1)? 6+ M V1 V2 5+0 15 +9 V3 2R ww 2R ww 2R ww 2R R R R VA VB 3+ 5+ ww Vc 2R 2R w FIGURE P4-70 +VO
A 5th bit is added to the R-2R DAC shown in Figure P4–70. What is the maximum possible magnitude of the output voltage? What is the resolution of the revised DAC?
A Chromel-Constantan thermocouple (curve E) has the characteristics shown in Figure P4–72. Design an interface that will produce a 0- to 5-V output where 0 V refers to 0 C and 5Vrefers to 1000 C. The transducer can be modeled as a voltage source in series with a 15-V resistor. mV 80- 70- 70 60 60
A Chromel-Alumel thermocouple (curve K in Figure P4–72) is used to measure the temperature of an electric oven used in the semiconductor industry. Design an interface that will produce a 0- to 5-Voutput where 0 V refers to 200 C and 5 V refers to 1200 C (assume a straight line out to 1200 C).The
An analog accelerometer produces a continuous voltage that is proportional to acceleration in gravitational units or g. Figure P4–74 shows the characteristics of the accelerometer in question. The black curve is the actual characteristics;the colored curve is an acceptable linearized model.Design
A small pressure transducer has the characteristics shown in Figure P4–75. Design an interface that will operate between 7- and 32-psi. An input of 7 psi should produce 5V and 32 psi should produce 5V. The transducer is modeled as a voltage source in series with a 500 V resistor that can vary 75
A medical grade pressure transducer has been developed for use in invasive bloodpressuremonitoring.The output voltage of the transducer is vTR¼(0.06P 0.75)mV, where P is pressure inmmHg.The output resistance of the transducer is 1 kV. The blood pressure measurement is to be an input to an
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 certain
A photoresistor varies from 50 V, in bright sunlight to 500 kV in total darkness. Design a suitable circuit using the photoresistor so that total darkness produces 5 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 AMP you may
Your engineering firm needs an instrumentation amplifier that provides the following input-output relationship: vO¼106vTR 3.5V. The transducer is modeled as a voltage source in series with a resistor that varies with the transducer voltage from 40 V to 750 V. Avendor is offering the amplifier
Your supervisor drew the Figure of P4–80 on the back of an envelope to show you what he expects as an output to a signal that varies between 5 V. Design a suitable comparator circuit to achieve his expectation. vs (t) 5 0 (a) -5 5 vo (t) 15 V 0 -15 V (b) FIGURE P4-80
The OPAMP in Figure P4–81 operates as a comparator.Find the output voltage when vS¼2 V. Repeat for vS¼2 V and vS¼6 V. 4R R ww +5 V VS + FIGURE P4-81 + Vo
The circuit in Figure P4–82 has VCC¼15 Vand vN¼3V.Sketch the output voltage vO on the range 0 t 2 s for vS(t)¼10 sin(2pt) V. vs(t) 1 + + +15 V 3 V Vo FIGURE P4-82
A signal varies as vS(t)¼10(1e100t) V. Design a comparator circuit that will switch from 0 to 5 Vat 2 ms. Use a single OPAMP that has þ VCC¼þ 5V and VCC¼0 V.
A 5-bit flash ADC in Figure P4–84 uses a reference voltage of 6 V. Find the output code for the analog inputs vS¼3.5V, 2.3V, and 5.3V. If the reference voltage is changed to 9 V, which of these codes would change? R VN1 REF VS Wo R R VN2 R VN3 R VN4 R VN5 R w www w + '+ + -ob -ob -ob3 + -ob4 +/
Bipolar Power Supply Voltages The circuit in Figure P4–85 produces bipolar power supply voltages VPOS > 0 and VNEG 0. Note that the OP AMP output is grounded and that its þVCC andVCC terminals are connected to VPOS and VNEG, respectively.(a) Show that VPOS¼þVREF=2 and VNEG¼VREF=2 even if
Thermometer Design Problem There is a need to design a thermometer that can read from 250 C to 1000 C to monitor the temperature of a rocket’s nose cone. The output will feed a 0- to 5-V ADC prior to transmission of the temperature data to the ground. A reading of 250 C will deliver 0 V to the
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 1 mV at 100 psi, its usual operating pressure, and increases by 1 mV per psi.The design must sound an alarm if the
Current Switching DAC The circuit in Figure P4–88 is a 4–bit digital-to-analog converter(DAC). TheDAC 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
( , ) OP AMP Circuit Analysis and Design(a) Find the input-output relationship of the circuit in Figure P4–89.(b) Design a circuit that realizes the relationship found in part (a) using only 10-kV resistors and one OP AMP. 5+5 R w 2R R R w w ww + www R www 2R V2 1/2R FIGURE P4-89 + + VO
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 200 mV per ohm change
Resistance Temperature Transducer A resistive transducer uses a sensing element whose resistance varies with temperature. For a particular transducer, the resistance varies as RTR¼0.375T þ 100 V, where Tis temperature in C. This transducer is to be included in a circuit to measure temperatures in
Sketch the following waveforms:(a) v1ðtÞ ¼ 5uðtÞ 5uðt 1Þ V(b) v2ðtÞ ¼ 3uðt þ 2Þ 2uðt 2Þ V(c) v3ðtÞ ¼Zt1 v1ðxÞdx(d) v4ðtÞ ¼ dV2ðtÞdt
Sketch the following waveforms(a) v1(t) ¼ 2 u(t) V(b) v2(t) ¼ 2u(t þ 200) þ 3u(t þ 100) u(t) V(c) Construct the waveforms in parts (a) and (b) using OrCAD.
Sketch the following waveforms:(a) v1(t) ¼ 4r(t þ 1) 4r(t 1) V(b) v2(t) ¼ 2 þ r(t þ 1) 2r(t 1) þ r(t 3) V(c) v3ðtÞ ¼ d v1ðtÞdt(d) v4ðtÞ ¼ d2 v2ðtÞdt2
Express each of the following signals as a sum of singularity functions.(a) v1ðtÞ ¼32 0t < 1 1 t < 2 2 t 8>>:
Express the waveform in Figure P5–6 as a sum of step functions. v (t) (V) 12 t(s) 0 1 2 34 5 -6 -12 FIGURE P5-6
Sketch the waveform described by the following:vðtÞ ¼ 1 e2 t þ 1 e ½uðt þ eÞ uðtÞþ 1 e2 t þ 1 e ½uðtÞ uðt eÞV
Sketch the waveform described by the following:vðtÞ ¼ 10dðtÞ 5dðt 5Þ þ 2dðt 10ÞV
Generate on OrCAD a waveform v(t) that starts at t ¼1 ms and consists of a pulse train of 1 V pulses with a 1 ms pulse width that repeat every 3 ms.
Sketch the following exponential waveforms. Find the amplitude and time constant of each waveform.(a) v1(t) ¼ [100 e100t] u(t) V(b) v2(t) ¼ [20 et/100] u(t 2) V(c) v3(t) ¼ [5 e2(t 5)] u(t 5) V (d) v4(t) ¼ [50 e10,000t] u(t) V
Write expressions for the derivative (t > 0) and integral(from 0 to t) of the exponential waveform i(t) ¼ [500 e5000t]u(t) mA.
Anexponentialwaveformdecays to 50%of its initial (t¼0)amplitude in 25 ms. Find the time constant of the waveform.
Write an expression for the waveform in Figure P5–14. v(t) (V) 10 3.68 0 10 20 30 40 50 60 FIGURE P5-14 t (ms)
The amplitude of an exponential waveform is 6 Vat t ¼ 0 and 3.5 V at t ¼ 3 ms. What is its time constant?
Construct an exponential waveform that fits entirely within the nonshaded region in Figure P5–16. v(t) (V) 1.0 0.6 0.5 0 0 0.01 FIGURE P5-16 t(s)
Construct an exponential waveform that fits entirely within the nonshaded region in Figure P5–17. v(t)(V) 10 9 6 2 0 01 5 10 12 20 20 t (ms) FIGURE P5-17
By direct substitution show that the exponential function v(t) ¼ VAeat satisfies the following first-order differential equation.dvðtÞdtþ avðtÞ ¼ 0
Find the period, frequency, amplitude, time shift, and phase angle of the following sinusoids.(a) v1(t) ¼ 240 cos(120pt) þ 240 sin(120pt) V(b) v2(t) ¼ 40 cos(100 kpt) þ 30 sin(100 kpt) V
(a) Plot the waveform of each sinusoid in Problem 5–19(b) UseOrCADto produce thewaveforminProblem5–19(b).
Write an expression for the sinusoid in Figure P5–21.What are the phase angle and time shift of the waveform? v(t) (V) 5 10 ms 0 -5 FIGURE P5-21 t (ms)
Write an expression for the sinusoid in Figure P5–22.What are the phase angle and time shift of the waveform? 3 v(t) (V) 2 s. -3- t (us) 0 1.6 FIGURE P5-22
Find the Fourier coefficients, cyclic frequency, and radian frequency of the following sinusoids:(a) v(t) ¼ 120 cos(120 pt þ 36.9) V(b) i(t) ¼ 12 cos(120pt 270) A
Use MATLAB or Excel to display two cycles of the following waveform:vS ¼ 19:1 sin 1000 pt þ 6:37 sin 3000 p tþ 3:82 sin 5000 pt þ 2:73 sin 7000 ptþ 2:1 sin 9000 ptV What are the period and amplitude of the resulting waveform? What common waveform is this waveform approximating?
For the following sinusoid:v(t) ¼ 100 cos(2p400t þ 30) V(a) Find the Fourier coefficients, cyclic frequency, and radian frequency(b) Plot the waveform.(c) Use MATLAB to produce the waveform.
Find the time shift of each sinusoid(a) in Problem 5–23.(b) in Problem 5–25.
Consider the following composite waveforms.(a) v1(t) ¼ 3 [1 e10,000t] u(t) V(b) v2(t) ¼ 15 [e10t – e5t] u(t) V Sketch each on paper and then generate each using OrCAD and MATLAB and plot the results.
Consider the following composite waveforms.(a) i1(t) ¼ 5 – 5 sin(1000pt) u(t) A(b) i2(t) ¼ 350 [e1000t þ cos(2000pt)] u(t) mA Sketch each on paper and then generate each using OrCAD and MATLAB and plot the results.

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