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computer science
systems analysis and design 12th
Questions and Answers of
Systems Analysis And Design 12th
Design the circuit shown in Figure P8.46 to deliver \(2 \mathrm{~W}\) to a 20 ohm load. The maximum output voltage should be a symmetrical \(8 \mathrm{~V}\) sine wave. V+= 10 V +Bias M3 M -OVO M2 RL
Describe the ideal op-amp model and describe the implications of this ideal model in terms of input currents and voltages.
Describe the op-amp model including the effect of a finite op-amp voltage gain.
Describe the operation and characteristics of the ideal inverting amplifier.
What is the concept of virtual ground?
What is the significance of a zero output resistance?
When a finite op-amp gain is taken into account, is the magnitude of the resulting amplifier voltage gain less than or greater than the ideal value?
Describe the operation and characteristics of the ideal summing amplifier.
Describe the operation and characteristics of the ideal noninverting amplifier.
Describe the voltage follower. What are the advantages of using this circuit.
What is the input resistance of an ideal current-to-voltage converter?
Describe the operation and characteristics of a difference amplifier.
Describe the operation and characteristics of an instrumentation amplifier.
Describe the operation and characteristics of an op-amp circuit using a capacitor as a feedback element.
Describe the operation and characteristics of an op-amp circuit using a diode as a feedback element.
Assume an op-amp is ideal, except for having a finite open-loop differential gain. Measurements were made with the op-amp in the open-loop mode. Determine the open-loop gain and complete the
The op-amp in the circuit shown in Figure P9.2 is ideal except it has a finite open-loop gain. (a) If \(A_{o d}=10^{4}\) and \(v_{O}=-2 \mathrm{~V}\), determine \(v_{I}\). (b) If \(v_{I}=2
An op-amp is in an open-loop configuration as shown in Figure 9.2.(a) If \(v_{1}=2.0010 \mathrm{~V}, v_{2}=2.000 \mathrm{~V}\), and \(A_{o d}=5 \times 10^{3}\), determine \(v_{O}\).(b) If
Consider the equivalent circuit of the op-amp shown in Figure 9.7(a). Assume terminal \(v_{1}\) is grounded and the input to terminal \(v_{2}\) is from a transducer that can be represented by a \(0.8
Consider the ideal inverting op-amp circuit shown in Figure 9.8. Determine the voltage gain \(A_{v}=v_{O} / v_{I}\) for(a) \(R_{2}=200 \mathrm{k} \Omega, R_{1}=20 \mathrm{k} \Omega\);(b) \(R_{2}=120
Assume the op-amps in Figure P9.6 are ideal. Find the voltage gain \(A_{v}=v_{O} / v_{I}\) and the input resistance \(R_{i}\) of each circuit. 20 www 200 www 20 k2 ww 200 ww 20 (a) www 20 Figure
Consider an ideal inverting op-amp with \(R_{2}=100 \mathrm{k} \Omega\) and \(R_{1}=10 \mathrm{k} \Omega\).(a) Determine the ideal voltage gain and input resistance \(R_{i}\).(b) Repeat part (a) for
(a) Design an inverting op-amp circuit with a closed-loop voltage gain of \(A_{v}=v_{O} / v_{I}=-12\). The current in each resistor is to be no larger than \(20 \mu \mathrm{A}\) when the output
Consider an ideal op-amp used in an inverting configuration as shown in Figure 9.8. Determine the closed-loop voltage gain for the following resistor values.(a) \(R_{1}=20 \mathrm{k} \Omega,
Consider the inverting amplifier shown in Figure 9.8. Assume the op-amp is ideal. Determine the resistor values \(R_{1}\) and \(R_{2}\) to produce a closed-loop voltage gain of (a) -3.0 , (b) -8.0 ,
(a) Design an inverting op-amp circuit with a closed-loop voltage gain of \(A_{v}=-6.5\). When in the input voltage is \(v_{I}=-0.25 \mathrm{~V}\), the magnitude of the currents is to be \(50 \mu
(a) Design an inverting op-amp circuit such that the closed-loop voltage gain is \(A_{v}=-20\) and the smallest resistor value is \(25 \mathrm{k} \Omega\).(b) Repeat part (a) for the case when the
(a) In an inverting op-amp circuit, the nominal resistance values are \(R_{2}=300 \mathrm{k} \Omega\) and \(R_{1}=15 \mathrm{k} \Omega\). The tolerance of each resistor is \(\pm 5 \%\), which means
(a) The input to the circuit shown in Figure P9.14 is \(v_{I}=-0.20 \mathrm{~V}\). (i) What is \(v_{O}\) ? (ii) Determine \(i_{2}, i_{O}\), and \(i_{L}\).(b) Repeat part (a) for \(v_{I}=+0.05
Design an inverting amplifier to provide a nominal closed-loop voltage gain of \(A_{v}=-30\). The maximum input voltage signal is \(25 \mathrm{mV}\) with a source resistance in the range \(1
The parameters of the two inverting op-amp circuits connected in cascade in Figure P9.16 are \(R_{1}=10 \mathrm{k} \Omega, R_{2}=80 \mathrm{k} \Omega, R_{3}=20 \mathrm{k} \Omega\), and \(R_{4}=100
Design the cascade inverting op-amp circuit in Figure P9.16 such that the overall closed-loop voltage gain is \(A_{v}=v_{O} / v_{I}=100\) and such that the maximum current in any resistor is limited
Design an amplifier system with three inverting op-amps circuits in cascade such that the overall closed-loop voltage gain is \(A_{v}=v_{O} / v_{I}=-300\). The maximum resistance is limited to \(200
Consider the circuit shown in Figure P9.19. (a) Determine the ideal output voltage \(v_{O}\) if \(v_{I}=-0.40 \mathrm{~V}\). (b) Determine the actual output voltage if the open-loop gain of the
The inverting op-amp shown in Figure 9.9 has parameters \(R_{1}=25 \mathrm{k} \Omega\), \(R_{2}=100 \mathrm{k} \Omega\), and \(A_{o d}=5 \times 10^{3}\). The input voltage is from an ideal voltage
(a) An op-amp with an open-loop gain of \(A_{o d}=7 \times 10^{3}\) is to be used in an inverting op-amp circuit. Let \(R_{2}=100 \mathrm{k} \Omega\) and \(R_{1}=10 \mathrm{k} \Omega\). If the output
(a) For the ideal inverting op-amp circuit with T-network, shown in Figure 9.12, the circuit parameters are \(R_{1}=10 \mathrm{k} \Omega, R_{2}=R_{3}=50 \mathrm{k} \Omega\), and \(R_{4}=5 \mathrm{k}
Consider the ideal inverting op-amp circuit with T-network in Figure 9.12. (a) Design the circuit such that the input resistance is \(500 \mathrm{k} \Omega\) and the gain is \(A_{v}=-80\). Do not use
An ideal inverting op-amp circuit is to be designed with a closed-loop voltage gain of \(A_{v}=-1000\). The largest resistor value to be used is \(500 \mathrm{k} \Omega\). (a) If the simple
For the op-amp circuit shown in Figure P9.25, determine the gain \(A_{v}=v_{O} / v_{I}\). Compare this result to the gain of the circuit shown in Figure 9.12, assuming all resistor values are
The inverting op-amp circuit in Figure 9.9 has parameters \(R_{1}=20 \mathrm{k} \Omega\), \(R_{2}=200 \mathrm{k} \Omega\), and \(A_{o d}=5 \times 10^{4}\). The output voltage is \(v_{O}=-4.80
(a) Consider the op-amp circuit in Figure P9.27. The open-loop gain of the op-amp is \(A_{o d}=2.5 \times 10^{3}\). (i) Determine \(v_{O}\) when \(v_{I}=-0.80 \mathrm{~V}\). (ii) What is the percent
The circuit in Figure P9.28 is similar to the inverting amplifier except the resistor \(R_{3}\) has been added. (a) Derive the expression for \(v_{O}\) in terms of \(v_{I}\) and the resistors. (b)
Design the amplifier in Figure P9.29 such that the output voltage varies between \(\pm 10 \mathrm{~V}\) as the wiper arm of the potentiometer changes from \(-10 \mathrm{~V}\) to \(+10 \mathrm{~V}\).
Consider the ideal inverting summing amplifier in Figure 9.14 (a) with parameters \(R_{1}=40 \mathrm{k} \Omega, R_{2}=20 \mathrm{k} \Omega, R_{3}=60 \mathrm{k} \Omega\), and \(R_{F}=120 \mathrm{k}
(a) Design an ideal inverting summing amplifier to produce an output voltage of \(v_{O}=-2.5\left(1.2 v_{I 1}+2.5 v_{I 2}+0.25 v_{I 3}\right)\). Design the circuit to produce the largest possible
Design an ideal inverting summing amplifier to produce an output voltage of \(v_{O}=-2\left(v_{I 1}+3 v_{I 2}\right)\). The input voltages are limited to the ranges of \(-1 \leq v_{I 1} \leq+1
Consider the summing amplifier in Figure 9.14 with \(R_{F}=10 \mathrm{k} \Omega\), \(R_{1}=1 \mathrm{k} \Omega, R_{2}=5 \mathrm{k} \Omega\), and \(R_{3}=10 \mathrm{k} \Omega\). If \(v_{I 1}\) is a
The parameters for the summing amplifier in Figure 9.14 are \(R_{F}=100 \mathrm{k} \Omega\) and \(R_{3}=\infty\). The two input voltages are \(v_{I 1}=4+125 \sin \omega t \mathrm{mV}\) and \(v_{I
(a) Design an ideal summing op-amp circuit to provide an output voltage of \(v_{O}=-2\left[\left(v_{I 1} / 4\right)+2 v_{I 2}+v_{I 3}\right]\). The largest resistor value is to be \(250 \mathrm{k}
An ideal three-input inverting summing amplifier is to be designed. The input voltages are \(v_{I 1}=2+2 \sin \omega t \mathrm{~V}, v_{I 2}=0.5 \sin \omega t \mathrm{~V}\), and \(v_{I 3}=-4
A summing amplifier can be used as a digital-to-analog converter (DAC). An example of a 4-bit DAC is shown in Figure P9.37. When switch \(S_{3}\) is connected to the \(-5 \mathrm{~V}\) supply, the
Consider the circuit in Figure P9.38. (a) Derive the expression for the output voltage \(v_{O}\) in terms of \(v_{I 1}\) and \(v_{I 2}\). (b) Determine \(v_{O}\) for \(v_{I 1}=+5 \mathrm{mV}\) and
Consider the summing amplifier in Figure 9.14 (a). Assume the op-amp has a finite open-loop differential gain \(A_{o d}\). Using the principle of superposition, show that the output voltage is given
Consider the ideal noninverting op-amp circuit in Figure 9.15. Determine the closed-loop gain for the following circuit parameters: (a) \(R_{1}=15 \mathrm{k} \Omega\), \(R_{2}=150 \mathrm{k}
(a) Design an ideal noninverting op-amp circuit with the configuration shown in Figure 9.15 to have a closed-loop gain of \(A_{v}=15\). When \(v_{0}=-7.5 \mathrm{~V}\), the current in any resistor is
Consider the noninverting amplifier in Figure 9.15. Assume the op-amp is ideal. Determine the resistor values \(R_{1}\) and \(R_{2}\) to produce a closed-loop gain of (a) 3 , (b) 9 , (c) 30 and (d)
For the circuit in Figure P9.43, the input voltage is \(v_{I}=5 \mathrm{~V}\). (a) If \(v_{O}=2.5 \mathrm{~V}\), determine the finite open-loop differential gain of the op-amp. (b) If the open-loop
Determine \(v_{O}\) as a function of \(v_{I 1}\) and \(v_{I 2}\) for the ideal noninverting op-amp circuit in Figure P9.44. Un o 50 ww ww 20 2 ww 40 Figure P9.44 50 ww
Consider the ideal noninverting op-amp circuit in Figure P9.45. (a) Derive the expression for \(v_{O}\) as a function of \(v_{I 1}\) and \(v_{I 2}\). (b) Find \(v_{O}\) for \(v_{I 1}=0.2
(a) Derive the expression for the closed-loop voltage gain \(A_{v}=v_{O} / v_{I}\) for the circuit shown in Figure P9.46. Assume an ideal op-amp. (b) Let \(R_{4}=50 \mathrm{k} \Omega\) and \(R_{3}=25
The circuit shown in Figure P9.47 can be used as a variable noninverting amplifier. The circuit uses a \(50 \mathrm{k} \Omega\) potentiometer in conjunction with an ideal op-amp. (a) Derive the
(a) Determine the closed-loop voltage gain \(A_{v}=v_{O} / v_{I}\) for the ideal opamp circuit in Figure P9.48. (b) Determine \(v_{O}\) for \(v_{I}=0.25 \mathrm{~V}\). (c) Let \(R=30 \mathrm{k}
For the amplifier in Figure P9.49, determine (a) the ideal closed-loop voltage gain, (b) the actual closed-loop voltage gain if the open-loop gain is \(A_{o d}=150,000\), and (c) the open-loop gain
Consider the voltage-follower circuit in Figure 9.17. Determine the closed-loop voltage gain if the op-amp open-loop voltage gain \(A_{o d}\) is (a) 20, (b) 200 ,(c) \(2 \times 10^{3}\), and (d) \(2
(a) Consider the ideal op-amp circuit shown in Figure P9.51. Determine the voltage gains \(A_{v 1}=v_{O 1} / v_{I}\) and \(A_{v 2}=v_{O 2} / v_{I}\). What is the relationship between \(v_{O 1}\) and
(a) Assume the op-amp in the circuit in Figure P9.52 is ideal. Determine \(i_{L}\) as a function of \(v_{I}\). (b) Let \(R_{1}=9 \mathrm{k} \Omega\) and \(R_{L}=1 \mathrm{k} \Omega\). If the op-amp
Consider the three circuits shown in Figure P9.53. Determine each output voltage for (i) \(v_{I}=3 \mathrm{~V}\) and (ii) \(v_{I}=-5 \mathrm{~V}\). 40 ww ww 20 10 (a) 40 ww www 20 10 10 www
A current-to-voltage converter is shown in Figure P9.54. The current source has a finite output resistance \(R_{S}\), and the op-amp has a finite open-loop differential gain \(A_{o d}\). (a) Show
Figure P9.55 shows a phototransistor that converts light intensity into an output current. The transistor must be biased as shown. The transistor output versus input characteristics are shown. Design
The circuit in Figure P9.56 is an analog voltmeter in which the meter reading is directly proportional to the input voltage \(v_{I}\). Design the circuit such that a \(1 \mathrm{~mA}\) full-scale
Consider the voltage-to-current converter in Figure 9.22 using an ideal opamp. (a) Design the circuit such that the current in a \(200 \Omega\) load can be varied between 0 and \(5 \mathrm{~mA}\)
The circuit in Figure P9.58 is used to drive an LED with a voltage source. The circuit can also be thought of as a current amplifier in that, with the proper design, \(i_{D}>i_{1}\). (a) Derive
Figure P9.59 is used to calculate the resistance seen by the load in the voltage-to-current converter given in Figure 9.22. (a) Show that the output resistance is given by\[R_{o}=\frac{R_{1} R_{2}
Consider the op-amp difference amplifier in Figure 9.24(a). Let \(R_{1}=R_{3}\) and \(R_{2}=R_{4}\). A load resistor \(R_{L}=10 \mathrm{k} \Omega\) is connected from the output terminal to ground.
Consider the differential amplifier shown in Figure 9.24(a). Let \(R_{1}=R_{3}\) and \(R_{2}=R_{4}\). Design the amplifier such that the differential voltage gain is (a) 40 , (b) 25 , (c) 5 , and (d)
Consider the differential amplifier shown in Figure 9.24(a). Assume that each resistor is \(50(1 \pm x) \mathrm{k} \Omega\). (a) Determine the worst case common-mode gain \(A_{C M}=v_{O} / v_{C M}\),
Let \(R=10 \mathrm{k} \Omega\) in the differential amplifier in Figure P9.63. Determine the voltages \(v_{X}, v_{Y}, v_{O}\) and the currents \(i_{1}, i_{2}, i_{3}, i_{4}\) for input voltages of (a)
Consider the circuit shown in Figure P9.64.(a) The output current of the op-amp is \(1.2 \mathrm{~mA}\) and the transistor current gain is \(\beta=75\). Determine the resistance \(R\).(b) Repeat part
The circuit in Figure P9.65 is a representation of the common-mode and differential-input signals to a difference amplifier. The output voltage can be written as\[v_{O}=A_{d} v_{d}+A_{c m} v_{c
Consider the adjustable gain difference amplifier in Figure P9.66. Variable resistor \(R_{V}\) is used to vary the gain. Show that the output voltage \(v_{O}\), as a function of \(v_{I 1}\) and
Assume the instrumentation amplifier in Figure 9.26 has ideal op-amps. The circuit parameters are \(R_{1}=10 \mathrm{k} \Omega, R_{2}=40 \mathrm{k} \Omega, R_{3}=40 \mathrm{k} \Omega\), and
Consider the circuit in Figure P9.68. Assume ideal op-amps are used. The input voltage is \(v_{I}=0.5 \sin \omega t\). Determine the voltages (a) \(v_{O B}\), (b) \(v_{O C}\), and (c) \(v_{O}\). (d)
Consider the circuit in Figure P9.69. Assume ideal op-amps are used. (a) Derive the expression for the current \(i_{O}\) as a function of input voltages \(v_{I 1}\) and \(v_{I 2}\). (b) Design the
The instrumentation amplifier in Figure 9.26 has the same circuit parameters and input voltages as given in Problem 9.67, except that \(R_{1}\) is replaced by a fixed resistance \(R_{1 f}\) in series
Design the instrumentation amplifier in Figure 9.26 such that the variable differential voltage gain covers the range of 5 to 200 . Set the gain of the difference amplifier to 2.5. The maximum
All parameters associated with the instrumentation amplifier in Figure 9.26 are the same as given in Exercise Ex 9.8, except that resistor \(R_{3}\), which is connected to the inverting terminal of
The parameters in the integrator circuit shown in Figure 9.30 are \(R_{1}=20 \mathrm{k} \Omega\) and \(C_{2}=0.02 \mu \mathrm{F}\). The input signal is \(v_{I}=0.25 \cos \omega t(\mathrm{~V})\). (a)
Consider the ideal op-amp integrator. Assume the capacitor is initially uncharged. (a) The output voltage is \(v_{O}=-5 \mathrm{~V}\) at \(t=1.2 \mathrm{~s}\) after a \(+0.25 \mathrm{~V}\) pulse is
The circuit in Figure P9.75 is a first-order low-pass active filter. (a) Show that the voltage transfer function is given by\[A_{v}=\frac{-R_{2}}{R_{1}} \cdot \frac{1}{1+j \omega R_{2} C_{2}}\](b)
(a) Using the results of Problem 9.75, design the low-pass active filter in Figure P9.75 such that the input resistance is \(20 \mathrm{k} \Omega\), the low-frequency gain is -15 , and the \(-3
The circuit shown in Figure P9.77 is a first-order high-pass active filter.(a) Show that the voltage transfer function is given by\[A_{v}=\frac{-R_{2}}{R_{1}} \cdot \frac{j \omega R_{1} C_{1}}{1+j
(a) Using the results of Problem 9.77, design the high-pass active filter in Figure P9.77 such that the high-frequency voltage gain is -15 and the \(-3 \mathrm{~dB}\) frequency is \(20
Consider the voltage reference circuit shown in Figure P9.79. Determine \(v_{O}, i_{2}\), and \(i_{\mathrm{Z}}\). Rs = 5.6 kQ +10 V + R = 1 k Vz=6.8 Viz ww Figure P9.79 R = 1 kQ ww
Consider the circuit in Figure 9.35. The diode parameter is \(I_{S}=10^{-14} \mathrm{~A}\) and the resistance is \(R_{1}=10 \mathrm{k} \Omega\). Plot \(v_{O}\) versus \(v_{I}\) over the range \(20
In the circuit in Figure P9.81, assume that \(Q_{1}\) and \(Q_{2}\) are identical transistors. If \(T=300 \mathrm{~K}\), show that the output voltage is\[v_{O}=1.0 \log _{10}\left(\frac{v_{2}
Consider the circuit in Figure 9.36. The diode parameter is \(I_{S}=10^{-14} \mathrm{~A}\) and the resistance is \(R_{1}=10 \mathrm{k} \Omega\). Plot \(v_{O}\) versus \(v_{I}\) for \(0.30 \leq v_{I}
Design an op-amp summer to produce the output voltage \(v_{O}=2 v_{I 1}-\) \(10 v_{I 2}+3 v_{I 3}-v_{I 4}\). Assume the largest resistor value is \(500 \mathrm{k} \Omega\), and the input impedance
Design an op-amp summer to produce an output voltage of \(v_{O}=3 v_{I 1}+\) \(1.5 v_{I 2}+2 v_{I 3}-4 v_{I 4}-6 v_{I 5}\). The largest resistor value is to be \(250 \mathrm{k} \Omega\).
Design a voltage reference source as shown in Figure 9.42 to have an output voltage of \(12.0 \mathrm{~V}\). A Zener diode with a breakdown voltage of \(5.6 \mathrm{~V}\) is available. Assume the
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