Essentials of Electrical and Computer Engineering

David V. Kerns, Jr., J. David Irwin

Chapter 9

Operational Amplifiers (Op Amps) - all with Video Answers

Educators

Chapter Questions

Problem 1

The input and output signals of an amplifier are shown in Figure P9.1. (a) Find the voltage gain of the amplifier. (b) Is it a linear amplifier? Explain your answer.
Figure P9.1 can't copy

WM

William Mead

Numerade Educator

Problem 2

The input and output signals of an amplifier are shown in Figure P9.2. (a) Find the voltage gain of the amplifier. (b) Is it a linear amplifier? Explain your answer.
Figure P9.2 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 3

Given an ideal op amp, what assumptions are normally made regarding
(a) the voltage gain of the op amp?
(b) the current into each of the inputs?
(c) the resistance between the input terminals

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 4

When negative feedback is established in an op amp circuit by connecting the output terminal through a network to the inverting input terminal, what is the value of the voltage at the inverting input?

Nikhil Kumar Rajpurohit

Nikhil Kumar Rajpurohit

Numerade Educator

Problem 5

An op amp is powered by dual power supplies, $V_{D D}=+5 \mathrm{~V}$ and $V_{S S}=-5 \mathrm{~V}$. The op amp is placed in an inverting op amp circuit with a closed-loop gain of 30 . What would be a reasonable estimate of the voltage at the output if
(a) $0.3 \mathrm{~V}$ is applied to the input?
(b) $0.1 \mathrm{~V}$ is applied to the input?
(c) $-0.17 \mathrm{~V}$ is applied to the input?

Nikhil Kumar Rajpurohit

Nikhil Kumar Rajpurohit

Numerade Educator

Problem 6

A noninverting op amp circuit is operated with $V_{D D}=5 \mathrm{~V}$ and $V_{S S}=0 \mathrm{~V}$, and the input signal ranges from $0.3 \mathrm{~V}$ to $0.6 \mathrm{~V}$. What is the largest value of the closed-loop gain for which the circuit will perform as a linear amplifier?

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Problem 7

Determine the voltage gain, $A_F$, for the circuit in Figure P9.7, assuming an ideal op amp.
Figure P9.7 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 8

Determine the voltage gain, $A_F$, for the circuit in Figure P9.8, assuming an ideal op amp.
Figure P9.8 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 9

Determine the voltage gain, $A_F$, for the circuit in Figure P9.9, assuming an ideal op amp.
Figure P9.9 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 10

Determine the voltage gain, $A_F$, for the circuit in Figure P9.7, assuming an ideal op amp, if $R_1=3 \mathrm{k} \Omega$ and $R_2=3 \mathrm{k} \Omega$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 11

Determine the voltage gain, $A_F$, for the circuit in Figure P9.8, assuming an ideal op amp, if $R_1=500 \Omega$ and $R_2=1 \mathrm{k} \Omega$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 12

Determine the voltage gain, $A_F$, for the circuit in Figure P9.9, assuming an ideal op amp, if $R_1=1.5 \mathrm{k} \Omega$ and $R_2=100 \mathrm{k} \Omega$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 13

Determine the voltage gain, $A_F$, for the circuit in Figure P9.13, assuming an ideal op amp.
Figure P9.13 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 14

For the circuit shown in Figure P9.14, assume the voltage source is given by $v_s=0.1 \mathrm{cos}$ $(2000 t) V$.
(a) Write an expression for $v_o$, the output voltage across the load resistor, $R_L$ ?
(b) What is the maximum current through $R_L$ ?
(c) What is the maximum current from the output of the op amp?
Figure P9.14 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 15

Repeat problem 9.14 for the case where $v_s=0.2+0.1 \cos (2000 t) V$.

Nikhil Kumar Rajpurohit

Nikhil Kumar Rajpurohit

Numerade Educator

Problem 16

Determine the value of $R_2$ required to establish the voltage gain of the circuit in Figure P9.16 at $A_F=25$; assume an ideal op amp and $R_1=3.0 \mathrm{k} \Omega$.
Figure P9.16 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 17

For the circuit shown in Figure P9.17, determine the voltage, $v_o$, across $R_L$.
Figure P9.17 can't copy

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Problem 18

Determine the voltage gain, $A_F$, for the circuit in Figure P9.18, assuming an ideal op amp.
Figure P9.18 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 19

Determine the voltage gain, $A_F$, for the circuit in Figure P9.18, assuming $R_1=3.3 \mathrm{k} \Omega$ $R_2=70 \mathrm{k} \Omega$ and the op amp is ideal.

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Problem 20

Determine the voltage gain, $A_F$, for the circuit in Figure P9.18, assuming an ideal op amp.
Figure P9.20 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 21

For the circuit shown in Figure P.20, find the voltage gain assuming an ideal op amp, $R_1=1 \mathrm{k} \Omega$ and $R_2=65 \mathrm{k} \Omega$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 22

Determine the voltage gain, $A_F$, for the circuit in Figure P9.22, assuming an ideal op amp.
Figure P9.22 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 23

Write an expression for the output voltage, $v_o$, across $R_L$ given that $v_s=2 \sin (\omega \mathrm{t})$.
Figure P9.23 can't copy

Ekaveera Kumar

Numerade Educator

Problem 24

Determine the output voltage, $v_o$, across $R_L$ in Figure P9.24, assuming an ideal op amp.
Figure P9.24 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 25

The signal from an electronic pressure transducer (sensor) has a maximum value of $10 \mathrm{mV}$, corresponding to maximum pressure. We would like to amplify this signal to a maximum of 3 volts. If an op amp circuit similar to that in Figure P9.8 is used, and $R_2=750 \Omega$, what is the proper value for $R_1$ ? (Assume an ideal op amp.)

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Problem 26

Repeat problem 9.25 using an op amp circuit similar to Figure P9.18 with $R_2=750 \Omega$.

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 27

For the circuit shown in Figure P9.27, determine the value of the output voltage, $v_o$.
Figure P9.27 can't copy

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Problem 28

For the circuit shown in Figure P9.28, show that if $R_1 / R_2=R_3 / R_4$, then $v_o=\left(R_2 / R_1\right)\left(v_1-v_2\right)$, assuming an ideal op amp.
Figure P9.28 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 29

In the circuit shown in Figure P9.29, the Wheatstone Bridge is part of a temperature sensing system, in which $R_a$ is nominally $100 \Omega$, and increases $1 \mathrm{ohm}$ for every $1^{\circ} \mathrm{C}$ temperature increase. Choose the value of $R_2$ that will provide a 2 volt change at the output, $v_o$, for every degree temperature change at the sensor.
Figure P9.29 can't copy

Vishal Gupta

Numerade Educator

Problem 30

Calculate the voltage gain of the circuit shown in Figure P9.30, assuming an ideal op amp. Are there values of $R$ that should be avoided?
Figure P9.30 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 31

For the circuit in Figure P9.31, determine an expression for the output voltage, $v_o$, in terms of the input voltages, $v_A, v_B$, and $v_C$; assume an ideal op amp.
Figure P9.31 can't copy

M Hassan Anwar

Numerade Educator

Problem 32

Using an ideal op amp, draw a circuit to implement the following function: $v_o=-\left[2 v_A+8 v_B\right]$.

Kajal Gautam

Numerade Educator

Problem 33

Using a summing amplifier, construct a circuit that will provide an output voltage that is the average of three input signals, $v_1(t), v_2(t)$, and $v_3(t)$, inverted (with a negative sign). Following the topology of the circuit in Figure 9.10, let $R_2=10 \mathrm{k} \Omega$, and find the appropriate values for $R_{1 A}, R_{1 B}$, and $R_{1 C}$.

Nikhil Kumar Rajpurohit

Nikhil Kumar Rajpurohit

Numerade Educator

Problem 34

Given the circuit in Figure P9.34, carefully plot the input and output voltage if the input voltage is defined as follows (time is in seconds, and the output is 0 at $t=0$.)
From $t=0$ to $t=1$, the input is at $+1 \mathrm{~V}$
From $t=1$ to $t=3$, the input is at $-0.5 \mathrm{~V}$
From $t=3$ to $t=5$, the input is at $+0.5 \mathrm{~V}$.
Assume $R_1=4 \mathrm{k} \Omega, C=20 \mu \mathrm{F}$, and an ideal op amp.
Figure P9.34 can't copy

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Problem 35

A circuit with an ideal op amp is shown in Figure P9.35(a); let $C=180 \mu \mathrm{F}$ and $R=5 \mathrm{k} \Omega$. (a) Plot the input waveform, $v_i$ versus time, for the output, $v_0$, shown in Figure P9.35(b). (b) If the input is connected to a constant voltage, $V_1$, show that the output is the solution of the equation:
$$
C \frac{d v_o(t)}{d t}+\frac{V_1}{R}=0
$$
Figure P9.35 can't copy

Arpit Gupta

Numerade Educator

Problem 36

The circuit shown in Figure P9.36(a) is obtained by interchanging the capacitor and resistor in an integrator circuit. (a) Show that the circuit acts as a differentiator, that is,
$$
v_o(t)=-R C \frac{d v_i(t)}{d t}
$$
(b) Sketch the output voltage for the circuit, $v_o(t)$, as a function of time if the input voltage, $v_i(t)$, is given in Figure P9.36(b); assume $R=10 \mathrm{k} \Omega, C=0.22 \mu \mathrm{F}$, and an ideal op amp.
Figure P9.36 can't copy

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Problem 37

Design a circuit to obtain the solution of the following differential equation:
$$
20 \frac{d v(t)}{d t}+\frac{5}{7}=0
$$

Arpit Gupta

Numerade Educator

Problem 38

The waveforms shown in Figure P9.38(a) are the input and output voltages of the op amp circuit of Figure P9.38(b). Specify the components and their values that should be placed in the boxes labeled $A$ and $B$ in order to obtain the given performance. (Assume the desired circuit input resistance is $2 \mathrm{k} \Omega$.)
Figure P9.38 can't copy

M Hassan Anwar

Numerade Educator

Problem 39

Plot the magnitude of the closed loop gain, $A_F$, of the circuit presented in Figure P9.39 as a function of frequency; let $R_1=1 \mathrm{k} \Omega$, $R_2=5 \mathrm{k} \Omega, C=20 \mu \mathrm{F}$, and assume the op amp is ideal.
Figure P9.39 can't copy

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Problem 40

Repeat Problem 9.39, assuming $C=35 \mu \mathrm{F}$, $R_2=10 \mathrm{k} \Omega$, and $R_1=2 \mathrm{k} \Omega$.

Km Neeraj

Numerade Educator

Problem 41

Determine the maximum gain and bandwidth of the filter shown in Figure P9.41; assume an ideal op amp.
Figure P9.41 can't copy

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Problem 42

Repeat Problem 9.41, assuming $R_1=600 \Omega$, $R_2=6 \mathrm{k} \Omega$, and $C=80 \mu \mathrm{F}$.

Narayan Hari

Numerade Educator

Problem 43

Plot the magnitude of the closed loop gain, $A_F$, of the circuit presented in Figure P9.43 as a function of frequency; let $R_1=2 \mathrm{k} \Omega$, $C_1=30 \mu \mathrm{F}, R_2=3 \mathrm{k} \Omega, C_2=2 \mu \mathrm{F}$, and assume the op amp is ideal.
Figure P9.43 can't copy

Kajal Gautam

Numerade Educator

Problem 44

The circuit shown in Figure P9.44 is an amplifier circuit that has a closed loop gain that can be controlled by the position of a switch. Obtain the gain (a) when the switch, $S_1$, is closed and (b) when the switch, $S_1$, is open.
Figure P9.44 can't copy

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Problem 45

The circuit given in Figure P9.45 is a currentto-voltage converter. Determine the transresistance of this circuit; assume an ideal op amp.
Figure P9.45 can't copy

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 46

The circuit of Figure P9.46 is an electronic radiation detector. The photodiode has a sensitivity of $10 \mu \mathrm{A} / \mathrm{mW}$ of incident radiation. If the voltmeter reads $8 \mathrm{~V}$, determine the power being deposited by the radiation.
Figure P9.46 can't copy

Vishal Gupta

Numerade Educator

Problem 47

(a) Determine the voltage gain of the inverting amplifier circuit shown in Figure P9.47 using the op amp model of Figure 9.3. Assume $A_v=50, R_2=10 \mathrm{k} \Omega, R_1=1 \mathrm{k} \Omega$. (b) Repeat (a) with $A_v=500$. (c) Repeat (a) taking the limit as $A_v \rightarrow \infty$.
Figure P9.47 can't copy

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Problem 48

For the circuit shown in Figure P9.47, find the voltage gain if $A_v=500, R_1=200 \Omega$, and $R_2=3.0 \mathrm{k} \Omega$.

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Problem 49

For the circuit shown in Figure P9.47, assume $R_2=15 \mathrm{k} \Omega$ and $R_1=800 \Omega$. What is the closed-loop gain of the circuit if
(a) $A_e=$ infinity
(b) $A_v=200$
(c) $A_v=60$

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Problem 50

An op amp with a slew rate of $30 \mathrm{~V} / \mu \mathrm{s}$ has a step change in the input voltage. Approximately how long will it take the output voltage to move from $-5 \mathrm{~V}$ to $+5 \mathrm{~V}$ ?

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Problem 51

With a step input voltage change applied to the input of an op amp, the output voltage changes from 0 to $10 \mathrm{~V}$ in $0.27 \mu \mathrm{s}$. What is the slew rate for this amplifier?

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Problem 52

An op amp with an open loop gain, $A_v$, of 10,000 also has a common mode gain, $A_c$, of 0.1 . What is the common mode rejection ratio, CMRR, expressed in decibels?

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Problem 53

If an op amp is a factor of 1000 more responsive to differential mode signals than common mode signals, what is the op amp's common mode rejection ratio, CMRR, expressed in decibels?

Narayan Hari

Numerade Educator