Essentials of Electrical and Computer Engineering

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

Chapter 7

Network Frequency Characteristics - all with Video Answers

Educators

Chapter Questions

Problem 1

Find the transfer function $\frac{\mathbf{V}_0}{\mathbf{V}_s}(j \omega)$ for the network in Figure P7.1.
Figure P7.1 can't copy

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

Find the transfer function $\frac{\mathbf{I}_0}{\mathbf{V}_s}(j \omega)$ for the network in Figure P7.2.
Figure P7.2 can't copy

Narayan Hari

Numerade Educator

Problem 3

Determine the poles and zeros of the transfer function $\frac{\mathbf{V}_0}{\mathbf{V}_1}(j \omega)$ for the network in Figure P7.3.
Figure P7.3 can't copy

Check back soon!

Problem 4

Find the poles and zeros of the transfer function $\frac{\mathbf{V}_0}{\mathbf{V}_1}(j \omega)$ for the network in Figure P7.4.
Figure P7.4 can't copy

Check back soon!

Problem 5

Determine the poles and zeros of the transfer function $\frac{\mathbf{V}_0}{\mathbf{V}_1}(j \omega)$ for the circuit shown in Figure P7.5.
Figure P7.5 can't copy

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 6

Find the poles and zeros of the transfer function $\frac{\mathbf{V}_0}{\mathbf{V}_1}(j \omega)$ for the circuit shown in Figure P7.6.
Figure P7.6 can't copy

Check back soon!

Problem 7

Plot the magnitude and phase of the transfer function $\frac{\mathbf{V}_0}{\mathbf{V}_1}(j \omega)$ in increments of $0.1 \mathrm{r} / \mathrm{s}$ from $0.5 \mathrm{r} / \mathrm{s}$ to $1.5 \mathrm{r} / \mathrm{s}$ for the circuit shown in Figure P7.7.
Figure P7.7 can't copy

Check back soon!

Problem 8

A simple low-pass filter is shown in Figure P7.8. If $R=2 \mathrm{k} \Omega$ and $C=75 \mu \mathrm{F}$, determine the half-power frequency of the filter.
Figure P7.8 can't copy

Check back soon!

Problem 9

We wish to design a low-pass filter of the form shown in Figure P7.8 to have a break frequency of $50 \mathrm{~Hz}$. If a $2 \mathrm{k} \Omega$ resistor is available, determine the required value of the capacitor.

Narayan Hari

Numerade Educator

Problem 10

An $\mathrm{RC}$ low-pass filter has the following parameters: $R=1 \mathrm{k} \Omega$ and $C=50 \mu \mathrm{F}$. Determine the half-power frequency of the filter.

Narayan Hari

Numerade Educator

Problem 11

The high-pass filter shown in Figure P7.11 has a cut-off frequency of $75 \mathrm{r} / \mathrm{s}$. If the resistor has
Figure P7.11 can't copy

Keshav Singh

Numerade Educator

Problem 12

An $R C$ high-pass filter has the following parameters: $R=10 \mathrm{k} \Omega$ and $C=200 \mu \mathrm{F}$. Determine the half-power frequency of the filter and the phase angle of the magnitude transfer function at this frequency.

Narayan Hari

Numerade Educator

Problem 13

A high-pass filter with a cut-off frequency of $500 \mathrm{~Hz}$ is needed. If a $2 \mu \mathrm{F}$ capacitor is available, determine the value of the resistor for the network in Figure P7.11 that will produce the desired filter.

Ajay Singhal

Numerade Educator

Problem 14

Determine the center frequency and bandwidth of the band-pass filter shown in Figure P7.14.
Figure P7.14 can't copy

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 15

A band-pass filter has a center frequency of $924 \mathrm{rad} / \mathrm{s}$. If the upper half-power frequency is $1132 \mathrm{rad} / \mathrm{s}$, determine the bandwidth of the filter.

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 16

Given the band-pass filter shown in Figure P7.14 with $C=2 \mu \mathrm{F}$ and $L=2 \mathrm{H}$, determine the center frequency and find the value of $\mathrm{R}$ that will yield a bandwidth of $100 \mathrm{r} / \mathrm{s}$.

Narayan Hari

Numerade Educator

Problem 17

Determine the cut-off frequencies of the bandpass filter in problem 7.16.

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 18

Compute the voltage transfer function for the network shown in Figure P7.18 and tell what type of filter the network represents.
Figure P7.18 can't copy

Narayan Hari

Numerade Educator

Problem 19

Determine what type of filter the network in Figure P7.19 represents by determining the voltage transfer function.
Figure P7.19 can't copy

Narayan Hari

Numerade Educator

Problem 20

Given the lattice network shown in Figure P7.20, determine what type of filter this network represents by determining the voltage transfer function.
Figure P7.20 can't copy

Narayan Hari

Numerade Educator

Problem 21

Determine the type of filter that is represented by the network in Figure P7.21.
Figure P7.21 can't copy

Check back soon!

Problem 22

In the network in Figure P7.22 the component values are $R=4 \Omega, C=2 \mu \mathrm{F}$, and $L=50 \mathrm{mH}$. Determine the resonant frequency of the network.
Figure P7.22 can't copy

Narayan Hari

Numerade Educator

Problem 23

Select a value for the variable capacitor in the network in Figure P7.22 that will place the circuit in resonance at $2000 \mathrm{r} / \mathrm{s}$.

Mahnoor Amin

Numerade Educator

Problem 24

Find the value of $C$ that will place the circuit in Figure P7.24 in resonance at $1800 \mathrm{r} / \mathrm{s}$. Then determine the $Q$ of the network and the magnitude of the voltage across the capacitor.
Figure P7.24 can't copy

Narayan Hari

Numerade Educator

Problem 25

Determine the bandwidth and half-power frequencies of the network in problem 7.24 .

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 26

Given the network in Figure P7.26, find the resonant frequency, the $Q$, and the magnitude of the voltage across the capacitor at resonance.
Figure P7.26 can't copy

Salamat Ali

Numerade Educator

Problem 27

In the network in Figure P7.27, at resonance the magnitude of the voltage across the capacitor is $120 \mathrm{~V}$. Determine the value of the resistor $R$.
Figure P7.27 can't copy

Vishal Gupta

Numerade Educator

Problem 28

The $Q$ and resonant frequency of a series RLC circuit are known to be 40 and $6000 \mathrm{r} / \mathrm{s}$, respectively. If the value of the resistor is $4 \Omega$, determine the values of the inductor and capacitor.

Narayan Hari

Numerade Educator

Problem 29

Given the series RLC circuit in Figure P7.29, if $R=10 \Omega$, find the values of $L$ and $C$ such that the network will have a resonant frequency of $100 \mathrm{kHz}$ and a bandwidth of $1 \mathrm{kHz}$.
Figure P7.29 can't copy

Narayan Hari

Numerade Educator

Problem 30

A series RLC circuit has a resistance at resonance of $3.2 \Omega$. The network has a bandwidth of $200 \mathrm{r} / \mathrm{s}$ and a resonant frequency of $2000 \mathrm{r} / \mathrm{s}$. Determine the circuit parameters.

Narayan Hari

Numerade Educator

Problem 31

A series resonant circuit has a $Q$ of 120 and a resonant frequency of $60,000 \mathrm{rad} / \mathrm{s}$. Determine the half-power frequencies and the bandwidth of the circuit.

Narayan Hari

Numerade Educator

Problem 32

Given the series RLC circuit in Figure P7.32,
(a) Derive the expression for the half-power frequencies, the resonant frequency, the bandwidth, and the quality factor for the transfer characteristic $\mathbf{I} / \mathbf{V}_{\mathrm{in}}$ in terms of $R, L$, and $C$.
(b) Compute the quantities in part (a) if $R=10 \Omega, L=100 \mathrm{mH}$, and $C=10 \mu \mathrm{F}$
Figure P7.32 can't copy

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 33

A parallel RLC circuit consists of the following elements: $R=4 \mathrm{k} \Omega, \mathrm{C}=100 \mu \mathrm{F}$, and $L=40 \mathrm{mH}$. Compute the resonant frequency and bandwidth of the circuit.

Narayan Hari

Numerade Educator

Problem 34

Given the parallel RLC circuit shown in Figure P7.34, determine the resonant frequency and the voltage across the elements at resonance.
Figure P7.34 can't copy

Mayukh Banik

Numerade Educator

Problem 35

Determine the $Q$ and the bandwidth of the network shown in Figure P7.35.
Figure P7.35 can't copy

Narayan Hari

Numerade Educator

Problem 36

The network in Figure P7.36 has a $Q=80$ and a $B W=800 \mathrm{r} / \mathrm{s}$. Determine the resonant frequency and the unknown circuit parameters.
Figure P7.36 can't copy

Narayan Hari

Numerade Educator

Problem 37

A variable frequency current source supplies the parallel RLC circuit shown in Figure P7.37. Determine the BW, $Q$, and the half-power frequencies of the network.
Figure P7.37 can't copy

Narayan Hari

Numerade Educator

Problem 38

Given the parallel RLC circuit in Figure P7.38,
(a) Derive the expression for the resonant frequency, the half-power frequencies, the bandwidth, and the quality factor for the transfer characteristic $\mathbf{V}_{\text {out }} / \mathbf{I}_{\text {in }}$ in terms of the circuit parameters $R, L$, and $C$.
(b) Compute the quantities in part (a) if $R=1 \mathrm{k} \Omega, L=10 \mathrm{mH}$, and $C=100 \mu \mathrm{F}$.
Figure P7.38 can't copy

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 39

A stereo receiver is tuned to $98 \mathrm{mHz}$ on the FM band. The tuning knob controls a variable capacitor in a parallel resonant circuit. If the inductance of the circuit is $2 \mu \mathrm{H}$ and the $Q$ is 100, determine the values of $C$ and $G$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 40

Given the data in problem 7.39 , suppose that another FM station in the vicinity is broadcasting at $98.1 \mathrm{mHz}$. Let us determine the relative value of the voltage across the resonant circuit at this frequency compared with that at $98 \mathrm{mHz}$, assuming that the current produced by both signals has the same amplitude.

Salamat Ali

Numerade Educator

Problem 41

Determine the value of $C$ in the network shown in Figure P7.41 in order for the circuit to be in resonance.
Figure P7.41 can't copy

Salamat Ali

Numerade Educator