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Essentials of Electrical and Computer Engineering

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

Chapter 8

Introdection to Electronics - all with Video Answers

Educators

Chapter Questions

03:25

Problem 1

For each of the following, decide if it is most analogous to digital information or analog information.
(a) the result of a coin toss
(b) the sound of a slide trombone
(c) the beat of a drum
(d) a human voice
(e) the ticking of a clock
(f) the sound of a siren
(g) the motion of a cat
(h) the motion of a frog

Gennady Notowidigdo
Gennady Notowidigdo
Numerade Educator
02:17

Problem 2

A solar-cell is placed outdoors on a clear day and has an output current of $2 \mathrm{~mA}$ at peak sun intensity (noon), and $0.01 \mathrm{~mA}$ when exposed to moonlight. Plot the approximate current output expected versus time over a 24 -hour period, assuming:
(a) The solar cell is unobstructed.
(b) A cat stands over the solar cell for one hour beginning at noon (assume an opaque cat).
(c) A cloud cover comes in at 3:00 PM, reducing the sun's intensity on the solar cell by one-half.

Chai Santi
Chai Santi
Numerade Educator

Problem 3

Plot serial digital signals representing the following sequences of bits, using pulses with a duration of $50 \mathrm{~ns}$.
(a) 101100101011
(b) 010110001001
(c) 001101010111

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Problem 4

Construct plots of digital voltage signals by drawing the pulse waveforms based on the following descriptions: high level $=5 \mathrm{~V}$; low level $=0.2 \mathrm{~V}$.
(a) High at $t=0$, negative going edge at $t=1$, positive going edge at $t=1.5$, negative going edge at $t=2.5$, positive going edge at $t=3$.
(b) Low at $t=0$, positive going edge at $t=2$, negative going edge at $t=3$, positive going edge at $t=4$.
(c) Assuming each bit requires the same time to transmit, what's the minimum number of bits represented by the pulse sequence in (a).
(d) Assuming each bit requires the same time to transmit, what's the minimum number of bits represented by the pulse sequence in (b).

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Problem 5

A 16-bit parallel data bus is used to transmit 1280 bits in 4 microseconds.
(a) How many bits are transmitted over one of the lines in the bus?
(b) If the same technology was used to transmit data over a single serial data line, how many bits could be transmitted in 1 second?

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Problem 6

In a particular system, 50 megabits is transmitted on a single serial data line in 1 second.
(a) What is the time required to transmit 1 bit?
(b) If this system utilized the same technology with an 8-bit parallel data bus, how long would it take to transmit 50 megabits?

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View

Problem 7

A modem connects to a phone line with a data rate of $56.6 \mathrm{k}$ bits per second. How long does it take to download
(a) 2 megabits of information?
(b) 2 megabytes of information?

James Kiss
James Kiss
Numerade Educator

Problem 8

The PCI bus found in many desktop computers transmits 64 bits per clock cycle at a $33 \mathrm{MHz}$ clock rate. How does the bandwidth of the PCI bus compare to the serial FireWire (IEEE 1394) serial bus specification, which is $400 \mathrm{Mbits} / \mathrm{s}$ ?

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02:25

Problem 9

Assume a computer is copying an entire 100-Gigabyte disk drive's worth of information over a $100 \mathrm{Mbit} / \mathrm{s}$ Ethernet connection, and that a protocol is utilized over the Ethernet that utilizes $50 \%$ of the available bandwidth of the connection. How long will the disk copy operation take?

Shelby Mohamed
Shelby Mohamed
Numerade Educator

Problem 10

A PC133 SDRAM supplies 64 bits ( 8 bytes) in parallel. It has the following timing specifications:
Clock frequency: $133 \mathrm{MHz}$
Delay for transfer of the first 8 -byte word: 7 clock cycles
Delay for transfer of successive adjacent 8 -byte word: 1 clock cycle
(a) If a computer without a cache fetches 64 bit words at random, what is the effective average bandwidth (in bytes/s) of the memory?
(b) If a computer with a cache fetches successive 64 bit words $95 \%$ of the time, and random words $5 \%$ of the time, what is the effective average bandwidth (in bytes/s) of the memory?

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Problem 11

An amplifier has a voltage gain $A_v=300$ and a load resistor connected between its output terminals of $2 \mathrm{k}$. If the input to the amplifier, $v_i=75 \mathrm{mV}$,
(a) what is the output voltage, $v_{\mathrm{s}}$ ?
(b) what power is delivered to the load resistor?

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02:47

Problem 12

The output of an amplifier drives an $8 \Omega$ speaker with a signal of $3 \mathrm{~V}$ in amplitude.
(a) What is the amplitude of the input voltage, assuming the voltage gain of the amplifier is 150 ?
(b) What is the power delivered to the speaker?

Aja S
Aja S
Numerade Educator
01:05

Problem 13

A radio receives a signal on its antenna of $2 \mu \mathrm{V}$, and we want to deliver 20 watts of power to an 8 -ohm speaker. What is the voltage gain of the entire system?

Salamat Ali
Salamat Ali
Numerade Educator
03:06

Problem 14

Consider an amplifier in which the input voltage is sinusoidal with an amplitude of $100 \mathrm{mV}$ and $\omega=500$. The complex gain is given by $20 \angle 30^{\circ}$. Write an expression for the output voltage as a function of time.

Narayan Hari
Narayan Hari
Numerade Educator
02:06

Problem 15

The input and the output signals of four different amplifiers are given below. Obtain the voltage gain and the phase shift for each of the amplifiers.
(a) $v_{\text {in }}(t)=3 \cos (\omega t) v_{\text {out }}(t)=27 \cos (\omega t)$
(b) $v_{\text {in }}(t)=5 \sin (10 t) \quad v_{\text {out }}(t)=15 \cos (10 t)$
(c) $v_{\text {it }}(t)=4 \sin (\omega t) \quad v_{\text {out }}(t)=20 \sin (\omega t+\pi / 2)$
(d) $v_{\text {in }}(t)=7 e^{20 j t} \quad v_{\text {out }}(t)=j 5 e^{20 j t}$

Narayan Hari
Narayan Hari
Numerade Educator

Problem 16

An electronic thermometer generates a voltage signal of $6 \mathrm{mV}$ for every $1^{\circ} \mathrm{C}$ rise in temperature. This signal is used to activate a switch, which requires an input signal of $5 \mathrm{~V}$ to operate. What is the voltage gain of the amplifier that will allow one to operate the switch at the boiling point of water $\left(100^{\circ} \mathrm{C}\right)$ if the thermometer generates $0 \mathrm{~V}$ at $0^{\circ} \mathrm{C}$ ?

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01:21

Problem 17

A solar cell is used to electronically detect when sunrise occurs. It is determined that the light at dawn produces $0.05 \mathrm{~mA}$, and the cell is connected to a current amplifier. The amplifier is used to increase the current to produce 3 $\mathrm{V}$ across a $1 \mathrm{k}$ resistor. What current gain is required for the amplifier?

Vinnu M
Vinnu M
Numerade Educator

Problem 18

A voltage of $35 \mathrm{mV}$ is applied to the input of a voltage amplifier. What gain is required to produce an output voltage of $10 \mathrm{~V}$,
(a) expressed as a voltage ratio.
(b) expressed in decibels.

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Problem 19

If a voltage amplifier has a gain of $60 \mathrm{db}$ and an output voltage of $5 \mathrm{~V}$, what is the input voltage?

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Problem 20

A current amplifier has a gain of $100 \mathrm{db}$, however, a stray leakage path at the output reduces the effective gain by $20 \mathrm{db}$. What is the effective current gain of the amplifier
(a) as a current ratio?
(b) in decibels?

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Problem 21

Calculate the upper-and lower-corner frequencies and the bandwidth of the amplifier whose frequency response is given in Figure P8.2.
Figure P8.2 can't copy

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Problem 22

An audio amplifier has a low-corner frequency, $f_{\mathrm{LO}}$, of $100 \mathrm{~Hz}$, and a bandwidth of $15 \mathrm{kHz}$. The amplifier has an input voltage of $20 \mathrm{mV}$ and an output voltage of 6 volts. Plot the frequency response (frequency on a log scale) of this amplifier showing the midband gain in decibels, the two corner frequencies, and the bandwidth.

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01:14

Problem 23

A dc amplifier has a voltage gain of 100 and this gain is down $3 \mathrm{db}$ at $10 \mathrm{MHz}$. What is the amplifier's bandwidth?

M Hassan Anwar
M Hassan Anwar
Numerade Educator
04:14

Problem 24

In a particular current amplifier the half-power frequencies are separated by $10^3 \mathrm{~Hz}$. If the gain is reduced from its midband value by $3 \mathrm{db}$ at $100 \mathrm{~Hz}$, what is the
(a) high corner frequency?
(b) bandwidth?

Amit Srivastava
Amit Srivastava
Numerade Educator
00:28

Problem 25

A dc current amplifier has an output current that is $40 \mathrm{db}$ larger than its input current. Plot the frequency response of the amplifier in decibels, assuming it has a bandwidth of $20 \mathrm{kHz}$.

Amy Jiang
Amy Jiang
Numerade Educator
03:56

Problem 26

A sinusoidal carrier signal of $1 \mathrm{MHz}$ is modulated with a message signal of $100 \mathrm{kHz}$. Sketch the resulting waveform for two cycles of the message signal for
(a) amplitude modulation
(b) frequency modulation

Nishant Kumar
Nishant Kumar
Numerade Educator
03:56

Problem 27

The message signal shown in Figure P8.27 modulates a sinusoidal carrier that has a period one-tenth that of the message signal. Sketch the resulting waveform for
(a) amplitude modulation
(b) frequency modulation
Figure P8.27 can't copy

Nishant Kumar
Nishant Kumar
Numerade Educator
01:01

Problem 28

The frequency spectrum of an AM-modulated signal has a carrier at $1 \mathrm{MHz}$ and an upper sideband at $1.01 \mathrm{MHz}$.
(a) What is the frequency of the message signal?
(b) What is the frequency of the lower sideband?

Narayan Hari
Narayan Hari
Numerade Educator
01:34

Problem 29

If the highest frequency component of message signal is $15 \mathrm{kHz}$ and this AM modulates a carrier signal of $500 \mathrm{kHz}$, what is the minimum bandwidth of a filter centered at the carrier frequency that will transmit the signal?

Narayan Hari
Narayan Hari
Numerade Educator
02:09

Problem 30

A message signal has frequency components at $400 \mathrm{~Hz}$ and $800 \mathrm{~Hz}$. This is used to AM modulate a $30 \mathrm{kHz}$ carrier signal. Plot the frequency spectrum of the AM-modulated signal.

Amit Srivastava
Amit Srivastava
Numerade Educator
02:48

Problem 31

A square wave (which contains frequency components at odd multiples of the fundamental frequency) is used to AM modulate a sinusoidal carrier. If the carrier frequency is $4 \mathrm{MHz}$, and the square wave has a frequency of $10 \mathrm{kHz}$, plot the frequency spectrum, and clearly designate the frequency of the carrier and all sidebands up to the third nonzero harmonic.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator

Problem 32

Find the minimum number of bits necessary to represent a $6 \mathrm{~V}$ analog signal with a resolution greater than $2 \mathrm{mV}$.

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Problem 33

An analog signal having values from -4 to +4 volts is represented using 8 bits.
(a) Calculate the voltage resolution.
(b) If you wished to increase the resolution by at least a factor of 5 , what's the minimum number of additional bits needed?

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Problem 34

An analog signal has values between 0 and $5 \mathrm{~V}$ and is represented using a 7-bit digital word. Due to a fault in the digital circuit, the middle bit is incorrect. Find the magnitude of the error in the analog representation of the signal.

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Problem 35

An analog-to-digital converter (A/D) has 10 bits and samples an analog signal with a range from -5 to $+5 \mathrm{~V}$ and a maximum frequency of $3 \mathrm{kHz}$.
(a) What is the voltage resolution of the sampling?
(b) What is the minimum sampling frequency?

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01:24

Problem 36

An analog-to-digital converter (A/D) samples an analog signal at a sampling rate of $10 \mathrm{kHz}$. To ensure accurate sampling, the signal should not have frequency components higher than what frequency?

Rashmi Sinha
Rashmi Sinha
Numerade Educator

Problem 37

A digital-to-analog converter (D/A) has 12 bits and an output analog voltage range of 0 to 10 volts.
(a) What is the voltage resolution of the ana$\log$ output?
(b) If the most significant input bit changes, by what amount does the output voltage change?

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Problem 38

Obtain the digital words corresponding to the indicated analog signal levels, a through $j$, as shown in Figure P8.38, that would be assigned by an $\mathrm{A} / \mathrm{D}$ system with:
(a) 2 bits
(b) 3 bits
(c) 4 bits
Figure P8.38 can't copy

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Problem 39

An analog signal with a maximum amplitude of 5 volts is sampled 15 times at intervals of 1 $\mathrm{ms}$ by a 4-bit A/D converter. The values are shown below. Reconstruct the analog signal and comment on the accuracy of the plot. Identify two ways of obtaining a better digital representation of the original analog signal.
$$
\begin{array}{cc}
\hline \text { Sample } & \text { 4-bit digital word } \\
\hline 1 & 0000 \\
2 & 0010 \\
3 & 0011 \\
4 & 0001 \\
5 & 0100 \\
6 & 0101 \\
7 & 0110 \\
8 & 1010 \\
9 & 1101 \\
10 & 1111 \\
11 & 1000 \\
12 & 0110 \\
13 & 0111 \\
14 & 1011 \\
15 & 1111 \\
\hline
\end{array}
$$

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Problem 40

An Exclusive OR gate (XOR) is a logic gate with an output that is high only when all its inputs are at the same logic value. (Either all inputs high, or all inputs low.) Construct the truth table for a two-input XOR gate.

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Problem 41

Construct the truth table for the logic circuit shown in Figure P8.41 (assume $A_1$ is the MSB).
Figure P8.41 can't copy

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Problem 42

Construct the truth table for the logic circuit shown in Figure P8.42 (assume $A_1$ is the MSB),
Figure P8.42 can't copy

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Problem 43

Construct the truth table for the logic circuit shown in Figure P8.43 (assume $A_1$ is the MSB).
Figure P8.43 can't copy

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Problem 44

(a) What is the purpose of a sensor?
(b) What is the purpose of an actuator?

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Problem 45

A temperature measurement system is designed to measure the temperature range of 50 to 100 degrees $\mathrm{C}^{\circ}$, and uses a temperature transducer that changes resistance in proportion to temperature. The resistance is $1 \mathrm{k} \Omega$ at 50 degrees, and increases $1 \Omega$ per degree. Assume this device is placed in a Wheatstone Bridge circuit with three other resistors, each of $1 \mathrm{k} \Omega$, and the bridge is supplied by a voltage source of $5 \mathrm{~V}$.
(a) What is the output voltage of the bridge at 50 degrees?
(b) What is the output voltage of the bridge at 100 degrees?
(c) What signal conditioning is needed to provide this signal to an $A / D$ converter with an input voltage range of 0 to $3 \mathrm{~V}$ ?

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02:30

Problem 46

An accelerometer is used as the sensor in a computer measurement system to measure the vibration of a motor turning at $2500 \mathrm{rpm}$.
(a) What is the fundamental frequency of vibration in $\mathrm{Hz}$ ?
(b) Is it possible to use a low-pass filter as signal conditioning to suppress interference from $60 \mathrm{~Hz}$ power lines?
(c) If so, what cutoff frequency would be appropriate for the low-pass filter?
(d) What is the minimum sampling frequency required of the A/D converter to ensure that the fundamental frequency is captured?

Eric Mockensturm
Eric Mockensturm
Numerade Educator