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chapter

3

Amplitude Modulation
Fundamentals
I

n the modulation process, the baseband voice, video, or digital signal modifies
another, higher-frequency signal called the carrier, which is usually a sine wave
...
The focus of this
chapter is amplitude modulation (AM)
...


■

Define overmodulation and explain how to alleviate its effects
...


■

■

Compute sideband frequencies, given carrier and modulating signal
frequencies
...


■

Explain what is meant by the terms DSB and SSB and state the main
advantages of an SSB signal over a conventional AM signal
...


93

3-1 AM Concepts
As the name suggests, in AM, the information signal varies the amplitude of the carrier
sine wave
...
Figure 3-1 shows a singlefrequency sine wave intelligence signal modulating a higher-frequency carrier
...
An increase in the amplitude of the modulating
signal causes the amplitude of the carrier to increase
...
An increase or a decrease in
the amplitude of the modulating signal causes a corresponding increase or decrease in both
the positive and the negative peaks of the carrier amplitude
...
3-1) gives the exact shape of the modulating
information signal
...

Because complex waveforms such as that shown in Fig
...
3-2
...

The signals illustrated in Figs
...
Time-domain signals—
voltage or current variations that occur over time—are displayed on the screen of an
oscilloscope
...
3-1); fc is the frequency of the
carrier sine wave; and t is a particular point in time during the carrier cycle
...
(a) The modulating or information signal
...

Carrier peak is
zero reference
for modulating signal
vc

Envelope

Vch

h

vc

AM
wave

Vc
0

0

Time

(a )

94

Time

Sinusoidal modulating wave

vmh Vm

Unmodulated
carrier wave
(b)

Chapter 3

Figure 3-2

A simplified method of representing an AM high-frequency sine wave
...
3-1, the modulating signal uses the peak value of the carrier rather than zero
as its reference point
...
That is, the zero reference line of the modulating signal coincides with the peak value of the unmodulated carrier
...
In general, the amplitude of the
modulating signal should be less than the amplitude of the carrier
...
In amplitude modulation, it is particularly important that the peak value of the modulating signal be less than the peak value
of the carrier
...
One radian
is approximately 57
...


Vm Ͻ Vc
Values for the carrier signal and the modulating signal can be used in a formula
to express the complete modulated wave
...
The instantaneous
value of either the top or the bottom voltage envelope ␷1 can be computed by using
the equation
␷1 ϭ Vc ϩ ␷m ϭ Vc ϩ Vm sin 2␲fmt
which expresses the fact that the instantaneous value of the modulating signal algebraically adds to the peak value of the carrier
...


95

Figure 3-3

Amplitude modulator showing input and output signals
...
It is the second part of the expression that is characteristic of
AM
...
The AM wave is the product of the carrier
and modulating signals
...
Its two inputs, the carrier
and the modulating signal, and the resulting outputs are shown in Fig
...
Amplitude
modulators compute the product of the carrier and modulating signals
...
A circuit that changes a lower-frequency
baseband or intelligence signal to a higher-frequency signal is usually called a modulator
...
Mixing and detection applications are discussed in detail in
later chapters
...
Therefore the relationship between the amplitude of
the modulating signal and the amplitude of the carrier signal is important
...

Multiplying the modulation index by 100 gives the percentage of modulation
...
5 V, the
modulation factor is 0
...
833 ϫ 100 ϭ 83
...


Overmodulation and Distortion
The modulation index should be a number between 0 and 1
...

Envelope is no longer the same shape as
original modulating signal

Clipping of
negative peaks
occurs

distortion of the modulated waveform
...
Distortion of voice transmissions produces garbled, harsh,
or unnatural sounds in the speaker
...

Simple distortion is illustrated in Fig
...
Here a sine wave information signal
is modulating a sine wave carrier, but the modulating voltage is much greater than
the carrier voltage, resulting in a condition called overmodulation
...
The received signal will produce an output waveform in the shape of the envelope, which in this case is a sine wave whose
negative peaks have been clipped off
...
The ideal condition for AM is
when Vm ϭ Vc , or m ϭ 1, which gives 100 percent modulation
...

Preventing overmodulation is tricky
...
Normally, the amplitude of the modulating signal is adjusted so that only the voice peaks produce 100 percent modulation
...
Automatic circuits called
compression circuits solve this problem by amplifying the lower-level signals and suppressing or compressing the higher-level signals
...

Distortion caused by overmodulation also produces adjacent channel interference
...
According to Fourier theory,
any nonsinusoidal signal can be treated as a fundamental sine wave at the frequency
of the information signal plus harmonics
...


Distortion

Overmodulation

GOOD TO KNOW
Distortion caused by overmodulation also produces adjacent
channel interference
...
However, it is more common
Amplitude Modulation Fundamentals

97

Figure 3-5

An AM wave showing peaks (Vmax) and troughs (Vmin)
...
When the AM signal is displayed on an oscilloscope, the modulation index
can be computed from Vmax and Vmin, as shown in Fig
...
The peak value of the modulating signal Vm is one-half the difference of the peak and trough values:
Vm ϭ

Vmax Ϫ Vmin
2

As shown in Fig
...
The Vmax is one-half the peak-to-peak
value of the AM signal, or Vmax (p –p) /2
...
One-half of that, of course, is simply the peak
value
...

The amount, or depth, of AM is more commonly expressed as the percentage of
modulation rather than as a fractional value
...
2 percent
...
At this time, Vmin ϭ 0
and Vmax ϭ 2Vm , where Vm is the peak value of the modulating signal
...
9 divisions and Vmin( p–p) is 1
...

a
...
9 Ϫ 1
...
7
ϭ
ϭ
ϭ 0
...
9 ϩ 1
...
1

b
...
(Hint:
Sketch the signal
...
9 ϩ 1
...
1
2V
ϭ
ϭ
ϭ 3
...
55 ϫ 2 V ϭ 7
...
9 Ϫ 1
...
7
ϭ
ϭ
2
2
2

ϭ 2
...
35 ϫ 2 V ϭ 4
...
7
ϭ
ϭ 0
...
1

3-3 Sidebands and the
Frequency Domain
Whenever a carrier is modulated by an information signal, new signals at different
frequencies are generated as part of the process
...
More specifically, the sidebands occur at frequencies
that are the sum and difference of the carrier and modulating frequencies
...


Sideband

Sideband Calculations
When only a single-frequency sine wave modulating signal is used, the modulation
process generates two sidebands
...

The upper sideband fUSB and lower sideband fLSB are computed as
fUSB ϭ fc ϩ fm

and

fLSB ϭ fc Ϫ fm

where fc is the carrier frequency and fm is the modulating frequency
...

For example, assume that a 400-Hz tone modulates a 300-kHz carrier
...
4 kHz
fLSB ϭ 300,000 Ϫ 400 ϭ 299,600 Hz or 299
...
This time-domain display gives no obvious or outward indication of the existence of the sidebands, although the modulation process does
indeed produce them, as the equation above shows
...
This is illustrated graphically in Fig
...


Figure 3-6

The AM wave is the algebraic sum of the carrier and upper and lower sideband sine waves
...
(b) Lower sideband
...
(d ) Upper sideband
...


(a)

Cycle

(b)
(c)

These instantaneous
amplitudes are added
to produce this sum
(d )

(e)

100

Chapter 3

Figure 3-7

A frequency-domain display of an AM signal (voltage)
...
It is a sine wave at
the carrier frequency whose amplitude varies as determined by the modulating signal
...
3-7
...
The signals may
be voltage, current, or power amplitudes and may be given in peak or rms values
...
A test
instrument known as a spectrum analyzer is used to display the frequency domain of
a signal
...
The time and frequency axes are perpendicular to each other
...

Whenever the modulating signal is more complex than a single sine wave tone, multiple upper and lower sidebands are produced by the AM process
...

Carrier
fc

Amplitude

Figure 3-8

Frequency-domain display

Lower
sideband
(fc Ϫ fm )

Upper
sideband
(f c ϩ fm )
ncy

Freque

Modulating
(intelligence)
signal
ϩ
Ϫ

Peak
amplitudes
of
sine waves
AM wave
(time domain)

Tim

e

fc Ϫ fm

fc

fc ϩ fm

AM wave (frequency domain)

Amplitude Modulation Fundamentals

101

Figure 3-9

The upper and lower sidebands of a voice modulator AM signal
...
Recall that voice frequencies occur in the 300- to 3000-Hz range
...
3-9
...
The total bandwidth of an
AM signal is calculated by computing the maximum and minimum sideband
frequencies
...
3-9)
...
8 MHz (2800 kHz), then the maximum and minimum sideband
frequencies are
fUSB ϭ 2800 ϩ 3 ϭ 2803 kHz

and

fLSB ϭ 2800 Ϫ 3 ϭ 2797 kHz

The total bandwidth is simply the difference between the upper and lower sideband
frequencies:
BW ϭ fUSB Ϫ fLSB ϭ 2803 Ϫ 2797 ϭ 6 kHz
As it turns out, the bandwidth of an AM signal is twice the highest frequency in the
modulating signal: BW ϭ 2fm , where fm is the maximum modulating frequency
...
If the AM station is transmitting on a frequency of 980 kHz, compute the
maximum and minimum upper and lower sidebands and the total bandwidth occupied
by the AM station
...

In addition, AM broadcast stations are spaced every 10 kHz across the spectrum from
540 to 1600 kHz
...
3-10
...
The highest channel frequency is 1600 kHz, with sidebands extending

102

Chapter 3

Figure 3-10

Frequency spectrum of AM broadcast band
...
There are a total of 107 10-kHz-wide channels for AM
radio stations
...
According to Fourier theory, complex signals such
as square waves, triangular waves, sawtooth waves, and distorted sine waves are simply
made up of a fundamental sine wave and numerous harmonic signals at different amplitudes
...
A modulating square wave will produce sidebands at frequencies based upon the fundamental sine wave as well as at the
third, fifth, seventh, etc
...
3-11
...
In order
for a square wave to be transmitted and faithfully received without distortion or degradation, all the most significant sidebands must be passed by the antennas and the transmitting and receiving circuits
...
In Fig
...
3-12(b), it is
100
...
Amplitude modulation by square waves or rectangular binary pulses is referred to
as amplitude-shift keying (ASK)
...

Another crude type of amplitude modulation can be achieved by simply turning the
carrier off and on
...


Figure 3-11

Amplitude-shift keying (ASK)

Frequency spectrum of an AM signal modulated by a square wave
...
(a) Fifty percent modulation
...


Modulating signal

(a)
Carrier

(b)

Continuous-wave (CW)
transmission
ON/OFF keying (OOK)

Splatter

A dot is a short burst of carrier, and a dash is a longer burst of carrier
...
The time duration of a dash is 3 times the length of a dot, and the spacing between
dots and dashes is one dot time
...
This kind of transmission is also referred to as
ON/OFF keying (OOK)
...
The sidebands result from the
frequency or repetition rate of the pulses themselves plus their harmonics
...
For example, the spectrum produced by a 500-Hz sine wave modulating a carrier of 1 MHz is shown in Fig
...
The total bandwidth of the signal
is 1 kHz
...
These harmonics also modulate the carrier, producing
many more sidebands, as illustrated in Fig
...
Assume that the distortion is such
that the harmonic amplitudes beyond the fourth harmonic are insignificant (usually less
than 1 percent); then the total bandwidth of the resulting signal is about 4 kHz instead
of the 1-kHz bandwidth that would result without overmodulation and distortion
...
Such harmonic sideband interference is sometimes called splatter
because of the way it sounds at the receiver
...


Figure 3-13

Sending the letter P by Morse code
...

Dash time ϭ three dot times
Carrier frequency

Dot
One dot time
spacing between
dots and dashes

104

Chapter 3

Dash

Dash

Dot

Figure 3-14

The effect of overmodulation and distortion on AM signal bandwidth
...
(b) Distorted 500-Hz sine wave with significant second, third, and fourth harmonics
...
9995 MHz

Harmonic sidebands

1
...
The AM signal is really a composite of several signal voltages, namely,
the carrier and the two sidebands, and each of these signals produces power in the
antenna
...

Now, remember that Vc and Vm are peak values of the carrier and modulating sine
waves, respectively
...

We can convert from peak to rms by dividing the peak value by 12 or multiplying by
0
...
The rms carrier and sideband voltages are then
␷AM ϭ

Vc
Vm
Vm
sin 2␲ fc t ϩ
cos 2␲t 1 fc Ϫ fm 2 Ϫ
cos 2␲t 1 fc ϩ fm 2
12
2 12
2 12

The power in the carrier and sidebands can be calculated by using the power formula P ϭ V 2/R, where P is the output power, V is the rms output voltage, and R is the
resistive part of the load impedance, which is usually an antenna
...
That leaves 500 W in both sidebands
...

For a 100 percent modulated AM transmitter, the total sideband power is always
one-half that of the carrier power
...
5 kW in each sideband
...

When the percentage of modulation is less than the optimum 100, there is much less
power in the sidebands
...
72
b ϭ 25011 ϩ 0
...
25 W
2

Of the total, 250 W is in the carrier, leaving 311
...
25 W in the sidebands
...
25/2 or 30
...


Example 3-3
An AM transmitter has a carrier power of 30 W
...
Calculate (a) the total power and (b) the power in one sideband
...
PT ϭ Pc a1 ϩ

10
...
7225
b ϭ 30 c 1 ϩ
d ϭ 30 a1 ϩ
b
2
2
2

PT ϭ 30(1
...
8 W

b
...
8 Ϫ 30 ϭ 10
...
8
ϭ
ϭ 5
...
However, it is easy to
measure the current in the load
...
When the antenna impedance is
known, the output power is easily calculated by using the formula
PT ϭ IT 2R

106

Chapter 3

where IT ϭ Ic 211 ϩ m2/22
...
For example, the total output power of an 85 percent modulated AM transmitter, whose unmodulated carrier current into a 50-⍀ antenna load
impedance is 10 A, is
IT ϭ 10

B

a1 ϩ

0
...
36125 ϭ 11
...
672 1502 ϭ 136
...
Then, by algebraically rearranging the formula above,
m can be calculated directly:
mϭ

IT 2
2c a b Ϫ 1d
B
Ic

Suppose that the unmodulated antenna current is 2
...
That is the current produced
by the carrier only, or Ic
...
6 A, the modulation index is
mϭ

B

2ca

2
...
182 2 Ϫ 1 4 ϭ 20
...
89
2
...

As you can see, the power in the sidebands depends on the value of the modulation
index
...
Of course, maximum power appears in the sidebands
when the carrier is 100 percent modulated
...

Pc

m2
4 Pc

fc Ϫ fm

m2
4 Pc

fc

fc ϩ fm

Assuming 100 percent modulation where the modulation factor m ϭ 1, the power in
each sideband is one-fourth, or 25 percent, of the carrier power
...
For example, if the
carrier power is 100 W, then at 100 percent modulation, 50 W will appear in the sidebands, 25 W in each
...
The goal in AM is to keep the percentage of modulation as high
as possible without overmodulation so that maximum sideband power is transmitted
...
Assuming
100-W carrier power and a total power of 150 W, the carrier power percentage is
100/150 ϭ 0
...
7 percent
...
333,
or 33
...

The carrier itself conveys no information
...
When modulation occurs,
sidebands are produced
...
Only one-third of the total transmitted power is
allotted to the sidebands, and the remaining two-thirds is literally wasted on the carrier
...
For
example, assuming a carrier power of 500 W and a modulation of 70 percent, the power
in each sideband is
PSB ϭ

Pc m2
500(0
...
49)
ϭ
ϭ
ϭ 61
...
5 W
...

As stated previously, complex voice and video signals vary over a wide amplitude and frequency range, and 100 percent modulation occurs only on the peaks of
the modulating signal
...

With less sideband power transmitted, the received signal is weaker and communication is less reliable
...
An unmodulated AM signal produces a current
of 4
...
The modulation is 90 percent
...

a
...


Pc ϭ I 2R ϭ 14
...
0421402 ϭ 921
...
92 2
m2
0
...
8 1 ϩ
ϭ 4
...
8 11
...
7 A

PT ϭ IT 2R ϭ 15
...
491402 ϭ 1295 W

c
...
6 ϭ 373
...
7 W each sideband2

Example 3-5
The transmitter in Example 3-4 experiences an antenna current change from 4
...
1 A
...
1 2
b Ϫ 1d
4
...
06252 2 Ϫ 1 4
ϭ 1211
...
132
ϭ 10
...
51
The percentage of modulation is 51
...
9) 2 (921
...
5
ϭ
ϭ
ϭ 186
...

It is used in AM radio broadcasting, CB radio, TV broadcasting, and aircraft tower communication
...
Examples are
garage door openers and remote keyless entry devices on cars
...


3-5 Single-Sideband Modulation

Single-sideband modulation

In amplitude modulation, two-thirds of the transmitted power is in the carrier, which
itself conveys no information
...

One way to improve the efficiency of amplitude modulation is to suppress the carrier
and eliminate one sideband
...
SSB is a form
of AM that offers unique benefits in some types of electronic communication
...
This type of signal is referred to as a double-sideband suppressed
carrier (DSSC or DSB) signal
...
Double-sideband suppressed carrier modulation is simply a special case of AM
with no carrier
...
3-15
...
The carrier is suppressed, and the timedomain DSB signal is a sine wave at the carrier frequency, varying in amplitude as shown
...


Double-sideband suppressed carrier (DSSC or DSB)

Time-domain display

Carrier frequency sine wave
Note phase transition

Time

Amplitude Modulation Fundamentals

109

Figure 3-16

A frequency-domain display of DSB signal
...
A unique characteristic of the DSB signal is the
phase transitions that occur at the lower-amplitude portions of the wave
...
3-15,
note that there are two adjacent positive-going half-cycles at the null points in the wave
...

A frequency-domain display of a DSB signal is given in Fig
...
As shown, the
spectrum space occupied by a DSB signal is the same as that for a conventional AM
signal
...
The purpose of the balanced modulator is to produce the sum and
difference frequencies but to cancel or balance out the carrier
...
4
...
One important application for DSB, however, is the transmission of the color
information in a TV signal
...
DSB
is, however, used to transmit the
color information in a TV signal
...
As it turns out, there
is no reason to transmit both sidebands in order to convey the information
...
SSB signals offer four major benefits
...
The primary benefit of an SSB signal is that the spectrum space it occupies is only
one-half that of AM and DSB signals
...

2
...
Alternatively, SSB transmitters
can be made smaller and lighter than an equivalent AM or DSB transmitter because
less circuitry and power are used
...
Because SSB signals occupy a narrower bandwidth, the amount of noise in the signal is reduced
...
There is less selective fading of an SSB signal over long distances
...
These are on different
Chapter 3

Figure 3-17

An SSB signal produced by a 2-kHz sine wave modulating a 14
...

Carrier

SSB signal
14
...
298

14
...
302

Frequency (MHz)
(a)

(b)

frequencies, so they are affected in slightly different ways by the ionosphere and
upper atmosphere, which have a great influence on radio signals of less than about
50 MHz
...
Such cancellation, or selective fading, is not a problem with SSB since only one sideband is being
transmitted
...
First, when no information or modulating signal is present, no RF signal is transmitted
...
This is the condition
that might occur during a voice pause on an AM broadcast
...

Sidebands are generated only during the modulation process, e
...
, when someone speaks
into a microphone
...

Figure 3-17 shows the frequency- and time-domain displays of an SSB signal produced when a steady 2-kHz sine wave tone modulates a 14
...
Amplitude
modulation would produce sidebands of 14
...
302 MHz
...
Figure 3-17(a) shows that only the upper sideband is generated
...
302-MHz sine wave
...
3-17(b)
...
A
more common modulation signal is voice, with its varying frequency and amplitude content
...
The waveform at the output of the SSB modulator has the same shape as the baseband waveform,
but it is shifted in frequency
...
Demodulation depends upon the carrier being present
...
To faithfully recover the intelligence signal, the reinserted carrier must have the
same phase and frequency as those of the original carrier
...

When SSB is used for voice transmission, the reinserted carrier can be made variable in
frequency so that it can be adjusted manually while listening to recover an intelligible
signal
...

Amplitude Modulation Fundamentals

111

Pilot carrier

To solve this problem, a low-level carrier signal is sometimes transmitted along
with the two sidebands in DSB or a single sideband in SSB
...

Such a low-level carrier is referred to as a pilot carrier
...


Signal Power Considerations

Peak envelope power (PEP)

In conventional AM, the transmitted power is distributed among the carrier and two
sidebands
...
The effective transmission power is the combined power in the sidebands, or
200 W
...
A given SSB
transmitter will have the same communication effectiveness as a conventional AM unit
running much more power
...
The power advantage of SSB over AM is 4:1
...
PEP is computed by the equation P ϭ V 2/R
...
The rms voltage is 0
...
In this example, the rms voltage is
0
...
26 V
...
26) 2
ϭ 324 W
50

The PEP input power is simply the dc input power of the transmitter’s final amplifier stage at the instant of the voice envelope peak
...
Because the carrier
has a low power level, the
benefits of SSB and DSB are
retained
...


112

For example, a 450-V supply with a peak current of 0
...
8) ϭ 360 W
...
During normal speech levels, the input and output power levels are much less than the PEP
level
...
Typical SSB transmitters
are designed to handle only the average power level on a continuous basis, not the PEP
...
This sideband will occupy the same bandwidth as one
sideband in a fully modulated AM signal with carrier
...
A filter is typically used to remove the unwanted
sideband
...
What is the PEP?
Vp ϭ

Vp–p
2

ϭ

Vrms ϭ 0
...
7071892 ϭ 62
...
92 2
V
ϭ
ϭ 52
...
8 W

Example 3-8
An SSB transmitter has a 24-V dc power supply
...
3 A
...
What is the PEP?
PEP ϭ Vs Im ϭ 2419
...
2 W
b
...
2
PEP
ϭ
ϭ 74
...
2
ϭ
ϭ 55
...
8 to 74
...
SSB signals are still
used in some two-way radios
...
DSB signals
are used in FM and TV broadcasting to transmit two-channel stereo signals and to transmit the color information for a TV picture
...
A TV signal consists of
the picture (video) signal and the audio signal, which have different carrier frequencies
...
The picture carrier is transmitted, but one sideband is partially
suppressed
...
2 MHz
...
2) ϭ 8
...
This is an
excessive amount of bandwidth that is wasteful of spectrum space because not all of it
is required to reliably transmit a T V signal
...


113

Figure 3-18

Vestigial sideband transmission of a TV picture signal
...
75 MHz fc

fcϩ 4
...
5 MHz

Vestigial sideband (VSB) signal

maximum allowed by the FCC for TV signals, a portion of the lower sideband of the TV
signal is suppressed, leaving only a small part, or vestige, of the lower sideband
...
3-18
...
75 MHz (750 kHz) are suppressed in the lower (vestigial) sideband, and
all video frequencies are transmitted in the upper sideband
...


3-6 Classification of Radio Emissions
Figure 3-19 shows the codes used to designate the many types of signals that can be
transmitted by radio and wire
...
For example,
a basic AM voice signal such as that heard on the AM broadcast band or on a CB or
aircraft radio has the code A3
...
Examples of
codes designating signals described in this chapter are as follows:
DSB two sidebands, full carrier ϭ A3
DSB two sidebands, suppressed carrier ϭ A3b
SSB single sideband, suppressed carrier ϭ A3j
SSB single sideband, 10 percent pilot carrier ϭ A3a
Vestigial sideband TV ϭ A3c
OOK and ASK ϭ A1
Note that there are special designations for fax and pulse transmissions, and that the
number 9 covers any special modulation or techniques not covered elsewhere
...
For
example, the designation 10A3 refers to a 10-kHz bandwidth voice AM signal
...

Another system used to describe a signal is given in Fig
...
It is similar to the
method just described, but with some variations
...
Some examples are
A3F
J3E
F2D
G7E

114

Chapter 3

amplitude-modulated analog TV
SSB voice
FSK data
phase-modulated voice, multiple signals

Figure 3-19
Letter

Radio emission code designations
...

Type
N
A
J
F
G
P
Type
0
1
2
3
7
8
9
Type
N
A
B
C
D
E
F
W

of Modulation
Unmodulated carrier
Amplitude modulation
Single sideband
Frequency modulation
Phase modulation
Series of pulses, no modulation
of Modulating Signals
None
Digital, single channel, no modulation
Digital, single channel, with modulation
Analog, single channel
Digital, two or more channels
Analog, two or more channels
Analog plus digital
of Intelligence Signal
None
Telegraphy, human
Telegraphy, machine
Fax
Data, telemetry, control signals
Telephony (human voice)
Video, TV
Some combination of any of the above

Amplitude Modulation Fundamentals

115

CHAPTER REVIEW
Summary
In amplitude modulation, an increase or a decrease in the
amplitude of the modulating signal causes a corresponding
increase or decrease in both the positive and the negative
peaks of the carrier amplitude
...

Using trigonometric functions, we can form mathematical expressions for the carrier and the modulating signal, and
we combine these to create a formula for the complete modulated wave
...

The relationship between the amplitudes of the modulating signal and the carrier is expressed as the modulation
index m, a number between 0 and 1
...

When a carrier is modulated by an information signal,
new signals at different frequencies are generated
...
An AM signal
is a composite of several signal voltages, the carrier, and the
two sidebands, each of which produces power in the antenna
...

AM signals can be expressed through time-domain displays or frequency-domain displays
...

One way to overcome this wasteful effect is to suppress the
carrier
...
Because both sidebands
are not necessary to transmit the desired information, one of
the remaining sidebands can be suppressed, leaving a singlesideband (SSB) signal
...

In SSB, the transmitter output is expressed as peak envelope power (PEP), the maximum power produced on voice
amplitude peaks
...
Two-way SSB communication is used in marine
applications, in the military, and by hams
...


Questions
1
...

2
...

3
...

4
...
True or false? The carrier frequency is usually lower
than the modulating frequency
...
What is the outline of the peaks of the carrier signal
called, and what shape does it have?
7
...
Write the trigonometric expression for a sine wave carrier signal
...
True or false? The carrier frequency remains constant
during AM
...
What mathematical operation does an amplitude modulator perform?
11
...
What is the modulation index called when it is expressed as a percentage?

116

Chapter 3

13
...

14
...
What is the name of the type of signal that is displayed
on an oscilloscope?
16
...
Explain why complex nonsinusoidal and distorted signals produce a greater bandwidth AM signal than a
simple sine wave signal of the same frequency
...
What three signals can be added to give an AM wave?
19
...
What is the value of phasor representation of AM signals?
21
...

22
...
Does the carrier of an AM signal contain any information? Explain
...
What is the name of a signal that has both sidebands but
no carrier?
25
...
What is the minimum bandwidth AM signal that can be
transmitted and still convey all the necessary intelligence?
27
...

28
...


29
...

Why is it used? Draw the frequency-domain spectrum of
the TV signal
...
Using Figs
...

31
...


Problems
1
...
◆
2
...
8 and Vmin ϭ 2
...
What is the percentage of modulation?
3
...
To achieve 75 percent modulation of a carrier of
Vc ϭ 50 V, what amplitude of the modulating signal
Vm is needed?
5
...
The peak-to-peak value of the modulating signal
is 20 V
...
What is the mathematical relationship of the carrier and
modulating signal voltages when overmodulation occurs?
7
...
9 MHz is
modulated by frequencies up to 4 kHz
...
What is the bandwidth of an AM signal whose carrier is
2
...
5-kHz square wave with
significant harmonics up to the fifth? Calculate all the
upper and lower sidebands produced
...
How much power appears in one sideband of an AM signal of a 5-kW transmitter modulated by 80 percent? ◆
10
...
An AM signal has a 12-W carrier and 1
...
What is the percentage of modulation?
12
...
The transmitter is modulated
by 60 percent
...
The antenna current produced by an unmodulated carrier is 2
...

When amplitude-modulated, the antenna current rises
to 2
...
What is the percentage of modulation?
14
...
How
much power is added to the signal when the transmitter
is 100 percent modulated?
15
...

On voice peaks, the final amplifier draws a current of
3
...
What is the input PEP?
16
...
What is the output PEP?
17
...
An SSB transmitter with a carrier of 2
...
2-kHz
range
...

◆ Answers

to Selected Problems follow Chap
...


Critical Thinking
1
...
How is the output power of an SSB transmitter
expressed?
3
...
1 and 6
...
The resulting AM signal is
then used to amplitude-modulate a carrier of
12
...
Calculate all sideband frequencies in the
composite signal, and draw a frequency-domain display of the signal
...

What is the bandwidth occupied by the complete signal?

4
...

5
...
What is the carrier
power?
6

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