Lesson 4
AMPLITUDE MODULATION
Modulation
 Modulation is the process of altering a characteristic of the carrier in
accordance with the instantaneous value of the intelligence signal.
 The characteristics of the carrier that can be varied are amplitude,
frequency and phase.
Demodulation is the process of recovering the intelligence signal from a
modulated carrier signal.
Consider a sine-wave carrier:
Carrier signal
Ec
t
-Ec
Mathematically,
e c  E c sin c t   
where:
ec = instantaneous carrier amplitude
Ec = peak carrier amplitude
c = carrier radian frequency
 = carrier phase
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LESSON 4 Amplitude Modulation
Reasons for Modulation
 For minimizing interference
 For frequency assignment
 For making antenna sizes practical
 For multiplexing
FCC Emission Designations
First Symbol
A - Amplitude
Modulation, Double
Sideband Full Carrier
Second Symbol
0 – No Modulating Signal
1 - Digitally Keyed
Carrier
Third Symbol
A - Telegraphy
(manual)
B - Telegraphy
B - Independent
2 - Digitally Keyed Tone
Sideband
3 - Analog (voice, music)
C - Facsimile
7 - Multiple Digital
D - Telemetry (Data)
C - Vestigial Sideband
D- Simultaneous/
Sequenced AM and
FM
F - Frequency
Modulation
Channel
(automatic)
E - Telephony (Sound
8 - Multiple Analog
Channel
Broadcasting)
F - Television (video
9 - Channels with Analog
and Digital
G - Phase Modulation
signal)
N - No Information
W - Combination of
H - Single Sideband Full
above
Carrier
J - Single Sideband
Suppressed Carrier
K - Pulse Amplitude
Modulation
L - Pulse Width
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LESSON 4 Amplitude Modulation
Modulation
M - Pulse Position
Modulation
N - Unmodulated
Carrier
P - Unmodulated Pulses
Q- Angle Modulated
during Pulses
R - Single Sideband
Reduced Carrier
V- Combination of any
Pulse Modulations
W- Combinations of any
two or more forms
of Modulation
X- Cases not covered
 In FCC Emission designation, the first symbol signifies the type of
modulation of the main carrier; the second symbol signifies the nature
of the modulation; and the third symbol signifies the type of information
being transmitted.
4.1 Amplitude Modulation (AM)
 Amplitude Modulation (AM) is the simplest way of superimposing the
characteristic of the intelligence signal onto a carrier. The AM signal is
produced by varying the amplitude of the carrier signal in proportion to
the instantaneous amplitude of the intelligence signal.
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LESSON 4 Amplitude Modulation
Em
em (Modulating Signal)
t
- Em
EC
ec (Carrier Signal)
t
- EC
EC + Em
EC
eAM (Resulting AM)
t
The trace of the peaks in the AM wave is called the envelope which has the
same shape as the modulating signal.
Mathematically, the instantaneous value of the AM signal is
e AM  A sin c t ,
where: A= EC + em
e AM  E c  e m  sin c t
where:
e m = instantaneous value of the intelligence signal
e m  E m sin m t
Substituting em, the AM equation becomes
e AM  ( E c  E m sin m t ) sin c t
e AM  E c sin c t  E m sin m t sin c t
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LESSON 4 Amplitude Modulation
Applying trigonometric identity,
sin A sin B 
Let A=ῳCt;
1
cos A  B   cos A  B 
2
B= ῳmt
The complete AM expression is,
e AM  E c sin c t 
Em
cos c  m t  cos c  m t 
2
e AM  E c sin c t 
Em
cos 2  f c  f m t  cos 2  f c  f m t 
2
The expression is composed of three signals, the carrier, lower sideband and
upper sideband.
Upper Sideband
Carrier Signal
Lower Sideband
AM Signal
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LESSON 4 Amplitude Modulation
Modulation Index
 The term that describes the amount of amplitude change in an AM
waveform is called the index of modulation.
 It is also called Coefficient of Modulation, Modulation Factor, or
Modulation Depth.
m 
Em
Ec
The graph shows that,
V max  E C  E m , and, V min  E C  E m
Thus, the modulation index can be expressed as
m 
E m V max V min

E c V max  V min
where:
Em
= peak voltage of the intelligence signal, (V)
Ec
= peak voltage of the carrier signal, (V)
Vmax
= maximum point in the AM wave, (V)
Vmin
= minimum point in the AM wave, (V)
m
= modulation index
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LESSON 4 Amplitude Modulation
Percentage of Modulation, %M
%M  m  100%
Classification According to the Degree of Modulation
 Undermodulation
m 1
Em  Ec
 Overmodulation
m 1
Em  Ec
 Perfect Modulation
m 1
Em  Ec
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LESSON 4 Amplitude Modulation
AM Spectrum
Bandwidth for AM
Ec
BW  f USB  f LSB
BW  f c  f m   f c  f m 
BW  2 f m
4.2 Power Calculations
 Unmodulated Carrier Power, Pc
Pc 
V c RMS
2
R
2
E
 c
2R
 Lower Sideband Power, PLSB and Upper Sideband Power, PUSB
V
PLSB  PUSB  LSB RMS
R
2
 Total Transmitted Power, PT
PT  PC  PLSB  PUSB

P T  Pc 1 

m2 
2 
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Pc m 2

4
LESSON 4 Amplitude Modulation
Where:
EC
= peak voltage of the unmodulated carrier, (V)
R
= load resistance, (R)
m
= modulation index
PC
= unmodulated carrier power, (W)
PT
= total transmitted power, (W)
PUSB
= upper sideband power, (W)
PLSB
= lower sideband power, (W)
Power Spectrum
2
PLSB 
Pc m 2
4
PC 
EC
2R
PUSB 
Pc m 2
4
Percent power in the carrier, %PC
%PC 
PC

PT
PC
PC ( 1 
m2
)
2
Percent power in the sidebands, %PSB
m2
P
2
%PSB  SB 
PT
m2
PC ( 1 
)
2
PC
Among the three signals comprising AM, only the sidebands contain the
information. The information found in the upper sideband is identical with the
lower one. Notice that at 100% modulation, 66.67% of the total power is
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LESSON 4 Amplitude Modulation
contained in the carrier and only 33.33% is in the sidebands. Thus, it is wasteful
to transmit the carrier and is redundant to transmit both sidebands.
Voltage Calculations
 Peak Voltage of the Modulated Carrier, ET
ET  E c 1 
m2
2
Current Calculations
 Peak Current of the Modulated Carrier, IT
IT  I c 1 
m2
2
Where:
IC = peak current of the unmodulated carrier, (A)
IT = peak current of the modulated signal, (A)
ET = peak voltage of the modulated signal, (V)
EC = peak voltage of the unmodulated carrier, (V)
4.3 Simultaneous Modulation
If f m3  f m 2  f m1 , then
BW  f USB  f LSB
BW  f c  f mN  f c  f mN 
BW  2 f mN
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LESSON 4 Amplitude Modulation
Where:
f mN = highest modulating frequency, (Hz)
Modulation Index for Simultaneous Modulation
m t  m12  m 22  m 32  ...  m N2
Where:
mt = Total or effective modulation index
m1 = Modulation index of the first tone
m 2 = Modulation index of the 2nd tone
mN = Modulation index of the nth tone
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LESSON 4 Amplitude Modulation
4.4 Practice Problems
1. What is the modulation index for an AM having Vmax and Vmin of 2.6V and
0.29V, respectively?
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2. An AM signal has the equation:
e AM  25  5 sin 44  10 3 t  sin 46.5  10 6 t  V
a) Find the carrier frequency.
b) Find the frequency of the modulating signal.
c) Find the value of m.
d) What are the frequencies comprising the AM signal?
e) Sketch the signal in the time domain and the frequency domain.
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LESSON 4 Amplitude Modulation
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3. Determine the bandwidth of an AM signal modulated by a 5-kHz tone.
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4. What is the bandwidth of an AM signal whose carrier is modulated by 1
kHz, 3 kHz and 5 kHz, simultaneously?
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5. An AM transmitter is modulated by two audio tones at 1 kHz and 2.5 kHz,
with modulation depths of 0.25 and 0.50, respectively. Find the effective
modulation index.
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6. Three audio waves with 100, 200 and 300 volts simultaneously modulate
a 450-V carrier. What is the total percent of modulation of the AM wave?
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LESSON 4 Amplitude Modulation
7. A 1000-W carrier is to be modulated to a 95% level. Determine the total
transmitted power.
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8. An AM transmitter radiates 100 W at 100% modulation. How much power
is required for the carrier?
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9. An AM broadcast station operates at its maximum allowed total output of
50 kW and at 85% modulation.
How much of the transmitted power
contains the intelligence?
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10. If a transmitter supplies 8 kW to the antenna when it is unmodulated,
what is the total radiated power when it is modulated at 30%.
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LESSON 4 Amplitude Modulation
11. For an AM DSBFC transmitter with an unmodulated carrier power, Pc =
500 W that is modulated simultaneously by four tones, m1 = 0.1, m2 =
0.2, m3 = 0.4 and m4 = 0.5, determine
a) the total modulation index
b) the total sideband power
c) the total transmitted power
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12. The antenna current of an AM transmitter is 11 A when unmodulated but
increases to 14 A when modulated. Find the %M.
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13. An AM transmitter has a carrier voltage of 50 VRMS at a carrier frequency
of 10 MHz. It is modulated at 75% by a 1-kHz sine wave. what is the
total RMS voltage transmitted?
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LESSON 4 Amplitude Modulation
14. The antenna current of an AM transmitter is 8 A when only the carrier is
sent but it increases to 8.93 A when the carrier is modulated by a single
sine wave. Find the percent modulation. If 80% modulation is desired,
what should be the modulation index of the second wave? What is the
antenna current then?
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15. A certain transmitter radiates 9 kW when the carrier is unmodulated and
10.75 kW when modulated. If another sine wave, corresponding to 30%
modulation, is transmitted simultaneously, what is the percent change of
the total power?
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LESSON 4 Amplitude Modulation
4.5 Multiple Choice Questions
1) An antenna transmits an AM signal having a total power content of 15 kW.
Determine the power being transmitted at each of the sidebands when the
percent modulation is 85%.
a. 1101.9W
b. 1990W
c. 3981 W
d. 1019 W
2) In the designation of bandwidth and emission, what letter in the first symbol
represents an ISB signal?
a. J
b. B
c. A
d. C
3) A modulator circuit performs what mathematical operation on its two inputs?
a. addition
b. multiplication
c. division
d. subtraction
4) An AM transmitter is modulated by two sine waves at 1 kHz and 2.5 kHz,
with modulations of 25% and 50%, respectively.
modulation index?
a. 0.56
b. 0.65
c. 0.75
d. 0.25
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What is the effective
LESSON 4 Amplitude Modulation
5) A 2000 Hz audio signal having amplitude of 15V amplitude modulates a 100
kHz carrier, which has a peak value of 25 V when not modulated. Calculate
the modulation factor of the modulated wave.
a. 0.4
b. 0.5
c. 0.6
d. 0.7
6) In the previous problem, what frequencies would show up in a spectrum
analysis of the AM wave?
a. 98 kHz,100 kHz,102 kHz
b. 90.8kHz,100kHz,102.8kHz
c. 98.8kHz,100kHz,102.2kHz
d. 198kHz,200 kHz,202 kHz
7) What is the required bandwidth to transmit the AM signal in the previous
problem?
a. 2KHz
b. 4KHz
c. 200KHz
d. None of the above
8) A bandwidth of 12 MHz becomes available for assignment. If assigned for
TV broadcast service, only two channels could be accommodated.
Determine
the
number
of
AM
stations
that
could
be
broadcast
simultaneously if the maximum modulating frequency is limited to 5 kHz.
a. 1000
b. 1200
c. 800
d. 1600
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LESSON 4 Amplitude Modulation
9) Which is true about over modulation?
a. A modulating voltage is less than a carrier voltage.
b. The modulating voltage is equal to the carrier voltage.
c. Overmodulation produces a distortion at the demodulated output.
d. None of the above.
10) The percentage of modulation for a maximum amplitude of information
transmission is ______%.
a. 0
b. 50
c. 75
d. 100
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