Chapter 4
Amplitude Modulation
Communication System Chart
Communication
System
Continuous Wave
Amplitude
Modulation
(AM)
Digital Wave
Angle
Modulation
Frequency
Modulation
(FM)
Pulse
Modulation
(PM)
Analogue Pulse
Modulation
Digital Pulse
Modulation
Introduction
What is modulation?
“Modulation is defined as the process of modifying a carrier
wave (radio wave) systematically by the modulating signal
(audio)”
This process makes the signal suitable for the transmission and
compatible with the channel. The resultant signal is called the
modulated signal
In the other words, it is the process of changing/varying one of
the parameters of the carrier wave by the modulating signal
Introduction

Modulation is operation performed at the transmitter to achieve
efficient and reliable information transmission

For analogue modulation, it is frequency translation method
caused by changing the appropriate quantity in a carrier signal

It involves two waveforms:
 A modulating signal/baseband signal – represents the
message
 A carrier signal – depends on type of modulation
Introduction

Analogue modulations - frequency translation
methods caused by changing the appropriate
quantity in a carrier signal.
Baseband
signal
MODULATION
Carrier
Modulated
signal
Introduction
Introduction
•Once this information is received, the low frequency information
must be removed from the high frequency carrier.
•This process is known as “ Demodulation”.
Types of Modulation
Three main type of modulations:

Analog Modulation

Amplitude modulation


Example: Double sideband with carrier (DSB-WC), Double
sideband suppressed carrier (DSB-SC), Single sideband
suppressed carrier (SSB-SC), Vestigial sideband (VSB)
Angle modulation (frequency modulation & phase modulation)

Example: Narrow band frequency modulation (NBFM), Wideband
frequency modulation (WBFM), Narrowband phase modulation
(NBPM), Wideband phase modulation (NBPM)
Types of Modulation

Pulse Modulation



Carrier is a train of pulses
Example: Pulse Amplitude Modulation (PAM), Pulse width
modulation (PWM) , Pulse Position Modulation (PPM)
Digital Modulation

Modulating signal is analog


Example: Pulse Code Modulation (PCM), Delta Modulation
(DM), Adaptive Delta Modulation (ADM), Differential Pulse
Code Modulation (DPCM), Adaptive Differential Pulse Code
Modulation (ADPCM) etc.
Modulating signal is digital (binary modulation)

Example: Amplitude shift keying (ASK), frequency Shift Keying
(FSK), Phase Shift Keying (PSK) etc.
Summary of Modulation Techniques
Analogue
Modulation
Volt
Hertz
Radians
AM
FM
PM
FSK
PSK
v(t) = V sin
Digital
Modulation
ASK
(2ft   )
Types of Modulation
•Changing of the amplitude produces
Amplitude Modulation signal
•Changing of the frequency produces
Frequency Modulation signal
•Changing of the phase produces
Phase Modulation signal
Learning Outcomes

Define AM concepts
 Calculate the AM voltage distribution,
modulation index, voltage ,power
distribution
 Calculate and draw AM in time and
frequency domain, bandwidth
Revision..

Why do we need modulation?
 What are the types of modulation?
 What is AM?
 What is bandwidth?
Basic Amplitude Modulation
•
Amplitude Modulation is the process of
changing the Amplitude of a relatively high
frequency carrier signal in accordance with
the amplitude of the modulating signal
(Information).

The carrier amplitude varied linearly by the modulating
signal which usually consist of a range of a audio frequencies.
The frequency of the carrier is not affected

Application of AM
-

Frequency range for AM
 Bandwidth

Radio broadcasting, TV pictures
(video), facsimile transmission
- 535 kHz – 1600 kHz
10 kHz
Amplitude Modulation
Various forms of Amplitude Modulation
• Conventional Amplitude Modulation (Alternatively
known as Full AM or Double Sideband Large carrier
modulation (DSBLC) /Double Sideband Full Carrier
(DSBFC)
• Double Sideband
modulation
Suppressed
carrier
• Single Sideband (SSB) modulation
• Vestigial Sideband (VSB) modulation
(DSBSC)
Amplitude Modulation ~ DSBFC (Full AM)
“Amplitude Modulation is the process of changing the
amplitude of the radio frequency (RF) carrier wave by the
amplitude variations of modulating signal”

The carrier amplitude varied linearly by the modulating
signal which usually consist of a range of a audio
frequencies. The frequency of the carrier is not affected
Application of AM
-
Radio broadcasting, TV pictures
(video), facsimile transmission
Frequency range for AM
- 535 kHz – 1600 kHz
Bandwidth
10 kHz
Basic Amplitude Modulation
Envelope
17
AM Envelope
•Wave and the shape of the Modulated Wave is called AM Envelope.
Envelope is the original modulating
signal
Carrier
Amplitude Modulation – What
really happened?? (you are not
required to memorized this)
carrier

We now know how AM wave looks like,
but how do we represent it
mathematically?
 Can you write the general equation of a
sinusoid wave?
AM wave equation
The expression of voltage in the electric circuit is given
by :
v(t )  V sin( 2ft   )
v(t )  V cos(2ft   )
or
V = Amplitude of the signal in Volts
f = The signal frequency in Herzt
(2ft + ) = The phase of the signal in radian
AM wave equation
An unmodulated modulating signal :
vm (t) = Em sin (2fmt)
Or
vm (t) = Vm sin (2fmt)
Em = Vm= peak
modulating signal
amplitude(volts)
22
AM Modulation

Envelope of the modulating signal varies above &
below the peak carrier amplitude
 In general Em < Ec, otherwise distortion will occur.
The modulating signal values adds or subtracts from
the peak value of the carrier.
 This instantaneous value either top or bottom voltage
envelope (new expression for Vm) :
v1  vc  vm
v1  vc  vm sin( 2f mt )
v1
AM wave equation

An unmodulated carrier (carrier signal) is described by
the following equation :-
vc (t) = Ec sin (2fct)
Or
Ec = Vc = peak carrier
amplitude (volts)
vc (t) = Vc sin (2fct)
25
AM Concepts
(Low frequency)
carrier
(nonlinear devices)
Modulation x carrier
(High frequency)
Figure 3-3: Amplitude modulator showing input and output signals.
26
The modulated wave can be
expressed as :-
Vam(t) =[Ec + Em sin (2fmt)] (sin 2fct) .........(1)
WHERE:
Ec + Em sin (2fmt) = Amplitude of the modulated
wave
Em = peak change in the amplitude of the envelope
fm = frequency of the modulating signal
27
AM wave equation
Expanding eq (1) we get:
Vam  Ec sin(2f ct )  Em sin(2f mt )sin(2f ct )........(2)
Carrier signal
Modulating
signal
Later we will see how this equation can be further improved to make it more
meaningful
28
AM wave equation
Vam  [ Ec  Em sin(2f mt )] sin(2f ct )........(2)
2
9
AM Concepts

In AM, it is particularly important that the
peak value of the modulating signal be
less than the peak value of the carrier.
Vm < V c

Distortion occurs when the amplitude of
the modulating signal is greater than the
amplitude of the carrier.
Amplitude Modulation ~ DSBFC (Full AM)
The amplitude-modulated wave can then be expressed as
v AM (t )  Vc cos(c t )  vm (t ) cos(c t )
v AM (t )  Vc  vm (t )cos(ct )
v AM (t )  Vc  Vm cos(mt )cos(ct )
Vm
v AM (t )  Vc cos(c t )1 
cos m t 
Vc
v AM (t )  Vc cos(ct )1 ma cos m t 
Amplitude Modulation ~ DSBFC (Full AM)
where notation m is termed the modulation index. It is
simply a measurement for the degree of modulation and
bears the relationship of Vm to Vc
Vm
ma 
Vc
Therefore the full AM signal may be written as
vAM (t )  Vc cos(ct )1  ma cos(m t 
Modulation Index and Percentage of
Modulation

modulation index (m) is a value that describes the
relationship between the amplitude of the modulating
signal and the amplitude of the carrier signal.
Em
m
Ec

Percentage of modulation.
Em
M
100
Ec
modulating factor or
coefficient, or degree of
modulation.
Modulation Index and Percentage of
Modulation

modulation index (m) can also calculate it using
1 Vmax  Vmin 

Vmax  Vmin 
2
m

1 Vmax  Vmin  Vmax  Vmin 
2
Vmax  Ec  Em
where
Vmin  Ec  Em
34
Modulation of complex signal
•
The modulating signal (information signal) is often a complex
form consists of many sinusoidal wave with different Amplitude
and Frequencies;
v(t) = V1sin(2f1t) + V2sin(2f2t) + V3sin(2f3t)+
V4sin(2f4t) + V5sin(2f5t) + ….
•
Thus, after modulation, the output wave will be in the form of :
vam(t) = Ecsin(2fct) - ½ m1Ec cos[2(fc+fm1)t] + ½
m1Ec cos[2(fc-fm1)t] - ½ m2Ec cos[2(fc+fm2)t] +
½ m2Ec cos[2(fc-fm2)t] - ½ m3Ec cos[2(fc+fm3)t]
+ ½ m3 Ec cos[2(fc-fm3)t] - …
•
The Total Modulation Index will be :
m = sqrt (m12 + m22 + m32 + mn2)
Modulation Index for Multiple Modulating Frequencies
Modulation
Index
for Multiple
Two or more sine waves
of different,
uncorrelated
frequencies modulating a single carrier is calculated
Modulating
Frequencies
by the equation:

m  m  m   
2
1
2
2

Consider
these
envelopes:
 Do they
look the
same?
Modulation Index and Percentage of
Modulation
Overmodulation and Distortion
The modulation index should be a number
between 0 and 1.
 If the amplitude of the modulating voltage is
higher than the carrier voltage, m will be
greater than 1, causing distortion.
 If the distortion is great enough, the
intelligence signal becomes unintelligible.

Modulation Index and Percentage of
Modulation
Overmodulation and Distortion
Distortion of voice transmissions produces
garbled, harsh, or unnatural sounds in the
speaker.
 Distortion of video signals produces a
scrambled and inaccurate picture on a TV
screen.

http://www.williamson-labs.com/480_am.htm
Over Modulation
Modulation Index and Percentage of
Modulation
Figure : Distortion of the envelope caused by overmodulation where the
modulating signal amplitude Vm is greater than the carrier signal Vc.
AM Modulation

Draw AM wave in time domain and
frequency domain
Voltage Distribution

An unmodulated carrier (carrier signal) is described by the following
equation :-
Vc (t) = Ec sin (2fct)

The Amplitude of the AM Wave varies proportional to the amplitude of
the modulation signal, and the maximum of the modulated wave equal to
Ec + Em.

Thus the amplitude of the modulated wave can be expressed as :-
Vam(t) =[Ec + Emsin(2fmt)] sin (2fct)

Ec + Emsin(2fmt)  Amplitude of modulated wave.

Em= Peak Change in the Amplitude of Envelope

fm= Frequency of Modulating signal
Voltage Modulation
•
Since Em = mEc and by developing the equation for modulated
wave, the final equation of the modulated wave can be expressed
in term of its Carrier Component and Side Frequencies
Component (usf & lsf):Vam  Ec sin( 2f c t ) 
mEc
mEc
cos[ 2 ( f c  f m )t ] 
cos[ 2 ( f c  f m )t ]
2
2
Where Ecsin(2fct) carrier signal (V)


•
•
mEc
cos[2 ( f c  f m )t ]
2
mEc
cos[2 ( f c  f m )t ]
2
 upper side frequency signal (V)
 lower side frequency signal (V)
Carrier wave is 90˚ out of phase with the upper and lower
side frequencies
The upper and lower side frequencies are 180 ˚ out of phase
with each other
Frequency Domain

The frequency domain provides an alternative
description of signal in which the time axis is
replaced by a frequency axis.
The relationship between the time
and frequency domains
Sidebands and
the Frequency Domain

Side frequencies, or sidebands are generated as
part of the modulation process and occur in the
frequency spectrum directly above and below the
carrier frequency.
•
•
Single-frequency sine-wave modulation generates two
sidebands.
Complex wave (e.g. voice or video) modulation generates a
range of sidebands.
Sidebands and
the Frequency Domain
Em
Elsb  Eusb 
2
Amplitude
fLSB = fc - fm
fLSB
fUSB = fc + fm
fC
fUSB
Frequency
Sidebands and
the Frequency Domain
Figure : The AM wave is the
algebraic sum of the
carrier and upper and
lower sideband sine
waves.
(a) Intelligence or modulating
signal.
(b) Lower sideband.
(c ) Carrier.
(d ) Upper sideband.
(e ) Composite AM wave.
Bandwidth



Signal bandwidth is an important characteristic of any
modulation scheme
In general, a narrow bandwidth is desirable
Bandwidth is calculated by:
B  2 fm
Bandwidth

Bandwidth is the difference between the upper and
lower sideband frequencies.
BW = fUSB−fLSB
Sidebands and the Frequency
Domain
Example:
A standard AM broadcast station is allowed to
transmit modulating frequencies up to 5 kHz. If the
AM station is transmitting on a frequency of 980 kHz,
what are sideband frequencies and total bandwidth?
1. Highlight and identify important information in the question:
fm
A standard AM broadcast station is allowed to
transmit modulating frequencies up to 5 kHz. If
the AM station is transmitting on a frequency of
980 kHz, what are sideband frequencies and
total bandwidth?
fc
2. Use the formulas to solve the problem:
fUSB = fc +fm =980 + 5 = 985 kHz
fLSB = fc -fm = 980 – 5 = 975 kHz
BW = fUSB – fLSB = 985 – 975 = 10 kHz
Or
BW = 2 (5 kHz) = 10 kHz
54
EXAMPLE :

AM DBSFC Modulator with a carrier frequency, fc =
100 kHz and maximum modulating signal frequency,
fm of 10 kHz, determine the following :
a. LSB & USB
b. Bandwidth
c. Upper and Lower side frequencies if the modulating
signal is a single frequency of 5kHz.
d. Draw the output frequency spectrum
Solution:
Lower side band
90kHz
fc-fm(max
95kHz
fLSF
Carrier
100kHz
fc
Upper side band
105kHz
fUSF
110kHz Frequency
fc+m(max
Amplitude Modulation
If fm consists of a range frequencies f1 to f2, the
component of the sidebands become:
Upper sideband (USB) range is from (fc+f1) to (fc+f2)
Lower sideband (LSB) range is from (fc-f2) to (fc-f1)
Amplitude,V
Amplitude,V
Baseband signal
f1
f2
freq
lower sideband
fc-f2
fc-f1
Modulated
signal
upper sideband
fc+f1
fc+f2
freq
AM spectrum when the modulating signal is a baseband signal from frequency f1 to f2
Bandwidth for this case,
B = (fc+f2) - (fc-f2)
= 2f2
Amplitude Modulation

For example, if voice signal with the band of frequency of
0 – 4 kHz is transmitted using a carrier of 100 kHz, the
modulated signal consists of
Carrier signal with frequency of 100 kHz
 upper side band with frequency of range of 100 – 104 kHz
 lower side band with frequency of range 96 – 100 kHz


The bandwidth is 104 – 96 = 8 kHz
Group Activity

a)
b)
c)
d)
e)
Given the first input to AM Modulator is 500 kHz Carrier signal
with Amplitude of 20V. The second input to AM Modulator is the
10kHz modulating signal with ± 7.5 Vp. Determine the following :USB & LSB
Modulation Index and percent modulation, M
Peak Amplitude of modulated carrier and Upper & Lower side
frequency voltage
Maximum & Minimum Amplitude of the envelope, Vmax and Vmin
Draw output in frequency domain & time domain
59
Solution
(a)
Upper and lower side frequencies:
f usb  500  10  510kHz
f lsb  500  10  490kHz
(b)
Modulation Index and percent modulation, M
Em 7.5
m

 0.375
Ec 20
M  0.375 100  37.5%
60
Solution (c)-method 1
(c) Peak Amplitude of modulated carrier and Upper & Lower side
frequency voltage
Ec (mod ulated )  Ec (un mod ulated )  20Vp
We can find Elsb and Eusb by using equation:
Elsb
Em
 Eusb 
2
Thus
Elsb
Em 7.5
 Eusb 

 3.75V p
2
2
61
Solution (c)- method 2
(c) Peak Amplitude of modulated carrier and Upper &
Lower side frequency voltage
Let’s say Em is unknown. Em can be found from
Em
m
Ec
Thus
Elsb
 Em  mEc
mEc (0.375)(20)
 Eusb 

 3.75V p
2
2
62
Solution
(d) Maximum & Minimum Amplitude of the
envelope, Vmax and Vmin
Vmax  Ec  Em  20  7.5  27.5V p
Vmin  Ec  Em  20  7.5  12.5V p
63
Solution
(e) frequency domain
Amplitude (Vp)
20
3.75
fLSB =490
3.75
fC = 500
fUSB = 510
f (kHz)
64
Solution
(e) time domain
Vmax=27.5 Vp
Vmin =12.5 Vp
65
How to
calculate AM
power ???
Amplitude
Pc
PT ????
PLSB
fLSB
PUSB
fC
fUSB
Frequency
AM Power

The AM signal is a composite of the
carrier and sideband signal voltages.
 Each signal produces power in the
antenna.
 Total transmitted power (PT) is the sum
of carrier power (Pc ) and power of the
two sidebands (PUSB and PLSB).
AM Power


Power in a transmitter is
important, but the most
important power
measurement is that of the
portion that transmits the
information
Power in an AM transmitter is
calculated according to the
formula at the right
 m 2 

Pt  P c
1
 2 


Measuring AM signal power

The greater the percentage of modulation, the higher the
sideband power and the higher the total power transmitted.
 Power in each sideband is calculated
PSB = PLSB = PUSB = Pcm2 / 4

Maximum power appears in the sidebands when the carrier is
100 percent modulated.
Pc = (Vc )2 / 2R
where Pc = carrier power (W)
Vc =peak carrier voltage(V)
R= load resistance (Ohm)
Measuring AM signal power

In reality it is difficult to determine AM
power by measuring the output voltage.
 However, antenna current is easy to
measure and output power can be
expressed
PT 

IT2 R
where IT  I c
m2
1
2
where IT is measured RF current and R is antenna
impedance
AC average power dissipation

Recall that the average power dissipated
by resistor R is with a sinusoidal source
of amplitude Vpk is given

2
V pk / 2
Vrms
P

R
R

2

Vpk2
2R
AM signal power

Since the vAM is composed of three sinusoids
vAM  Vc sin 2 fct 
Vm
V
sin 2 ( f c  f m )t  m sin 2 ( f c  f m )t
2
2
the total average power dissipated by the antenna R is
given
PT  Pc  PLSB  PUSB
V / 2  V



2
c
R
Vc2 Vm2 Vm2



2 R 8R 8R
m
/2 2
R
  V
2
m
/2 2
R

2
AM signal power

Remembering that the modulation index
m = Vm /Vc we can write
PT

2
2
2
Vc   mVc   mVc  Vc2  m2 m2 





1

2R
8R
8R

2R 
4

4 
The common term is the just the carrier
power, thus the total power can also be
written
 m2 
PT  PC 1 

2


AM power efficiency

Therefore given the equation for power of
an AM waveform, the efficiency is:
m2
h
 100%
2
2m

It can be seen from this equation that the
efficiency of AM modulation increases as
the modulation index, μ, increases.
Example Problem 1
An AM transmitter has a carrier power of 30 W. The
percentage modulation is 85%. Calculate (a) the total
power, and (b) the power in one sideband.
2
1.5
0.5
1
Voltage (V)
0.4
0.5
0
0.3
0.2
-0.5
0.1
-1
0
-1.5
-2
0
0.001
0.002
0.003
0.004
0.005
0.006
T ime (sec)
0.007
0.008
0.009
0.01
0
1000
2000
3000
Frequency (Hz)
4000
5000
6000
AM power efficiency

From the previous example, what percentage of the total
power was dedicated to transmitting the carrier?
Pc = 30 W
PLSB = 5.4 W

PT= 42.75 W
PUSB = 5.4 W
Is any information conveyed by the carrier itself?
 How could we maximize the power in the sidebands?
AM power efficiency

Sideband power is maximized by setting m
= 1.
P
c
 m2 
PT  Pc 1 

2



m2
Pc
4
m2
Pc
4
For m = 1, what percentage of the total
power is dedicated to the sidebands?
AM power efficiency

At maximum modulation, the sideband power is at most
33% of the total transmitted power.
Percentage of total power (% PT)
100
Pc
80
m2
Pc
4
60
m2
Pc
4
Power in carrier ( Pc)
40
20
Power in sidebands ( PSB)
0
100
90
80
70
60
50
40
Percentage modulation (% m)
30
20
10
0
 m2 
PT  Pc 1 

2


AM power efficiency

Two-thirds of the power is wasted in the carrier.
Further, 100% modulation only occurs at peaks in the
modulating signal, thus the average sideband power is
considerably worse than the ideal.
100% modulation only occurs
at peaks
Speech as a modulating signal
0.3
0.2
Voltage (V)

0.1
0
-0.1
-0.2
-0.3
0
0.5
1
1.5
T ime (sec)
2
2.5
3
Improving on AM


Besides the 67% power loss due to the carrier,
the sidebands contain redundant information.
To maximize the efficiency of AM we need to
 Suppress the carrier
 Eliminate one of the sidebands
Upper and lower
sidebands contain the
same information.
AM modulated speech signal
Why is still widely used?

AM is still widely used because it is simple
and effective.
AM broadcast radio
 CB radio (11m range)
 TV broadcasting
 Air traffic control radios
 Garage door opens, keyless remotes

Aircraft VHF Communications Transceiver
Types of AM
1) Double sideband full carrier (DSBFC)
- Contains USB, LSB and Carrier
- This is the most widely used type of AM modulation. In fact, all radio
channels in the AM band use this type of modulation.
2) Double sideband suppressed carrier (DSBSC)
- Contains only USB & LSB
- A circuit that produces DSBSC is Balanced modulator
3) Single sideband (SSB)
- In this modulation, only half of the signal of the DSBSC is used
- Contains either LSB or USB
- Produce efficient system in term of power consumption and bandwidth
4) Vestigial Sideband (VSB):
- This is a modification of the SSB to ease the generation and reception
of the signal.
EXAMPLE :
For AM DSBFC wave with an unmodulated
carrier voltage, Vc = 10 Vp , a load resistance
of 10  and modulation index of 1, determine
the following :
a. Power of the carrier, and sideband
frequencies (Plsf & Pusf)
b. Total Power of sideband, PT
c. Draw Power Spectrum
EXAMPLE :
An AM Transmitter has a carrier power output of 50W. Determine
the total power that produced 80% modulation.
SOLUTION :
1. Total Power is defined as :
PT = Pc[1 + (m2 /2)]
Thus,
PT = (50 W)[1 + ((0.8)2 /2)]
= 66 W
EXAMPLE:
•
For AM DSBFC transmitter with an unmodulated
carrier Power, Pc = 100 W is modulated
simultaneously with 3 other modulating signals with
coefficient index of m1 = 0.2, m1 = 0.4, m1 = 0.5,
determine the following :a. Total Modulation Index or Coefficient
b. Upper and Lower sideband power
c. Total transmitted power
m  m  m   
2
1
2
2