Adama Science and Technology University

School of Electrical Engineering and Computing

Department of Electronics and Communication Engineering

Chapter Two: Amplitude Modulation (AM)

April 16, 2024

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Outlines

1 Introduction

2 Amplitude Modulation (AM) –Linear modulation

3 Time and Frequency domain representation of AM signal

4 Double sideband suppressed Carrier (DSB-SC) modulation and
demodulation techniques
5 Single Side Band (SSB) and Vestigial Side Band (VSB) modulation and
demodulation techniques

6 AM Transmitters

7 AM Receivers

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Introduction

The purpose of a communication system is to transmit information

bearing signals through a communication channel separating the
transmitter from the receiver
Information bearing signals are baseband signals
Baseband is used to designate the band of frequencies representing the
original signal as delivered by a source of information
The baseband signal is also referred to as a modulating signal
Modulation is the process by which some characteristic of a carrier
(amplitude, phase and frequency) is varied in accordance with
modulating (message) signal
A common form of the carrier is a sinusoidal wave
The result of modulation process is referred to as the modulated signal
The original baseband signal to be restored by demodulation process

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Introduction. . . .

In order to make use of the wireless channels, the information is to be

converted into a suitable form (electromagnetic waves) with the help
of a transmitting antenna
For efficient radiation, the size of the antenna should be λ/10 or more
(preferably around λ/4), where λ is the wavelength of the signal to be
radiated.
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 Introduction. . . .

Example 1: Calculate the antenna diameter to radiate a signal of 4KHz and 1GHZ
The advantages of modulation
Modulation for ease of radiation
Modulation for efficient transmission
Modulation for multiplexing
Modulation for frequency assignment
There are three different types of modulation:
Analog Modulation: A process of changing amplitude, frequency or
phase of an analog carrier in accordance with analog message signal
It has three different forms AM, FM, PM.
Pulse Modulation: a process or method of converting message signal in
to pulse forms for transferring pulses from a source to a destination
The predominant methods are PAM, PPM, PWM and PCM.
Digital Modulation: ASK, FSK, PSK.

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Amplitude Modulation (AM) –Linear modulation
Amplitude Modulation is analog modulation, which is the process of
changing the amplitude of a relatively high frequency carrier signal in
accordance with the amplitude of the modulating message signal
AM is a relatively inexpensive, low quality form of modulation that is
used for broadcasting of both audio and video signals.
There are four types of AM:
1 DSB-with carrier
2 DSB-SC
3 SSB
4 Vestigial AM
This is the form of modulation used for commercial AM broadcasting.
It has the advantage that the receiver is extremely simple (good for
commercial applications, since radio receivers can be made very
cheaply).
The power efficiency at the transmitter is very poor.
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Amplitude Modulation (AM) –Linear modulation. . . .

Let the carrier be c(t) and message signal be m(t)

c(t) = Ac cosωc t = Ac cos2πfc t
Mathematically, standard AM wave s(t) is described by
s(t) = Ac [1 + ka m(t)]cos2πfc t (1)
Where Ac is un-modulated carrier amplitude, ka is modulation
sensitivity, m(t) is the message signal (voice, music, data, etc), fc is
carrier frequency
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Amplitude Modulation (AM) –Linear modulation. . . .

The amplitude of the envelop a(t) = Ac [1 + ka m(t)]

ka m(t) ≤ 1 for all t

The envelope (amplitude) of the wave varies in accordance with m(t),
hence, m(t) can be recovered from the envelope a(t) of s(t).
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Amplitude Modulation (AM) –Linear modulation. . . .

where equation ka m(t) ≤ 1 is violated; i.e. —ka m(t) ≥ 1, when

m(t) < 0.
This causes the amplitude of s(t) to go negative during this interval,
which results in a phase reversal in the carrier waveform.
Note that this condition results in distortion of the envelope of s(t).

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Amplitude Modulation (AM) –Linear modulation. . . .

The envelop of the modulated wave has the same shape as the
baseband signal m(t) provided two requirements are satisfied:
ka m(t) ≤ 1 for all t. This assure that, avoiding phase reversal of c(t).
fc ≫ fm , where fm is the highest frequency component of m(t).
Otherwise, the envelope cannot be visualized and hence, cannot be
detected satisfactorily.
The maximum absolute value of the quantity ka m(t) is called
modulation index.
If it is multiplied by 100, the result is referred to as the percentage
modulation.
Modulation index is a factor that shows the degree of modulation.
If modulation index is greater than 1, the message signal is said to be
over-modulated and the process is called over-modulation.

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Time and Frequency domain representation of AM signal
A time domain signal may be translated to a new spectral range by
multiplying the signal with an auxiliary sinusoidal signal
Let s(t) & S(f) and m(t) & M(f) be Fourier transform pairs and also
m(t) be a band limited signal, what does the spectrum S(f) look like
for a specific message spectrum M(f)?
The multiplication of m(t) with an auxiliary sinusoidal signal c(t)
s(t) = Ac [1 + ka m(t)]cos2πfc t = Ac cos2πfc t + ka m(t)cos2πfc t
The frequency domain representation of the first term is a set of
Ac
δ-functions of amplitude at frequencies ±fc .
2
Using the frequency-shifting property of the Fourier transform for the
Ac
second term, become ka [M(f − fc ) + M(f + fc )]
2
This is an important result: multiplication of m(t) in the time domain
by shifts M(f ) upwards and downwards by fc Hz
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Time and Frequency domain representation of AM signal.
...

Combining these two terms together, we have:

Ac Ac
S(f ) = [δ(f − fc ) + δ(f + fc )] + ka [M(f − fc ) + M(f + fc )] (2)
2 2
This spectrum contains the message spectrum shifted upwards and
Ac
downwards by fc, weighted by the factor ka .
2
It also contains two delta-functions of weight at frequencies ±fc.
These δ-functions are the most predominant components present, yet
they carry no information.
Thus, we see that an AM modulation is wasteful in terms of the
power of the overall modulated signal to power in the message
componen

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Time and Frequency domain representation of AM signal.
...
The two sided spectral amplitude pattern of this signal

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Time and Frequency domain representation of AM signal.
...

the portion of the spectrum of an AM wave above fc for positive

frequency and below −fc for negative frequencies is referred to as
upper side band (USB)
and the portion of the spectrum of an AM wave below fc for positive
frequency and above −fc for negative frequencies is referred to as
lower side band (LSB).
For positive frequencies, the highest frequency component of the AM
wave is fc + w and the lowest frequency component is fc − w
The difference between these two frequencies define the transmission
bandwidth of the AM wave and it is exactly equal to twice the
highest frequency of the message signal i.e., BT = 2W

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Time and Frequency domain representation of AM signal.
...
Modulation Index and Percentage Modulation Index
The ratio of change of modulation index to the amplitude of the carrier
wave is modulation index
is also known as modulation factor, modulation coefficient, modulation
depth, degree of modulation
Am
µ= or µ = ka AM (3)
Ac
% modulation index
Am
%µ = × 100 or %µ = ka AM × 100 (4)
Ac
Total transmitted power
The AM wave has three components: Unmodulated carrier, lower and
upper sideband
The total power of AM wave is the sum of the carrier power(PC ) and
powers in the two sidebands(PUSB and PLSB )
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Time and Frequency domain representation of AM signal.
...

µ2
PT = PC + PUSB + PLSB = PC (1 + ) (5)
2
Exercise: Derive equation.5
For 100 modulation (µ = 1), we have
PT = 1.5PC , PC = 0.6667PT
An amplitude modulation wave, the 66.67% of the transmitter power is
used by the carrier signal and remaining 33.33% of the power is used
by the sidebands(PUSB &PLSB )
Transmission efficiency of an AM wave
The ratio of the power carried by sidebands to the transmitted power is
transmission efficiency η
PUSB + PLSB µ2
η= = 2 (6)
PT µ +2
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Exercise

1. Derive the following

i. Modulation index interms of PT and PC
ii. Current relation of AM wave
iii. Modulating index interms of IT and IC
iv. Voltage relation of AM wave
v. Modulating index interms of VT and VC
2. Let c(t) = Ac cos2πfc t and m(t) = Am cos2πfm t where fc ≫ fm
1 Derive s(t)
2 Identify the portion of lower sideband and upper side band
3 Find the modulation index
4 Find modulation index by assuming the message signal is displayed on
an oscilloscope i.e by considering the maximum (Vmax ) and the
minimum (Vmin ) amplitude of the modulated wave
5 Sketch two-sided frequency spectrum of modulated wave

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Generation of AM waves
Two basic ways to produce amplitude modulation
Multiply the carrier by a gain or attenuation factor that varies with the
modulating signal
Linearly mix or add the carrier and the modulating signals and then
apply the composite signal to a nonlinear device or circuit
2. Switching modulation – Diode Modulator

assume Ac ≫ m(t)∀t , and that the diode acts as an ideal switch.

Thus, the output voltage v2 (t) can be expressed as
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Generation of AM waves . . . .
assume Ac ≫ m(t)∀t , and that the diode acts as an ideal switch.
Thus, the output voltage v2 (t) can be expressed as
(
v1 (t) c(t) > 0
v2 (t) = (7)
0 c(t) ≤ 0

Since v1 (t) = m(t) + Ac cos2πfc t

v2 (t) = (m(t) + Ac cos2πfc t)gp (t) (8)

where gp (t) is a periodic waveform [even signal] with period To = 1/fc ,

expressed in a Fourier series as
∞
X
gp (t) = C0 + 2 Cn cos(2πf0 t) (9)
n=1

1 πn 1 sin(nπ/2)
For duty cycle = 1/2, Cn = sinc =
2 2 2 nπ/2
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Generation of AM waves . . . .

 1 (−1)k−1

n = 2k − 1 (k = 1, 2, 3, . . . .)
Cn = π 2k − 1 (10)
0 otherwise


1 2 P∞ (−1)n−1
∴ gp (t) = + cos[2πfc t(2n − 1)]
2 π n=1 2n − 1

1 2 2
∴ v2 (t) = [m(t) + Ac cos2πfc t][ + cos(2πfc t) − cos(6πfc t) + . . . .]
2 π 3π
m(t) 1 2m(t) 2Ac
= + Ac cos(2πfc t) + + cos 2 (2πfc t)+
2 2 π π
higher order terms
 
Ac 4
= 1+ m(t) cos(2πfc t) + unwanted terms (11)
2 πAc

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Generation of AM waves . . . .
The unwanted terms have out-of-band frequency components (DC
and ≥ 2fc ). These components can be eliminated by band-pass
filtering.
4
Comparing (11) with (1), the modulation index ka = and (11)
πAc
describes an AM waveform.
- Resistive mixing network: diode modulator

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Generation of AM waves . . . .

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Generation of AM waves . . . .

The diode current is clipped. The clipped half cycle will be generated
by the LC tuned circuit.
Each pulse of diode current, if it were the only one, would initiate a
damped oscillation in the tuned circuit.
The oscillation would have an initial amplitude proportional to the size
of the current pulse and a decay rate dependent on the time constant
of the circuit.
Since series of diode current pulses are applied to the tuned circuit,
each pulse will cause a complete sine wave proportional in amplitude to
the size of the pulse, generating signal waveform shown in fig. (e)
which is good approximation of AM wave.

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Generation of AM waves . . . .
2. Op amp as AM modulator
simpler amplitude modulator, consists of an operational amplifier (op
amp) and a field-effect transistor (FET) used as a variable resistor
The op amp is connected as a non-inverting amplifier for the carrier
signal.
Rf
The gain A of the circuit for the oscillator signal is A = 1 +
Ri
This modulator works on the first method of generating AM wave.

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Generation of AM waves . . . .

3. Class A amplifier as AM - Emitter modulator

A small signal class A amplifier is the

amplifier operates in class A, which is
extremely inefficient

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Generation of AM waves . . . .
4. Collector Modulator - Medium and High Power AM Modulator

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Generation of AM waves . . . .

When the modulation signal occurs, the ac voltage across the

secondary of the modulation transformer will be added to and
subtracted from the collector supply voltage.
This varying supply voltage is then applied to the class C amplifier.
Naturally, the amplitude of the current pulses through transistor Q, will
vary.
As a result, the amplitude of the carrier sine wave varies in accordance
with the modulated signal.

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Generation of AM waves . . . .
5. Linear IC AM Modulator
Linear IC AM modulators are basically low-level modulators
The location of modulator in a transmitter determines whether the
circuit is a low level or high-level transmitter.
In low-level modulation, the modulation takes place prior to the output
element of the final stage of the transmitter.
In high-level modulators, the modulation takes place in the final
element of the final stage.

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Example

An AM signal is represented by the equation

v (t) = [15 + 3cos(10π × 103 t]cos(π ∗ 106 t)volts

i. What are the values of the carrier and modulating frequencies?

ii. What are the amplitudes of the carrier and of the upper and lower side
frequencies?
iii. What is the modulation index?
iv. What is the bandwidth of this signal?

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Demodulation of AM wave

The function of AM detector or demodulator is to recover or

reproduce modulating signal or the original source
information/message signal from the modulated wave at the receiver
Envelope Detector (Peak detector or Diode Detector)
The simplest and most widely used amplitude demodulator is the
diode detector

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Demodulation of AM wave. . . .

During the positive half-cycle of the input signal, the diode is

conducting and the capacitor charges up to the peak value of the
input signal.
When the input falls below the voltage on the capacitor, the diode
becomes reverse-biased and the input becomes disconnected from the
output.
During this period, the capacitor discharges slowly through the load
resistor R.
On the next cycle of the carrier, the diode conducts again when the
input signal exceeds the voltage across the capacitor.
The capacitor charges up, to the peak value of the input signal and
the process is repeated again.

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Demodulation of AM wave. . . .

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Demodulation of AM wave. . . .
The time constant RC must be selected so as to follow the variations
in the envelope of the carrier-modulated signal.
1 1
In effect, ≤ R1 C1 ≤
fc w
In such a case, the capacitor discharges slowly through the resistor
and, thus, the output of the envelope detector closely follows the
message signal.

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques

Major draw back AM is that carrier power (contains no information)

constitutes two-third or more power of the total power
To overcome AM drawback, suppressing the carrier component from
the modulated wave resulting in DSB-SC modulation (by suppressing
the carrier one will get a DSB-SC wave), which is given by

SDSBS C (t) = mVc cos(2πfc t)cos(2πfm t)

mVc
= (cos(2π(fc + fm )t) + cos(2π(fc − fm )t)) (12)
2
DSB-SC undergoes phase reversal whenever the baseband signal m(t)
crosses zero

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

Unlike AM, the envelope of DSB-SC wave is different from the base
band signal.
DSB-SC has a higher efficiency than AM
Bandwidth of DSB-SC is the same as that of the conventional AM.
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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

DSB-SC modulator
The DSB-SC consists of simply the product of the baseband and the
carrier wave.

A device performing the multiplication is called product modulator.

This can be either balanced modulator or ring modulator.

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .
1. Balanced Modulator

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .
The carrier c(t) is considerably higher in amplitude and frequency than
the message signal m(t).
It turns on and off the diodes at high rate
Assuming the +ve reference for the carrier generator is the right
terminal, the signal at the primary of T3 is given by,
(
m(t), c(t) > 0
v (t) = (13)
0, c(t) ≤ 0

The output DSB-SC signal where gp (t) is a periodic waveform [even

signal] with period To = 1/fc , and amplitude of unity.
gp (t) can be expressed in a Fourier series as
∞
X
gp (t) = C0 + 2 Cn cos(2πf0 t) (14)
n=1

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .
For duty cycle = 1/2,

 1 (−1)k−1

n = 2k − 1 (k = 1, 2, 3, . . . .)
Cn = π 2k − 1 (15)
0 otherwise


1 2 P∞ (−1)n−1
∴ gp (t) = + cos[2πfc t(2n − 1)]
2 π n=1 2n − 1

1 2 2
∴ s(t) = m(t)[ + cos(2πfc t) − cos(6πfc t) + . . . .]
2 π 3π
m(t) 2m(t) 2
= + cos(2πfc t) − cos(6πfc t) + higher order terms
2 π 3π
2
= m(t)cos(2πfc t) + unwanted terms (16)
π

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

Therefore, rejecting the unwanted terms by using BPF that allows only
components centered around fc at the output of the modulator,
DSB-SC signal can be obtained.

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

2. Ring Modulator

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

c(t) controls the behavior of diodes which would be acting as ON-OFF

devices.
Consider the carrier cycle where the terminal 1 is positive and terminal
2 is negative.
T1 is an audio frequency transformer which is essentially an open
circuit at the frequencies of the carrier.
With the polarities assumed for c(t) , D1 , D4 are forward biased, where
as D2 , D3 are reverse biased.
As a consequence, the voltage at point a gets switched to a′ and
voltage at point b to b ′ .
During the other half cycle of c(t), D2 and D3 are forward biased
where as D1 and D4 are reverse biased. As a result, the voltage at a
gets transferred to b ′ and that at point b to a′ .

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

This implies, during, say the positive half cycle of c(t) , m(t) is
switched to the output whereas, during the negative half cycle,
−m(t) is switched.
v (t) can be taken as
(
m(t), c(t) > 0
v (t) =
−m(t), c(t) ≤ 0
= m(t)xp (t) (17)

Where xp (t) is a square wave

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

The Fourier series expansion

4 P∞ (−1)n−1
xp (t) = cos[2πfc t(2n − 1)]
π n=1 2n − 1

4 4
∴ s(t) = m(t)[ cos(2πfc t) − cos(6πfc t) + . . . .]
π 3π
4m(t)
= cos(2πfc t) + unwanted terms (18)
π
The signal at the output of the BPF is

4m(t)
SDSB−SC = cos(2πfc t) (19)
π

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

Demodulation of DSB-SC
Coherent detection is used in DSB-SC demodulation

In the absence of noise, and with the assumption of an ideal channel,

the received signal is equal to the modulated signal; i.e.,

r (t) = s(t) = Ac m(t)cos(2πfc t + φc ) (20)

Suppose we demodulate the received signal by first multiplying r (t) by

a locally generated sinusoid cos(2πfc t + φ), and then passing the
product signal through an ideal lowpass filter having a bandwidth W

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

The multiplication of r (t) with cos(2πfc t + φ) yields

r (t)cos(2πfc t + φ) = Ac m(t)cos(2πfc t + φ)cos(2πfc t + φ)

Ac m(t)
= ((cos(4πfc t + φc + φ) + cos(φc t + φ))
2
The lowpass filter rejects the double frequency components and passes
only the lowpass components.
Hence, its output is

y (t) = 1/2Ac m(t)cos(φc − φ) (21)

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Double sideband suppressed Carrier (DSB-SC) modulation
and demodulation techniques. . . .

The desired signal is scaled in amplitude by a factor that depends on

the phase difference between the phase φc of the carrier in the received
signal and the phase φ of the locally generated sinusoid.
When φc is not equal to φ,the amplitude of the desired signal is
reduced by the factor cos(φc − φ).
If φc − φ = 45 , the amplitude of the desired signal is reduced by 2 and
the signal power is reduced by a factor of two.
If φc − φ = 90◦ , the desired signal component vanishes.
the phase φ of the locally generated sinusoid should ideally be equal to
the phase φc of the received carrier signal.
Costas Loop
Reading Assignment

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques

SSB modulation
Conventional AM and DSB-SC are wasteful of bandwidth because they
both require transmission bandwidth equal to twice the message
bandwidth.
As the transmission of information is concerned, only one sideband is
necessary.
Thus it is possible to transmit only one of the side bands because the
lower side band and upper sideband carries the same information.
When only one sideband is transmitted, the modulation system is
referred to as single sideband system (SSB).

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .
SSB modulation provides the following advantages as compared to
conventional AM and DSB-SC.
It conserves frequency spectrum since only one of the side band is
transmitted.
It requires relatively low power as compared to conventional AM.
Noise decrease since the BW has decreased by half.
The benefit of using SSB is therefore derived from the reduced
bandwidth requirement and the elimination of the high power carrier
wave.
The principal disadvantage of the SSB system is its cost and complexity
Mathematically- SSB wave is given by

[
U(t) = Ac m(t)cos2πfc t ∓ Ac m(t)sin2πfc (t) (22)

[ is the Hilbert transform of m(t).

where m(t)
The plus-or-minus sign determines which sideband we obtain.
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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

SSB modulators
The are two methods of generating SSB
1 Frequency Discrimination Method (Filter Method)
2 Phase Discrimination Method
1 Frequency Discrimination Method (Filter Method)
An SSB modulator based on frequency discrimination consists basically
a ring modulator and a filter, which is designed to pass the desired
sideband of the DSB-SC wave.
In designing the bandpass filter in the SSB generator system, the filter
must have a pass band at the same frequency range as the spectrum of
the desired sideband.
This type of frequency discrimination can be satisfied only by using
highly selective filter, which can be realized using crystal and ceramic
filters.

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

2. Phase Discriminator Method

This method involves two separate simultaneous modulation processes
and subsequent combination of the resulting modulation products.
The derivation of this system follows directly from
1 1
SSSB (t) = Ac m(t)cos(2πfc t) + Ac m(t)sin(2πfc t) (23)
2 2
This defines the canonical representation of SSB waves for USB
transmission.

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

Demodulation of SSB : Coherent Detection

To demodulate an SSB wave and extract the baseband signal m(t), we
have to shift the spectrum of the sideband by ±fc so as to convert the
transmitted sideband back to the baseband signal.
This can be accomplished by using coherent detection, which involves
applying the SSB wave, together with a locally generated sinusoidal
wave Ac cos(2πfc t) to a product modulator and then low pass filtering
the modulator output will produce m(t).

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

Thus, for the USSB signal, we have

r (t)cos2πfc t = u(t)cos(2πfc t + ϕ)
= 1/2Ac m(t)cosϕ + 1/2Ac m̃(t)sinϕ+
double frequency terms

By passing the product signal through an ideal lowpass filter, the

double frequency components are eliminated, leaving us with

yl(t) = 1/2Ac m(t)cosϕ + 1/2Ac m̃(t)sinϕ (24)

Note that the effect of the phase offset is not only to reduce the
amplitude of the desired signal m(t) by cosϕ, but it also results in an
undesirable sideband signal due to the presence of m̃(t) in yl (t).

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

The transmission of a pilot tone at the carrier frequency is a very

effective method for providing a phase-coherent reference signal for
performing synchronous demodulation at the receiver.
The spectral efficiency of SSB AM makes this modulation method very
attractive for use in voice communications over telephone channels
(wire lines and cables).
The filter method for selecting one of the two signal sidebands for
transmission is particularly difficult to implement when the message
signal m(t) has a large power concentrated in the vicinity of f = 0.
The sideband filter must have an extremely sharp cutoff in the vicinity
of the carrier in order to reject the second sideband, very difficult to
implement in practice.

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

VSB modulation
When the information signal contains significant components at
extremely low frequencies as in TV signals, the SSB modulation is
inappropriate in transmitting such baseband signals due to the difficulty
of isolating one side band.
This difficulty suggests another scheme known as VSB modulation,
which is a compromise between SSB and DSB-SC modulation.
VSB is a form of amplitude modulation in which the carrier and one
complete sideband are transmitted, but only part of the second
sideband is transmitted.
Probably the most widely known VSB system is the picture portion of
a commercial TV-broadcasting signal.
The bandwidth required by a VSB system is smaller than the DSB-SC
system but higher than the SSB system.

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

VSB modulation can be generated by passing a DSB-SC wave through

an appropriate filter with transfer function H(f )

Ac
SVSB (f ) = [M(f + fm ) + M(f − fm )] (25)
2
, where M(f ) is Fourier transform of m(t)

To generate a VSB AM signal we begin by generating a DSB-SC AM

signal and passing it through a sideband filter with frequency response
H(f )

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .
In the time domain the VSB signal may be expressed as

u(t) = [Ac m(t)cos2πfc t] ∗ h(t) (26)

where h(t) is the impulse response of the VSB filter.

In the frequency domain, the corresponding expression is

U(f ) = Ac[M(f − fc) + M(f + fc)]H(f ) (27)

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .
VSB modulation
We multiply u(t) by the carrier component cos2πfc t and pass the
result through an ideal lowpass filter.

v (t) = u(t)cos2πfc t (28)

1
V (f ) = [U(f + fc ) + U(f − fc )] (29)
2
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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

If we substitute U(f ), we obtain

V (f ) = Ac/4[M(f −2fc)+M(f )]H(f −fc)+Ac/4[M(f )+M(f +2fc)]H(f +f

(30)
The lowpass filter rejects the double-frequency terms and passes only
the components in the frequency range |f | ≤ fm

Vl (f ) = Ac/4M(f )[H(f − fc ) + H(f + fc )] (31)

We require that the message signal at the output of the lowpass filter
be undistorted.
Hence, the VSB filter characteristic must satisfy the condition
H(f − fc ) + H(f + fc ) =constant, |f | ≤ fm
This condition is satisfied by a filter that has the frequency-response
characteristic shown.

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Single Side Band (SSB) and Vestigial Side Band (VSB)
modulation and demodulation techniques. . . .

H(f ) selects the upper sideband and a vestige of the lower side band.
It has odd symmetry about the carrier frequency fc , in the frequency
range fc − fa < f < fc + fa , where fa is a conveniently selected
frequency that is some small fraction of fm ; i.e., fa ≪ fm
To avoid distortion of the message signal, the VSB filter should be
designed to have linear phase over its passband fc − fa ≤ |f | ≤ fc + fm .
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AM Transmitters

The transmitter is a part of communication system that accepts the

message signal to be transmitted and converts it into an RF signal
capable of being transmitted over long distances.
Every transmitter has three basic functions.
First, the transmitter must generate a signal of the correct frequency at
a desired point in the spectrum.
Second, it must provide some form of modulation that causes the
information signal to modify the carrier signal.
Third, it must provide sufficient power amplification to ensure that the
signal level is high enough so that it will carry over the desired distance.

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AM Transmitters. . . .

To design an AM transmitter one should know about the main blocks

of the transmitter.
RF oscillators, Buffer amplifiers, Driver amplifiers, power amplifiers,
filters and impedance matching.

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AM Transmitters. . . .

An oscillator generates the final carrier frequency.

In most applications, this will be a crystal oscillator due to high
frequency stability of the crystal.
The carrier signal is then fed to a buffer amplifier whose primary
purpose is to isolate the oscillator from the remaining power amplifier
stages.
The signal from the buffer is applied to the driver amplifier.
This is class C amplifier.
It is designed to provide an intermediate level of power amplification.
The purpose of this circuit is to generate sufficient output power to
drive the final power amplifier stage.
The final power amplifier, normally referred to as the final, also
operates class C at very high power.
The actual amount of power depends upon the application.

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AM Receivers

A conventional AM receiver simply converts an amplitude-modulated

wave back to the original source information.
The RF section detects, select and amplify the received RF signal.
The mixer/converter section down-converts the RF frequency in to IF
frequency.
The primary function of the IF section is for amplification and
selectivity.
The AM detector demodulates the AM wave and the audio section
simply amplifies the recovered information.

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