Analog & Digital Communications

By
KASULA RAGHU
Assistant Professor
Dept. of E.C.E.
MGIT

11/03/2025 KASULA RAGHU 1

Course Objectives Subject Code: EC402PC

• To develop ability to analyse system requirements of analog and

digital communication systems.

• To understand the generation, detection of various analog and digital

modulation techniques.

• To acquire theoretical knowledge of each block in AM, FM

transmitters and receivers.

• To understand the concepts of baseband transmissions.

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Course Outcomes
Upon completing this course, the student will be able to
• Analyse and design of various continuous wave and angle modulation and demodulation
techniques

• Understand the effect of noise present in continuous wave and angle modulation
techniques.

• Attain the knowledge about AM , FM Transmitters and Receivers

• Analyse and design the various Pulse Modulation Techniques.

• Understand the concepts of Digital Modulation Techniques and Baseband transmission.

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What we will Learn?
Analog Communications

UNIT – I Amplitude Modulation

UNIT – II Angle Modulation
UNIT – III Transmitters
UNIT – IV Pulse Modulation (PAM,PWM,PPM)

Digital Communications

UNIT – IV Pulse Code Modulation

UNIT – V Digital Modulation Techniques
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 UNIT - I
• Amplitude Modulation

Need for modulation, Amplitude Modulation - Time and frequency

domain description, single tone modulation, power relations in AM waves,
Generation of AM waves - Switching modulator, Detection of AM Waves -
Envelope detector, DSBSC modulation - time and frequency domain
description, Generation of DSBSC Waves - Balanced Modulators,
Coherent detection of DSB-SC Modulated waves, COSTAS Loop, SSB
modulation - time and frequency domain description, frequency
discrimination and Phase discrimination methods for generating SSB,
Demodulation of SSB Waves, principle of Vestigial side band modulation.

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 Fourier Transforms & Inverse Fourier Transform Formula

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 Representation
• F.T. of
x(t) = X(f) General Notation
m(t) = M(f) Used for Message Signal(KHz)
c(t) = C(f) Used for Carrier Signal(MHz)
s(t) = S(f) Used for Modulated Signal(MHz)

I.F.T. of
X(f) = x(t)
G(f) = g(t)
M(f) = m(t)
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 F.T. of Cos & Sin A A
___
____
2 2

A cos (2 f t) = A
__ [ ( f  f )   ( f  f )]
m m m
2 - fm 0 fm
A
____ A
____
2 2

A cos (2 f t) = A [ ( f  f )   ( f  f )]
__
c c c
2 - fc 0
fc

A [ ( f  f )  ( f  fc )]
A sin (2 f t) = A
____
c __
c 2j
2j - fc

0
fc
A
____
2j
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 A
____ A
____
2 2

A [M ( f  f ) 
m ( t ) A cos (2 f t) = __ M( f  fc )]
c c
2 - fc 0 fc

A
___
m( t ) A sin (2 f t) = __
A [M ( f  f )  M( f  f c )] 2j
c c
2j - fc

0 f
c
A
____
2j

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KASULA RAGHU 9
 In Time Domain

Message Signal (or)

Base Band Signal (or)
Modulating Signal (or)
Information Signal

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 In Frequency Domain

Band width = ( W - 0) Hz = W Hz

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 Introduction
Elements of Communication System:
Communication: It is the process of conveying or transferring
information from one point to another.
(Or)
It is the process of establishing connection or link between two
points for information exchange.

11/03/2025 KASULA RAGHU 12

 Elements of Communication System
Information source :
The message or information to be communicated originates in
information source. Message can be words, group of words,
code, data, symbols, signals etc.
Transmitter :
The objective of the transmitter block is to collect the
incoming message signal and modify it in a suitable fashion
(if needed), such that, it can be transmitted via the chosen
channel to the receiving point.
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 Elements of Communication System:
Channel :
Channel is the physical medium which connects the
transmitter with that of the receiver. The physical medium
includes copper wire, coaxial cable, fibre optic cable, wave
guide and free space or atmosphere.
Receiver :
The receiver block receives the incoming modified version
of the message signal from the channel and processes it to
recreate the original (non- electrical) form of the message
signal.
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 Signal, Message, Information
Signal:
It is a physical quantity which varies with respect to time or space or
independent or dependent variable.
(Or)
It is electrical waveform which carries information.
Ex: m(t) = Acos(ωt+ϕ)
Where, A= Amplitude or peak amplitude(Volts)
w = Frequency ( rad/sec)
ϕ = Phase (rad)
11/03/2025 KASULA RAGHU 15
 Types of Signals
• Analog or Continuous Signal
• Digital Signal
Analog or Continuous Signal: If the amplitude of signal
continuously varies with respect to time or if the signal contains
infinite number of amplitudes, it is called Analog or continuous
signal.

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 Types of Signals
Digital Signal: If the signal contains only two discrete
amplitudes , then it is called digital signal.

With respect to communication , signals are classified into,

• Baseband signal
• Bandpass signal
Baseband signal:
If the signal contains zero frequency or near to zero frequency, it is
called baseband signal.
Ex: Voice, Audio, Video, Bio-medical signals etc.
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 Types of Signals
Bandpass signal: If the signal contains band of frequencies far away
from base or zero, it is called bandpass signal.
Ex: AM, FM signals.

Message: It is sequence of symbols. Ex: Happy New Year 2021.

Information: The content in the message is called information. It is

inversely proportional to probability of occurrence of the symbol.

Information is measured in bits, decits, nats.

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 Limitations of Communication System
• Technological Problems:
To implement communication systems, Tx, Rx, channel are required
which requires hardware. Communication system is expensive and
complex.
• Bandwidth & Noise:
The effect of noise can be reduced by providing more bandwidth to
stations but due to this less number of stations can only be
accommodated.
• Signal to Noise Ratio (SNR): Noise should be low to increase channel
capacity but it is an unavoidable aspect of communication system.
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 Types of Modulation

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 Modulation : Any Low Frequency/Message Signal
m(t) is Multiplied by a High Frequency/Carrier Signal
c(t) then the signal get shifted to Right side and Left
side to the Frequency of Carrier signal ( i. e M Hz).

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 Different Modulations

c(t) = Ac cos(2π fct+ϕ)

S.NO Modulation What Changed Constant Constant

1 AM Amplitude Frequency Phase

2 FM Frequency Amplitude Phase

3 PM Phase Amplitude Frequency

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*****w. r. t Amplitude
KASULA RAGHU
of Message Signal 22
 Modulation
 The process by which some characteristic of a carrier wave
is varied in accordance with an information-bearing signal.
 Continuous-wave modulation
 Amplitude modulation
 Frequency modulation
 AM modulation family
 Amplitude modulation (AM)
 Double sideband-suppressed carrier (DSB-SC)
 Single sideband (SSB)
 Vestigial sideband (VSB)
11/03/2025 KASULA RAGHU 23
 Modulation
It is the process of varying the characteristics of high frequency
carrier in accordance with instantaneous values of modulating or
message or baseband signal.
(Or)
It is a frequency translation technique which converts
baseband/low frequency signal to band pass/high frequency
signal.

Modulation is used at the transmitter. (Filter Used ?)

Demodulation is used at the Receiver. (Filter Used ?)
11/03/2025 KASULA RAGHU 24
 Types of Modulation
• Amplitude Modulation: Amplitude of the carrier is varied in
accordance with the instantaneous values of modulating signal.

• Frequency Modulation: Frequency of the carrier is varied in

accordance with the instantaneous values of modulating signal.

• Phase Modulation: Phase of the carrier is varied in accordance

with the instantaneous values of modulating signal.

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 Need for Modulation
• To Reduce the height of an antenna
• For Multiplexing
• For Wideband Signal to Narrow banding
• To reduce noise effects
• To avoid equipment limitation or to reduce the size of the
equipment.

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 Amplitude Modulation
The amplitude of the carrier signal varies in accordance with the
instantaneous amplitude of the modulating signal.

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 Carrier & Message Signals
The carrier signal is given by,

c(t) = Ac Cos2πfct

Where, Ac = Maximum amplitude of the carrier signal.

fc = Frequency of the carrier signal.

Modulating or baseband signal is given by,

m(t) = Am Cos2πf mt

Where,
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Am = Amplitude ofKASULA
theRAGHU
baseband signal. 28
 c(t) = Ac Cos2πfct Carrier Wave

S(t) = [AC + m(t)] Cos2πfct

= Ac [1+ Ka m(t)] Cos2πfct Time Domain Equation of AM

Ka = Amplitude Sensitivity of the Modulator

when m(t) = Zero
then s(t)= c(t) which is called as Unmodulated Carrier

Before Modulation , Magnitude is : Ac

After Modulation , Magnitude is : Ac [1+ Ka m(t)]

11/03/2025 KASULA RAGHU 29

 Amplitude Modulation

 The envelope of s(t) has essentially the same shape as the message signal m(t)
provided that two conditions are satisfied :
 The amplitude of kam(t) is always less than unity

μ = m = kam(t)  1, for all t

μ = m = Ka[Maximum Voltage of Message signal ] = Ka[m(t)]max
 The carrier frequency fc is much greater than the highest frequency component W of the
message signal

fc  W
 Envelope detector
11/03/2025  A device whose output traces KASULA
the envelope
RAGHU of the AM wave acting as the input signal30
 S(t) = Ac [1+ Ka m(t)] Cos2πfct
S(t) = Ac Cos2πfct + Ac Ka m(t) Cos2πfct
Note: In A.M. Carrier is also Transmitting along with the Modulated signal which is
used at the Receiver for Demodulation

 The Fourier transform or spectrum of the AM wave s(t)

Ac
S( f )  [ ( f  f )   ( f  f )]  ka Ac [M ( f  fc )  M ( f + fc )]
c c
2 2

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 S (f)

Ac/2 Ac/2

KaAcM (0)/2

-fc-W -fc -fc+W 0 fc-W fc fc +W f

Fig : Spectrum of AM signal

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11/03/2025 KASULA RAGHU BW of AM = ?
33
 For positive frequencies, the highest frequency
component of the AM wave equals fc+W, and the lowest
frequency component equals fc-W. The difference
between these two frequencies defines the transmission
bandwidth BT of the AM wave, which is exactly twice
the message bandwidth W

BT  2W

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AM Wave Contains

Carrier Component at fc

LSB from fc-W to fc

USB from fc to fc+W

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11/03/2025 KASULA RAGHU 37
 Modulation Index
Modulation index or depth of modulation is given by,
V_________________
max - Vmin
μ = Vmax + Vmin = Am/Ac

Percentage of modulation index is,

Vmax - Vmin
_________________
% μ = Vmax + Vmin X100 = [Am/Ac ]X100

Types of AM with respect to modulation index:

• Under Modulation (μ <1)
• Critical Modulation (μ =1)
• 11/03/2025
Over Modulation (μ >1) KASULA RAGHU 38
 Types of AM

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 Single Tone Modulation of A.M.

S(t) = Ac [1+ Ka m(t)] Cos2πfct

= Ac [1+ Ka Am Cos2πfm t] Cos2πfct
S(t) = Ac [1+ μ Cos2πfm t] Cos2πfct Standard Form of A.M.
μ = AmKa = A m/Ac = Modulation Index

11/03/2025 KASULA RAGHU 40

s(t) = Ac Cos2πfct + Ac μ Cos2πfct Cos2πfm t
S(t) = AcCos2πfct + μAc/2Cos[2π(fc+fm)]t + μAc/2Cos[2π (fc-fm)]t
I term II term III term
I term: Carrier signal with amplitude Ac and frequency fc.
II.term: Amplitude= μAc/2, frequency= fc+fm , Upper sideband frequency
III.term: Amplitude= μAc/2, frequency= fc-fm , Lower sideband frequency

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Expanding the equation (2), we get

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 f c -fm f c +fm

Frequency Domain characteristics of single tone AM

S.No Message FT BW of Message BW of AM Signal

1 m(t) M(f) W 2W

2 Cos2πf mt 0.5 [ ( f  f m )   ( f  f m )] fm 2fm

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11/03/2025 KASULA RAGHU 44
 Power Calculation of AM Wave
AM Wave Contains

Total Power = Carrier Power + USB Power + LSB Power

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• Power relations in AM waves:
Consider the expression for single tone/sinusoidal AM wave

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11/03/2025 KASULA RAGHU 47
•μ =0 Pt = Pc

• μ = 0.5 Pt = 1.125Pc

•μ =1 Pt = 1.5 Pc

Note : When μ is increased from 0 to 1 Power Increased by 50%

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 Relationship Between Carrier Power & Side Band Power

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 Power Efficiency or Modulation Efficiency
It is the ratio of Utilized Power to the total power in the modulated wave.

μ =1 η = 33.33%

μ = 0.75 η = 22.22%

μ = 0.5 η = 11.11 %

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 Exercise for Multi Tone Modulation

BW= 2fm2 if (fm2 > fm1)

BW= 2fm1 if (fm1 > fm2)

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 Multi Tone Modulation
• S(t) = Ac [1+ Ka m(t)] Cos2πfct

Where m(t) = Am1 Cos2πfm1 t + Am2 Cos2πfm2 t (for multi-tone) (fm2> fm1 )

= Ac [1+ Ka Am1 Cos2πfm1 t + Ka Am2 Cos2πfm2 t ] Cos2πfct

• S(t) = Ac Cos2πfct + Ac μ1 Cos2πfct Cos2πfm1 t + Ac μ2 Cos2πfct Cos2πfm2 t ]

where μ = Ka Am ; μ1 = Ka Am1 ; μ2 = Ka Am2

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11/03/2025 KASULA RAGHU 53
11/03/2025 KASULA RAGHU 54
11/03/2025 KASULA RAGHU 55
Generation of AM waves
• Square Law Modulator
• Switching Modulator

Detection of AM Wave
• Envelop Detector

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 Generation of AM Wave
Square Law modulator:
• Contains 1) non-linear device ,2) Band pass filter, 3) Carrier source and modulating signal

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11/03/2025 KASULA RAGHU 58
11/03/2025 KASULA RAGHU 59
Switching Modulator

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The total input for the diode at any instant is given by

When the peak amplitude of c(t) is maintained more than that of

information signal, the operation is assumed to be dependent on only c(t)
irrespective of m(t).

When c(t) is positive, v2=v1 since the diode is forward biased.

Similarly,
when c(t) is negative, v2=0 since diode is reverse biased.

Based upon above operation, switching response of the diode is periodic

rectangular wave with an amplitude
11/03/2025
unity and is given by
KASULA RAGHU 61
11/03/2025 KASULA RAGHU 62
The required AM signal is centered at fc can be separated using band pass
filter.

The lower cut off-frequency for the band pass filter should be between w
and fc-w and the upper cut-off frequency between fc+w and 2fc.

The filter output is given by the equation

11/03/2025 KASULA RAGHU 63
11/03/2025 KASULA RAGHU 64
 Envelope Detector
• Note: In AM the Peak Amplitude of the carrier which is also called as the
Envelop is varied according to the message signal. So, the envelop of the AM
Signal represents the message. E.D is used to track the peak amplitude of the
signal
AM Wave m (t)

i/p
E.D o/p

A c o s (2 f c t) A
10 sin (2 f c t) 10
-t
e cos (2 f c t) e-t
2 2
A c o s (2 f c t) + B sin (2 f c t) √ (A + B )

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Envelope Detector

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• The charge time constant (rf + Rs) C must be short compared with the
carrier period

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Sketch the Output of the Below Signals when Passed through
Envelop Detector

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11/03/2025 KASULA RAGHU 69
• Advantages
1) Generation and demodulation of AM wave are
easy
2) One Tx & Many Rx

• Disadvantages
1) More Power taken by Carrier is 66.66%
2) BW = 2W Hz of 2fm

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11/03/2025 KASULA RAGHU 71
11/03/2025 KASULA RAGHU 72
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11/03/2025 KASULA RAGHU 74
11/03/2025 KASULA RAGHU 75
11/03/2025 KASULA RAGHU 76
 Double Side Band- SC Modulation

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 DSB-SC MODULATION

The Advantage of Suppressing the Carrier is Power Saved (66.66%)

Note : We are not Transmitting the Carrier along with Modulated Signal
as in AM.

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11/03/2025 KASULA RAGHU 79
• What about Bandwidth & Power of DSB-SC Wave?

Carrier Power is Saved.

BW Remains Same

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 Single Tone Modulation of DSB-SC

S(t) = Ac [1+ Ka m(t)] Cos2πfct

= Ac Cos2πfct + Ac Ka Am Cos2πfct Cos2πfm t

= Ac Ka Am Cos2πfct Cos2πfm t = c(t) m(t)

S(t) = Ac μ Cos2πfct Cos2πfm t

μ = AmKa = A m/Ac = Modulation Index

11/03/2025 KASULA RAGHU 81

s(t) = Ac μ Cos2πfct Cos2πfm t
S(t) = Acμ/2Cos[2π(fc+fm)]t + Acμ/2Cos[2π (fc-fm)]t
I term II term
= Acμ/4 [ ( f  (fc+fm ))   ( f  (fc+fm ))] + Acμ/4 [ ( f  ( fc-fm ))   ( f  ( fc-fm ))]

I term: Amplitude= μAc/2, frequency= fc+fm , Upper sideband frequency

II term: Amplitude= μAc/2, frequency= fc-fm , Lower sideband frequency

11/03/2025 KASULA RAGHU 82

 Spectrum of Single tone Modulation
S(f)

Ac Am/4 Ac Am/4 Ac Am/4 Ac Am/4

-fc-fm -fc -fc+fm 0 fc-fm fc fc+fm

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11/03/2025 KASULA RAGHU 84
Total Power Required for DSB-SC Wave
• S(t) = Ac μ Cos2πfct Cos2πfm t
= Acμ/2Cos[2π(fc+fm)]t + Acμ/2Cos[2π (fc-fm)]t

Total Power = Power in LSB + Power in USB

2 2
= (Acμ/2√2) + (Acμ/2√2)
= A2cμ2/4
= Pcμ2 /2

Power Efficiency of Modulation Efficiency = 100%

11/03/2025 KASULA RAGHU 85
Generation of DSBSC Waves
Balanced Modulator (Product Modulator)
Ring Modulator

Detection of DSB-SC waves

Coherent Detection or Synchronous Detection or Heterodyne Detection
Costas Receiver

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 Balanced Modulator (Product Modulator)

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Ring Modulation

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11/03/2025 KASULA RAGHU 89
 Thus the ring modulator in its ideal form is a product modulator for
square wave carrier and the base band signal m(t). The square wave carrier can be
expanded using Fourier series as

11/03/2025 KASULA RAGHU 90

 [M ( f  fc )  M ( f  fc )] [M ( f  3fc )  M ( f  3fc )]

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 S (f)

-fc-W -fc+W 0 fc-W fc +W f

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 Coherent or Synchronous or Heterodyne
Detection

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11/03/2025 KASULA RAGHU 94
 From the spectrum, it is clear that the unwanted component (first term
in the expression) can be removed by the low-pass filter, provided that
the cut-off frequency of the filter is greater than W but less than 2fc-
W. The filter output is given by

 The quadrature null effect

 The zero demodulated signal, when occurs for Φ=±π/2
 The phase error Φ in the local oscillator causes the detector output to be attenuated
by a factor equal to cos Φ

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11/03/2025 KASULA RAGHU 96
Costas Receiver

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• Advantages
One to One Communications (Walkie Talkie)

• Disadvantages
Less Power than AM
100% Modulation efficiency
BW = AM = DSC-SC = 2W Hz

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 Single Side Band- SC Modulation

11/03/2025 KASULA RAGHU 99

11/03/2025 KASULA RAGHU 100
 Single-Sideband Modulation
 Single-Sideband Modulation
 Suppress one of the two sideband in the DSB-SC modulated wave
 Theory
 A DSB-SC modulator using the sinusoidal modulating wave
m(t)  Am cos(2f mt)
 The resulting DSB-SC modulated wave is
S DSB (t)  c(t)m(t )
 A A cos(2f t) cos(2f t)
c m c m

1 1
 Ac Am cos[2 ( f c  f m )t]  A cA m cos[2 ( f c  f m)t]
2 2
 Suppressing the second term in the above Eq. the upper and lower SSB modulated wave are
1
A A cos[2 ( f c  f m )t] (3.14)
SUSSB (t) 
2 c m
1 1
SUSSB (t)  Ac Am cos(2f ct) cos(2f mt)  Ac A m sin(2f ct) sin(2f mt)
2 2
1 1
S LSSB (t)  Ac Am cos(2f ct) cos(2f mt)  A cA m sin(2f ct) sin(2f mt)
2 2
11/03/2025 KASULA RAGHU 101
 A sinusoidal SSB modulated wave

S SSB (t)  1 Ac A m cos(2f ct) cos(2f mt) + 1 Ac A m sin(2f ct) sin(2f mt)
2 2
Ac Ac 
S SSB (t)  m(t) cos(2f ct) +_ m(t) sin(2f ct) Equation of SSB-SC
2 2

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Total Power & Power or Modulation efficiency
Total Power = Power in LSB or
= Power in USB
= (Acμ/2√2)
= Acμ /8
= Pcμ /4

Power Efficiency of Modulation Efficiency = 100%

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Generation of SSB-SC Wave
Frequency Description Method
Phase Description Method

Detection of SSB-SC waves

Coherent Detection

11/03/2025 KASULA RAGHU 104

Frequency Description Method

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• Upto 500Khz Mechanical Filter
• Upto 20 MHz RC Filter
• Greater Than 20 MHz Crystal filter

11/03/2025 KASULA RAGHU 106

Phase Description Method

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Coherent Detection

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3/11/2025 KASULA RAGHU 109
 ˄

Output of Product Modulator is S(t) x (LO)o

˄

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Time Domain Equation of SSB -SC

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11/03/2025 KASULA RAGHU 112
11/03/2025 KASULA RAGHU 113
11/03/2025 KASULA RAGHU 114
11/03/2025 KASULA RAGHU 115
11/03/2025 KASULA RAGHU 116
• Following the same procedure, we can find the canonical representation for an
SS wave
• s(t) obtained by transmitting only the lower side band is given by

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• Advantages
Voice Communications

• Disadvantages
Sharp Cut-off Frequency Filters are not Available
Practically
Less Power than AM & DSB-SC
100% Modulation efficiency
BW = WHz or fm Hz
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 Vestigial Side Band Modulation

BW= W + fv
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Generation of VSB Modulated Wave

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 Distorted Output

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 Perfect Output (Loss is Compensated with the Gain)

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Envelope detection of a VSB Wave plus Carrier

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Comparisons of AM,DSBSC,SSB-SC,VSB

S.NO Parameters AM DSB-SC SSB VSB

1 General Equation
2 Singletone Equation
3 General BW
4 Singletone BW
5 Total Power

*****Complete the Following

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S.NO Parameters AM DSB-SC SSB VSB
6 Generation Methods
7 Detection Methods
8 Power or Modulation efficiency
9 Applications

*****Complete the Following

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 Thank You
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