ADC Unit 1.pdf

Dr Krishna Samalla
Analog and Digital Communications

• Prerequisites:
 Signals and Systems
 Probability theory and Stochastic Processes
• Textbooks:
– Analog and Digital Communications by Simon Haykin, John Wiley, 2005.
– Electronics Communication Systems-Fundamentals through Advanced by
Wayne Tomasi, 5th Edition, 2009, PHI.
• Reference Books:
– Principles of Communication Systems by Herbert Taub, Donald L Schilling,
GoutamSaha, 3rd Edition, McGraw-Hill, 2008.
– Electronic Communications by Dennis Roddy and John Coolean , 4th Edition ,
PEA, 2004.
– Electronics & Communication System by George Kennedy and Bernard Davis,
TMH 2004.
– Analog and Digital Communication by K. Sam Shanmugam, Willey, 2005.

Electronic Communication?
• Communication is the transfer of information
from one place to another.
• Sending information from one point to another
point, using electricity/magnetism – Electronic
communication.
• Radio, TV, Mobile, Browsing Web, CD, DVD are
some of the applications of electronic
communication.

Signal
• In electronics and telecommunications, a signal
refers to any time varying voltage, current, or
electromagnetic wave that carries information.
• The basic attributes of a signal are: Amplitude,
Frequency and Phase.

Analog vs Digital signals
Analog signal: If the amplitude of a signal continuously varies with respect to time or if
the signal contains infinite number of amplitude levels, it is called an analog signal.
Digital signal: If the signal contains only a finite number of (countable) amplitude
levels, then it is called a digital signal.

Information source:
• The information to be communicated originates in information source.
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.
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/atmosphere.
Receiver:
• The receiver block receives the incoming modified version of the message signal from
the channel and processes it to recreate the original form of the message signal.

Block Diagram of a Communication System
• In general, a communication system can be represented by the functional block
diagram as shown in Figure.

Contents
• Need for Modulation
• Amplitude Modulation - Time and Frequency domain description
• Single tone AM
• 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 DSBSC 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 VSB modulation.

MODULATION
• Modulation is defined as the process of changing some characteristics
of the carrier signal in accordance with the message signal.
• Basically, the modulation process converts a low-frequency signal into
a high-frequency signal or a base-band signal into a band-pass signal.
• Modulation techniques can be broadly classified in to several types as
shown in figure below.

• Following are the three types of signals that we see in the modulation process.
Modulating Signal
The signal which contains information to be transmitted, is called as a message
signal. It is a base-band signal, which has to undergo the process of modulation,
to get transmitted. Hence, it is also called as the modulating signal.
Carrier Signal
The high-frequency signal, which has a certain amplitude, frequency and phase
but contains no information is called as a carrier signal. It is an empty signal and
is used to carry the signal to the receiver.
Modulated Signal
The resultant signal after the process of modulation is called as a modulated
signal. This signal is a combination of modulating signal and carrier signal. In fact,
it is the carrier signal carrying the modulating signal, hence it is also known as
modulated carrier signal.

Continuous-wave Pulse
Modulation
VSB
SSB-SC
DSB-SC
Amplitude
WBFM
NBFM
PM
FM
Pulse-digital
Pulse-analog
DM
PCM
PWM/PDM
PAM
Angle
ADM
DPCM
PPM
PTM
Analog
Digital
(based on carrier signal)
QPSK
PSK
FSK
ASK (based on
modulating signal)
AM

• In the continuous-wave modulation, a parameter of a high-frequency
sinusoidal carrier signal is varied instantaneously with the message
signal.
• In pulse-analog, a parameter (amplitude, width or position) of a
periodic pulse carrier is varied in accordance with the message signal.
• Pulse-digital modulation techniques are more like analog to digital
conversion mechanisms.

Need for Modulation
• It is often advantageous and convenient, in processing a signal in a
communication system, to translate the signal from one region in the frequency
domain to another region.
Need 1: Practicability of antennas.
– When free space/atmosphere is the communication channel, antennas
radiate and receive the signal.
– The antennas operate effectively only when their dimensions are of the order
of magnitude of the wavelength of the signal being transmitted.
– A signal of frequency 1KHz (an audio tone) corresponds to a wavelength of
3,00,000m, an entirely impractical length.
– The required length may be reduced to the point of practicability with
modulation.

• Need 2: Frequency Multiplexing
– Transmission of several different signals, all of which encompass the same
spectral range, through a single communication channel (called multiplexing) is
possible with modulation.
– If no overlapping of newly transformed frequency ranges is ensured, then the
signals may be separated at the receiving end by appropriate band-pass filters.
• Need 3: Narrowbanding
– The process of modulation may be used to change a wide-band gap signal into a
narrow-band gap signal.

• Need 4: Common Processing
– It may be required to process a number of signals similar in general character
but occupying different spectral ranges.
– Then instead of every time adjusting the frequency range of processing
apparatus to correspond to the frequency range of the signal to be
processed, the processing apparatus can be made operate in some fixed
frequency range with modulation.

Amplitude Modulation
• Amplitude modulation, called as AM in short, is the oldest and the
most popular technology. It is also popular as conventional AM.
• It is widely used in Radio, TV.
• Definition: The process by which the amplitude of a high-frequency
carrier signal is varied in accordance with the instantaneous amplitude
of the modulating signal.
• The high-frequency (RF) carrier, c(t), is a sinusoidal signal and is
represented by
c(t) = Vc sin (2πfct)
• The message signal m(t) can be in any form that contains information.
• The AM modulated signal, s(t), will have an amplitude that is
proportional to m(t).

• Note that the frequency and phase of the carrier are unchanged by
the AM process.
• Hence, the amplitude Vc of the unmodulated carrier will be varied in
proportion to the instantaneous amplitude of the modulating signal.

AM – Time and Frequency domains
• The time-domain representation of AM wave is given by
s(t) = Vc[1 + kam(t)] sin (2πfct)
where, ka = Amplitude Sensitivity of the modulator
• The envelope of the AM wave is given by Vc[1+kam(t)].
• When a carrier is amplitude-modulated, the instantaneous
modulating voltage variations are superimposed onto the
carrier amplitude.
• Thus when there is temporarily no modulation, the amplitude
of the modulated carrier is equal to its unmodulated value.

• The frequency-domain representation of AM wave is derived by taking Fourier
Transform of the AM modulated signal s(t), i.e.
S(f) = Vc/2 [δ(f-fc) + δ(f+fc)] + Vcka /2[M(f-fc) + M(f+fc)]
• The two impulses at ± fc represent the carrier. The two terms M(f – fc) & M(f+fc)
are two versions of the spectrum of the message signal located around ± fc.
• The band of frequencies of M(f+fc), i.e. above ‘fc’ is called the Upper Side Band
(USB).
• Similarly, the band of frequencies of M(f-fc), i.e. below ‘fc’ is called Lower Side
Band (LSB).
• Hence, the frequencies present in AM wave are the carrier frequency and the
first pair of sideband frequencies.
• If m(t) is a signal with bandwidth W, then the bandwidth of the modulated signal
s(t) will be 2W.

Frequency-Shifting Property
Statement: x(t)  X(f)
x(t)*e j2πf0t
 X(f-f0)
Proof: X(f) = x(t) e -2π ft dt
F{x(t) * e j2πf0t
}= x(t) e j2πf0t
e -2π ft dt
= x(t) e j2π(f-f0)t
dt
= X (f-f0)

Find Fourier Transform of cos 2πfot
• Solution :
cos 2πfot = (ej2πfot +e-j2πfot )/2 --(1)
Rewrite eq.1 as: 1* ej2πfot/2+1* e-j2πfot/2 --(2)
F[1] = δ(f) --- (3)
From eq.3
F[1* ej2πf
o
t/2] = δ(f-fo)/2
F[1* e-j2πf
o
t/2] = δ(f+fo)/2
Hence, F[cos 2πfot]= {δ(f-fo)+ δ(f+fo)}/2

Find Fourier Transform of m(t) cos2πfot
• Solution :
cos 2πfot = (ej2πfot +e-j2πfot )/2 --(1)
m(t) cos2πfot = m(t) ej2πfot/2+m(t) e-j2πfot/2 --(2)
F[m(t) cos 2πfot] = F[m(t) ej2πfot/2]+F[m(t) e-j2πfot/2] –(3)
By frequency-shifting property
F[m(t) ej2πfot/2] = M(f-fo)/2 (4)
F[m(t) e-j2πfot/2] = M(f+fo)/2 (5)
Substituting eq.s 4 and 5 in eq. 3, we get
F[m(t)cos 2πfot] = {M(f-fo)+ M(f+fo)}/2

• It is to be noted that the envelope of the AM wave s(t) has same shape
as the baseband signal m(t) provided two requirements are satisfied:
– the amplitude of kam(t) is always less than unity, i.e. │kam(t)| < 1 for
all t.
– the carrier frequency fc is much greater than the highest frequency
component W of the message signal m(t), i.e. fc >> W.
• If │kam(t)│ > 1 for any value of t, the carrier wave becomes over
modulated and shape of the envelope is not same as message signal.
• If the condition fc >> W is not satisfied, the spectral overlapping occurs
and the envelope gets distorted.

• Hence, the instantaneous voltage of the AM wave is
v = A sin θ = A sin ωct = Vc (1 + m sinωmt) sin ωct
• By applying trigonometry,
----- (2)
• m < 1 ---- Under Modulation
• m = 1 ---- Critical Modulation
• m > 1 ---- Over Modulation (leads to Envelope distortion) and hence
never be used.
• Modulation Index, m must be in the range 0 ≤ m ≤ 1 and usually it is
expressed in %.

• The spectrum of the resulting signal can be obtained by taking Fourier transform of
eq. (2). Thus,
• It has three discrete frequencies: carrier frequency fc,
upper side band fc + fm and lower side band fc – fm.
• The carrier frequency has the highest amplitude and
the other two are having amplitudes which are equal
to each other, but can never exceed half the carrier
amplitude.

• There is standard method of evaluating the modulation index when calculating
from a waveform such as may be seen on an oscilloscope. From the fig.,
--------- (1)
and
--------- (2)
Dividing eq. (1) by (2), we have

Power relations in AM wave
• For single-tone modulation, the AM wave is given by
----- (1)
• The carrier component of the modulated wave has the same amplitude as the
unmodulated carrier.
• Since the modulated wave contains extra two sideband components, the
modulated carrier contains more power than the carrier had before modulation
took place.
• Hence, the total power in the modulated wave will be
----- (2)
where R is the resistance (e.g., antenna resistance), in which the power is
dissipated.

• The first term of eq. 1 is the unmodulated carrier power and is given by
----- (3)
• Similarly,
----- (4)
• Substituting eq.s (3) and (4) in eq. (1), we have

* Transmission Efficiency (η T)

Current calculations in AM wave
• In AM, the modulated and unmodulated currents are easily measurable, and it is
then necessary to calculate the modulation index from them.
• Let Ic be the unmodulated current and It be the total, or unmodulated current of
an AM transmitter, both being rms values.
• If R is the resistance in which these currents flow, then

Problem 1
A modulating signal m(t) = 10 cos(2π × 103t) is amplitude modulated with a carrier signal c(t) = 50 cos(2π ×
105t). Find the modulation index, the carrier power, and the power required for transmitting AM wave.
Solution:
By comparing the given modulating signal with the standard equation of modulating signal, we will get
Am = 10 volts
fm = 103Hz = 1KHz
Similarly,
Ac = 50volts
fc = 105Hz = 100KHz
Substituting, Am and Ac values in m

Problem 2
The equation of amplitude wave is given by s(t) = 20 [1 + 0.8 cos(2π × 103t)] cos(4π × 105t). Find the
carrier power, the total sideband power, and the band width of AM wave.
Solution
Re-write the above equation as
s(t) = 20 [1 + 0.8 cos(2π × 103t)] cos(2π × 2 × 105t)
We know the equation of Amplitude modulated wave is
s(t) = Ac [1 + μ cos(2πfmt)]cos(2πfct)
By comparing the above two equations, we will get
Ac = 20volts
μ = 0.8
fm = 103Hz = 1KHz
fc = 2 × 105Hz = 200KHz
Assuming, R = 1 Ω

Modulation by several sine waves
• In practice, modulation of a carrier by several sine waves simultaneously is the rule
rather than the exception.
• Hence, to calculate the resulting total power, first the total modulation index has to
be calculated. And, then substitute it into power equation.
• There are two methods of calculating the total modulation index.
1) Let V1, V2, V3, etc., be the simultaneous modulation voltages. Then the total
modulating voltage Vt will be
Dividing both sides by Vc, we get

that is,
2) Power equation may be rewritten as
Pt = Pc + PSBT
PSBT
= PSB1
+ PSB2
+ PSB3
+ …
Now, the substitution of into above eq. gives
mt
2 = m1
2 + m2
2 + m3
2 + …
If the square root of both sides is taken, it will again becomes

Generation of AM waves - Switching modulator
• A typical switching modulator can be realised with the help of the arrangement
shown in fig. (a).
• The carrier wave applied to the diode has been assumed to be of large amplitude
so as to swing right across the characteristics curve of the diode.
• The diode has been assumed to be ideal in the sense that it offers zero resistance
in the forward direction and infinite resistance in the reverse direction. Hence, the
transfer characteristics of the diode load resistor combination can be shown as in
fig. (b).
• The input voltage v1(t) can be written as
v1(t) = c(t) + m(t)
= Ac cos(ωct) + m(t)
where |m(t)| << Ac
• The resulting load voltage v2(t) is

v2(t) = v1(t), c(t) > 0
= 0, c(t) < 0
• This means that, the load voltage v2(t) varies periodically between the values v1(t)
and zero at a rate equal to the carrier frequency, fc. Thus, v2(t) can be
mathematically expressed as,
v2(t) = [Ac cos(ωct) + m(t)] gp(t) ……(1)
• Where gp(t) is a periodic pulse train of duty cycle to one-half, and period T0 = 1/fc as
shown in below fig.

• The function gp(t)can be expressed in Fourier series as,
……(2)
• Therefore, substituting eq. (2) in eq. (1), we get the load voltage v2(t) as follows,
…… (3)
• The first term in eq. (3) is the desired AM wave with amplitude sensitivity ka = 4/πAc.
• The unwanted terms are removed from the load voltage v2(t) by using band-pass
filter.

Demodulation
• The process of extracting an original message signal
from the modulated wave is known as detection or
demodulation.
• The circuit, which demodulates the modulated wave
is known as the demodulator.

Detection of AM Waves - Envelope detector
• It is simple, yet highly effective device which can demodulate AM wave.
• An envelope detector produces an output signal that follows the envelope of the
input signal waveform, hence the name.
• A typical version of the circuit shown in Fig. is used in almost all commercial radio
receivers.
• The detector consists of a diode and a resistor-capacitor filter.
Operation:
• Consider the case of an AM wave in where fc is much larger than the message
bandwidth and the % modulation is less than 100%.
• On the positive half-cycle of the input signal, the diode is forward-biased and the
capacitor C charges up rapidly to the peak of the input signal.
• When the input falls below this value, the diode becomes reverse biased and the
C discharges through the load resistor RL.

• The discharge process continues until the next positive half-cycle.
• When the input signal becomes greater than the voltage across the capacitor, the
diode conducts again and the process is repeated.
• We have assumed the diode is ideal and the voltage source suppyling AM wave has
a series resistance, Rs.
• The charging time constant RsC must be short compared with Tc so that the C
charges rapidly and thereby follows the applied voltage when the diode is
conducting.

• On the other hand, the discharging time constant RLC must be too large to ensure
that the C discharges slowly through the RL between positive peaks of the carrier
wave, but not so long that the capacitor voltage will not discharge at the maximum
rate of change of the modulating wave.
• The result is that the capacitor voltage which is the detector output is very nearly
same as the envelope of the AM wave.
• In the detected output some ripples may be present which may be finally removed
by using a low-pass filter.
Conditions:
 Rs C << Tc = 1/ fc
 (1/ fc ) << RL C << 1/W
where W is the message bandwidth

Envelope Detector waveforms: (a) RC too large (b) RC too small

Double Side Band Suppressed Carrier (DSBSC) Modulation
• In AM, the modulated wave consists of the carrier wave and two sidebands.
• However, the carrier signal, fc carries no information and the information is carried by
only the sidebands.
• Moreover, the carrier signal consumes a lot of power i.e., 66.7% (two-thirds of total
power) and sideband utilizes only 33.3%.
• Hence, such a transmission is inefficient.
• If this carrier is suppressed, then such a process is
called as Double Sideband Suppressed Carrier
system or simply DSBSC.
• It is plotted as shown in the following figure.

DSBSC: Time and Frequency Domains
• Let us consider the modulating and carrier signals as
m(t) = Am cos(2πfmt) and
c(t) = Ac cos(2πfct)
• Mathematically, the equation of DSBSC wave can be represented as the product of
modulating and carrier signals.
s(t) = m(t).c(t)
⇒ s(t) = AmAc cos(2πfmt) cos(2πfct)
• The bandwidth of the DSBSC modulation is 2fm.
• Thus, the bandwidth of DSBSC wave is same as that of AM wave and it is equal to
twice the frequency of the modulating signal.

DSBSC waveforms for single-tone modulating signal

S(t) = c(t) m(t)
S(t) = Ac cos(2πfct) m(t)
Spectrum of DSBSC signal

Problem 1: If the highest frequency component of
message is 5 KHz. Bandwidth of DSBSC is ------
Solution:
B.W = 2w = 2 * 5K = 10KHz
Problem 2: If the message signal m(t) = 5 cos 2000πt + 5
cos 3000 πt. Bandwidth of DSBSC is ------
Sol: Given w1=1000Hz, w2=1500Hz
B.W = 2(Max input Freq.) = 2(w2) = 2*1500 = 3KHz

Power calculations of DSBSC
• Consider the following eq. of DSBSC modulated wave
• Power of DSBSC wave is equal to the sum of powers of upper sideband and lower
sideband frequency components.
Pt = PUSB + PLSB

Generation of DSBSC: Balanced Modulator
• Balanced modulator consists of two identical AM modulators.
• These two modulators are arranged in a balanced configuration in order to suppress
the carrier signal. Hence, it is called as Balanced modulator.
• The same carrier signal c(t) = Ac cos(2πfct) is applied as one of the inputs to these two
AM modulators.
• The modulating signal m(t) is applied as another input to the upper AM modulator.
Whereas, the modulating signal m(t) with opposite polarity, i.e., −m(t) is applied as
another input to the lower AM modulator.
• Output of the upper AM modulator is
• Output of the lower AM modulator is

• We get the DSBSC wave by subtracting s2(t) from s1(t). The summer block is used to
perform this operation. s1(t) with positive sign and s2(t) with negative sign are applied
as inputs to summer block. Thus, the summer block produces an output s(t),
• By comparing the output of summer block with the standard eq. of DSBSC wave, we
will get the scaling factor as 2ka.

Coherent detection of DSBSC wave
• The same carrier signal (which is used for generating DSBSC signal) is used to detect
the message signal. Hence, this process of detection is called as coherent or
synchronous detection.
• The block diagram of the coherent detector is shown in the fig.
• In this process, the message signal can be extracted from DSBSC wave by multiplying it
with a carrier, having the same frequency and the phase of the carrier used in DSBSC
modulation.
• The resulting signal is then passed through a Low Pass Filter. Output of this filter is the
desired message signal.
• Let the DSBSC wave be
• The output of the local oscillator is
where, ϕ is the phase difference between the local oscillator signal and the carrier signal, which is used
for DSBSC modulation.

• From the figure, we can write the output of product modulator as
• Substituting s(t) and c(t) in the above equation,
• In the above equation, the first term is the scaled version of the message signal. It is extracted by
passing the above signal through a low pass filter.
• Therefore, the output of low pass filter is

• The demodulated signal amplitude will be maximum, when ϕ = 00. This indicates that the local oscillator
signal and the carrier signal should be in phase, i.e., there should not be any phase difference between
these two signals.
• Let’s consider the following two situations:
• The local oscillator
• The demodulated signal amplitude will be zero, when ϕ=±900. This effect is called as quadrature null
effect.

Costas Loop
• Costas loop is used to make both the carrier signal (used for DSBSC modulation) and
the locally generated signal in phase.
• Following is the block diagram of Costas loop.
• Costas loop consists of two product modulators with common input s(t), which is
DSBSC wave. The other input for both product modulators is taken from Voltage
Controlled Oscillator (VCO) with −900 phase shift to one of the product modulator as
shown in figure.
• We know that the equation of DSBSC wave is
• Let the output of VCO be
• This output of VCO is applied as the carrier input of the upper product modulator.
Hence, the output of the upper product modulator is

• Substituting s(t) and c1(t) values in the above equation
• After simplifying we will get v1(t) as
• This signal is applied as an input of the upper low pass filter. The output of this low
pass filter is
• Therefore, the output of this low pass filter is the scaled version of the modulating
signal. The output of −900 phase shifter is
• This signal is applied as the carrier input of the lower product modulator. The output
of the lower product modulator is

• Substituting s(t) and c2(t) values in the above equation
• After simplifying we will get v2(t) as
• This signal is applied as an input of the lower low pass filter. The output of this low pass filter
is
• The output of this Low pass filter has −900 phase difference with the output of the upper low
pass filter.
• The outputs of these two low pass filters are applied as inputs of the phase discriminator.
• Based on the phase difference between these two signals, the phase discriminator produces
a DC control signal.
• This signal is applied as an input of VCO to correct the phase error in VCO output. Therefore,
the carrier signal (used for DSBSC modulation) and the locally generated signal (VCO output)
are in phase.

Single Side Band Suppressed Carrier (SSBSC) Modulation
• The DSBSC modulated signal has two sidebands. Since, the two sidebands carry the
same information, there is no need to transmit both sidebands. One sideband can be
eliminated.
• The process of suppressing one of the sidebands along with the carrier and
transmitting a single sideband is called as Single Sideband Suppressed Carrier system
or simply SSBSC. It is plotted as shown in the following figure.
• In the figure, the carrier and the lower sideband
are suppressed. Hence, the upper sideband is
used for transmission.
• Similarly, the carrier and the upper sideband can
be suppressed while transmitting the lower
sideband.

• This SSBSC system, which transmits a single sideband has high power, as the
power allotted for both the carrier and the other sideband is utilized in
transmitting this Single Sideband.
Advantages
• Bandwidth or spectrum space occupied is lesser than AM and DSBSC waves.
• Transmission of more number of signals is allowed.
• Power is saved or High power signal can be transmitted.
• Less amount of noise is present.
• Signal fading is less likely to occur.
Disadvantages
• The generation and detection of SSBSC wave is a complex process.
• The quality of the signal gets affected unless the SSB transmitter and receiver
have an excellent frequency stability.

Applications
• For power saving requirements and low bandwidth requirements.
• In land, air, and maritime mobile communications.
• In point-to-point communications.
• In radio communications.
• In television, telemetry, and radar communications.
• In military communications, such as amateur radio, etc.

SSB: Time and Frequency Domains
• Let us consider the modulating and carrier signals as
m(t) = Am cos(2πfmt) and
c(t) = Ac cos(2πfct)
• Mathematically, the equation of SSBSC wave can be represented as
• Since the SSBSC modulated wave contains only one sideband, its bandwidth is half of
the bandwidth of DSBSC modulated wave, i.e., fm.
• Therefore, the bandwidth of SSBSC modulated wave is equal to the frequency of the
modulating signal.

Power calculations of DSBSC
• Consider the following eq. of SSBSC modulated wave
• Power of SSBSC wave is equal to the power of any one sideband frequency
components.
• The power of the upper sideband is

Generation of SSBSC: Frequency discrimination method
• The following figure shows the block diagram of SSBSC modulator using
frequency discrimination method.
• In this method, first the DSBSC wave is generated with the help of the product
modulator.
• Then, this DSBSC wave is applied as an input of band pass filter.
• The band pass filter produces an output, which is SSBSC wave.
• Select the frequency range of band pass filter as the spectrum of the desired
SSBSC wave.
• This means the band pass filter can be tuned to either upper sideband or lower
sideband frequencies to get the respective SSBSC wave having upper sideband
or lower sideband.

Generation of SSBSC: Phase discrimination method
• The following figure shows the block diagram of SSBSC modulator using phase
discrimination method.
• This block diagram consists of two product modulators, two −900 phase shifters,
one local oscillator and one summer block.
• The product modulator produces an output, which is the product of two inputs.
The −900 phase shifter produces an output, which has a phase lag of −900 with
respect to the input.
• The local oscillator is used to generate the carrier signal. Summer block
produces an output, which is either the sum of two inputs or the difference of
two inputs based on the polarity of inputs.
• The modulating signal Am cos(2πfmt) and the carrier signal Ac cos(2πfct) are
directly applied as inputs to the upper product modulator. So, the upper
product modulator produces an output, which is the product of these two
inputs.

• The output of upper product modulator is
• The modulating signal Am cos(2πfmt) and the carrier signal Ac cos(2πfct) are phase
shifted by −900 before applying as inputs to the lower product modulator. So, the lower
product modulator produces an output, which is the product of these two inputs.
• The output of lower product modulator is

• Add s1(t) and s2(t) in order to get the SSBSC modulated wave s(t) having a lower
sideband.
• Subtract s1(t) and s2(t) in order to get the SSBSC modulated wave s(t) having a upper
sideband.
• Hence, by properly choosing the polarities of inputs at summer block, the SSBSC
wave having a upper sideband or a lower sideband can be produced.

Coherent detection of SSBSC wave
• The process of extracting an original message signal from SSBSC wave is known
as detection or demodulation of SSBSC.
• Coherent detector is used for demodulating SSBSC wave.
• Here, the same carrier signal (which is used for generating SSBSC wave) is used
to detect the message signal. Hence, this process of detection is called as
coherent or synchronous detection.
• Following is the block diagram of coherent detector.
• In this process, the message signal can be extracted from SSBSC wave by
multiplying it with a carrier, having the same frequency and the phase of the
carrier used in SSBSC modulation.
• The resulting signal is then passed through a Low Pass Filter. Output of this filter
is the desired message signal.

• Consider the following SSBSC wave having a lower sideband.
• From the figure, we can write the output of product modulator as
• Substitute s(t) and c(t) values in the above equation.

• In the above equation, the first term is the scaled version of the message signal. It
can be extracted by passing the above signal through a low pass filter.
• Therefore, the output of low pass filter is
• Here, the scaling factor is .
• We can use the same block diagram for demodulating SSBSC wave having an upper
sideband. Consider the following SSBSC wave having an upper sideband.

• We can write the output of the product modulator as
• Substitute s(t) and c(t) values in the above equation
• By passing the signal through a LPF and the output would be
• Here too the scaling factor is .

Vestigial Side Band Suppressed Carrier (VSBSC) Modulation
• SSBSC modulated signal has only one sideband frequency. Theoretically, we can get one
sideband frequency component completely by using an ideal band pass filter.
• However, practically we may not get the entire sideband frequency component. Due to
this, some information gets lost.
• To avoid this loss, a technique is chosen, which is a compromise between DSBSC and
SSBSC. This technique is known as Vestigial Side Band Suppressed Carrier (VSBSC)
technique. The word “vestige” means “a part” from which, the name is derived.
• VSBSC Modulation is the process, where a part of the signal called as vestige is
modulated along with one sideband.
• The frequency spectrum of VSBSC wave is shown in the following figure.
• Along with the upper sideband, a part of the lower sideband is also being transmitted in
this technique. Similarly, we can transmit the lower sideband along with a part of the
upper sideband.
• A guard band of very small width is laid on either side of VSB in order to avoid the
interferences.

Bandwidth of VSBSC Modulation
• Since the VSBSC modulated wave contains the frequency components of one side
band along with the vestige of other sideband, the bandwidth of it will be the sum
of the bandwidth of SSBSC modulated wave and vestige frequency fv.
i.e., Bandwidth of VSBSC Modulated Wave = fm + fv
Advantages
• Highly efficient.
• Reduction in bandwidth when compared to AM and DSBSC waves.
• Filter design is easy, since high accuracy is not needed.
• Possesses good phase characteristics.
Disadvantages
• Bandwidth is more when compared to SSBSC wave.
• Demodulation is complex.

Applications
• Widely used in television transmissions.
Generation of VSBSC
• Generation of VSBSC wave is similar to the generation of SSBSC wave.
• The VSBSC modulator is shown in the following figure.
• In this method, first we will generate DSBSC wave with the help of the product
modulator. Then, apply this DSBSC wave as an input of sideband shaping filter. This
filter produces an output, which is VSBSC wave.
• The modulating signal m(t) and the carrier signal Ac cos(2πfct)are applied as inputs to
the product modulator.
• Therefore, the output of the product modulator is

VSBSC Modulator
VSBSC Demodulator

• Apply Fourier transform on both sides
• Let the transfer function of the sideband shaping filter be H(f). This filter has the
input p(t) and the output is VSBSC modulated wave s(t). The Fourier transforms of
p(t) and s(t) are P(f) and S(f)respectively.
• Mathematically, we can write S(f) as
S(f) = P(f). H(f)
• Substituting P(f) value in the above equation

Demodulation of VSBSC
• Demodulation of VSBSC wave is similar to the demodulation of SSBSC wave.
• Here, the same carrier signal (which is used for generating VSBSC wave) is used to
detect the message signal. Hence, this process of detection is called as coherent or
synchronous detection.
• The VSBSC demodulator is shown in the following figure.
• In this process, the message signal can be extracted from VSBSC wave by multiplying
it with a carrier, which is having the same frequency and the phase of the carrier
used in VSBSC modulation.
• The resulting signal is then passed through a Low Pass Filter. The output of this filter
is the desired message signal.
• Let the VSBSC wave be s(t) and the carrier signal is Ac cos(2πfct).
• The output of the product modulator is

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