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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
CHAPTER-4 : AMPLITUDE MODULATION (AM)
,
PERSONAL REMARK :

The purpose of communication system is to transmit informationbearing signals through a communication channel seprating the
transmitter from the receiver. Information bearing signals are also
referred to as baseband signals.
,
In amplitude modulation the amplitude of the high frequency carrier
wave is varied in accordance to the instantaneous amplitude of the
modulating or base band signal keeping angle constant.

Consider a message signal m(t) = A m cos 2f mt = A m
cos mt. Where Am is the amplitude of massage signal and fm
is the frequency of the message signal/modulating signal/base
band signal, and

Consider a carrier signal c(t) = Ac cos 2fc t = Ac cos ct
where Ac is the amplitude of carrier signal and fc is the
frequency of the carrier signal (where fc >> fm)
fm
Note:
fc
,
50 Hz to 15 KH z
550 KHz to 1650 KHz (for AM)
88 MHz to 108 MHz (for FM)
Figure shows the AM signal produced by single tone (i.e. when
modulating signal or message signal contain only one frequency
component)
Carrier
wave
Modulating
Signal
Amplitude
Modulated signal
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
,
The Block Diagram of the Amplitude Modulator
Figure given below shows the block diagram of amplitude
modulator.Conventional AM consists of a large carrier component
in addition to AM modulated signal.
modulating signal
Carrier Wave
Amplitude
Modulator
Am(max)
Envelop |AC+m(t)|
Am(min)
AM modulated signal
Experimentally
modulation index can be
expressed as
<1

A m ( max )  A m ( min )
A m ( max )  A m ( min )
PERSONAL REMARK :

Ex. A given AM broadcast station
transmits an average carrier
power output of 40 kW and
uses a modulation index of
0.707 for sine wave
modulation. What is the
maximum (peak) amplitude of
the output if the antenna is
represented by a 50 W
resistive load?
[IES-EE-2005]
(a) 50 kV
(b) 50 V
(c) 3.414 kV (d) 28.28 kV
Sol.(c)Amlitude of carrier
Figure : Actual view of Amplitude modulated signal
Ac  Pc  2R L  2 kV
The standard equation for sinusoidal amplitude modulated wave may
Amplitude of message signal
be expressed as , s(t) = m(t) cos c t + Ac cos c t
A m  A c  1.414 kV
s(t) = Ac [1 +
m(t)
] cos c t or s(t) = E (t) cos c t
AC
Where, s(t) = Ac [1 +
So, total amplitude is
Ac + Am = 3.414 kV
m(t)
], called the envelop of AM wave.
AC
NOTE-1: Complex envelop of s(t) is given by s(t) = s(t) + j sh(t)
where sh(t) is the hilbert transform of s(t). This is the desired condition
for conventional DSB AM that makes it easy to demodulate.
NOTE-2: When the modulation index of AM wave is less than
unity the output of the envelop detector is the envelop of AM
wave.However ,When the modulation index of AM wave is greater
than unity the output of the envelop detector is not the envelop but
,
mode (i.e. magnitude) of envelop of AM wave.
As long as |m(t)|  1 the amplitude Ac [1 + m(t)] is positive. This is
the desired condition for conventional DSB AM that makes it easy
,
to demodulate.
On the other hand if m(t) < –1 for some t, the AM signal is said to be
,
overmodulated and its detection is rendered more complex.
Since this envelop consist of baseband signal m(t). Hence the
modulating signal may be recovered from an AM wave
[i.e. modulated signal s(t)] by detecting the envelop.
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
Ex.1The complex envelope of the bandpass signal(GAE-EC-2015 : SET-3)
PERSONAL REMARK :

1

 sin( t / 5) 

x(t)   2 
sin  t   , centered about f  Hz is

 t / 5 

2
4

(a)

 sin( t / 5)  j 4

e
t / 5 
 sin( t / 5)   j 4
(b) 
e
 t / 5 

(c)
 sin( t / 5)  j 4
2
e
 t / 5 

(d)
 sin( t / 5)  j 4
2
e
 t / 5 
Sol.(c)Given that bandpass signal (i.e. modulated signal)

 sin(t / 5) 
x(t)   2 
sin t   ,
 t / 5  
4
can be written as


 sin(t / 5) 
or x(t)   2 
 sin t cos  cos t sin 

4
4
 t / 5 
1
1 
 sin(t / 5)  
sin t 
 cos t 
or x(t)   2 



2
2
 t / 5  
 sin(t / 5) 
(cos t  sin t)
or x(t)  
 t / 5 
So, x(t) = XC(t) cos2  fCt  XC(t) sin2  fCt
(Low pass represetation of band-pass signal)
 sin(t / 5) 
Where, XC(t) = XS(t) = 
 t / 5 
We know that complex envelop of signal x(t) is given by , S(t) = x(t) +
jxh(t) , where xh(t) is the hilbert transform of x(t)
 sin(t / 5) 
S(t) = 
(1 + j) or S(t) =
 t / 5 
π
 sin(t / 5)  j 4
2
e
 t / 5 
Ex.2 The amplitude modulated waveform
s(t) =Ac [1 + Kam(t)] cos wct is fed to an ideal envelope detector. The
maximum magnitude of Kam(t) is greater than 1. Which of the following
could be the detector output?
[GATE-EC-2000]
(a) Acm(t)
(b) Ac2[1 + Kam(t)]2
(c) Ac[1 + Kam(t)]
(d) Ac[1 + Kam(t)]2
Sol.(c)The envelop detector detect only the signal content in the envelop.The
envelop is defined as the magnitude of pre- envelop Pre  envelop of
s(t) i.e. M = s(t) + j sh(t) = Ac[1 + Kam(t)] cos  ct
+j Ac[1 + Kam(t)]sin  c t
= Ac [1 + Kam(t)]ejwct
|M| = Ac[1 + Ka m(t)] is the envelop of signal S(t)]
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
Ex.2
PERSONAL REMARK :
Let m( t )  e t and carrier signal c ( t )  A C cos  c t
C(t)
cos 2  fc t
e
–t
=
t
t
Modulating signal
For an AM wave, the
maximum voltage was found
to be 10 V and the minimum
voltage was found to be 5 V.
The modulation index of the
wave would be
(IES-EC-2001)
(a) 0.33
(b) 0.52
(c) 0.40
(d) 0.1
Sol.(a)Modulation index is given by
Ex.
Then modulated signal, s ( t )  m ( t )  c ( t )  e  t A c cos c t
m(t)

Carrier signal

-t
E max  E min 10  5 5 1

 
E max  E min 10  5 15 3
NOTE : Message signal m(t)
e cos ct
with nonzero offset : On rare
occusion ,the message signal m(t) will
have a nonzero offset such that its
t
maximum Amax. and its minimum
Amin.are not symmetric i.e.
envelop
Amax.= Amin. in this case , envelop
Modulated signal with high frequency
detection will would remain
,
The time domain equation of AM wave is given by relation
s ( t )  A c  1   cos m t  cos c t
| m(t) |
....(A)
A
distortionless if
/

E max  E min
2A  E max  E min
max
m
Where,  = Modulation index = carrier amplitude  A
c
A m = Modulating signal amplitude
,
A c = Carrier signal amplitude
The amplitude variation in AM about an unmodulated carrier amplitude
is measured in terms of a factor called modulation index or depth
,
of modulation or degree of modulation.
When the message contains single frequency, then the modulation is
called single tone modulation. Equation (A) represents single tone
modulation.
Equation (A) may also written as

s(t)  A c cos  c t 
A c .cos (  c  m ) t   A cos (    )t


 2



c
c

m
2


Carrier
Lower side band
....(B)

upper side band
From equation (B), we conclude
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
(i)
(ii)
Beside the carrier there are two sidebands at
c  m and c  m
The amplitude of sideband become half of amplitude of
modulating signal i.e.
Am 

A 
since
Ac  m 
2 
2
2 
PERSONAL REMARK :

 sin(t / 5) 
S(t) = 
(1 + j)
 t / 5 
π
or S(t) =
 sin(t / 5)  j 4
2
e
 t / 5 
S(
)
Ac
2
Am
LSB
2
USB
–C – m – c –C + m C – m
2 m
(iii)
C C + m
2 m
The bandwidth requirement is 2 m .
From equation (A), frequency domain analysis can be written as
Ac
A µ
[ ( – c ]   (  c )]  c
2
2
[M ( – c) + M ( + c)]
s(t) 
....(C)
Bandwidth of the A.M signal = 2 m = 2 × message bandwidth
Bandwidth of USB = m and Bandwidth of LSB = m
AC
2
S()
AC
2
Ac .
4
Ac .
4
–C – m – C –C + m C – m C C + m 
2 m
2 m
Spectrum of modulated signal S(  )
POWER CALCULATION OF AM WAVE
,
As we know that power is given by relation , P  I2 R or


Power in carrier wave, Pc   A c 


2
2 
2
R
 A . µ/2 

Power in sideband, PLSB = PUSB =  c
2 

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Ac
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
So, total power ( PT )  Pc  PL S B  PU S B or PT 
PT
or
 μ2
1 

2

Pc



Transmitted power
Carrier power




 µ2 
1 






µ2

and
µ2

Power in sideband
Modulation efficiency,  
Total power
2
or  
2
Ac
8R
Ac
8R
2


1   

2 

or  
1.

Show that the efficiency of
single tone AM is 33.3 % for
the modulation index to be
equal to unity.
[IES-EE-2001:10 Marks]
The antenna current of an AM
transmitter is 7.5 A, when only
the carrier is sent, but it
increases to 8.65 A, when the
carrier is sinusoidally
modulated.
Find
the
percentage modulation.
Determine the antenna current
when the depth of modulation
is0.75
(IES-EE-2010)
(a) 8.49 A
(b) 4.49 A
(c) 18.49 A
(d) 6.32 A
Sol.(a)Given antenna current,
It = 8.65 A and carrier
current, Ic = 7.5 A
modulation index ,  = 0.75
we know that ,
2.
In terms of current, ITrms = ICrms 1 
2
PERSONAL REMARK :
2


 PC  A c when, R  1 


2


In terms of voltage, VTrms  VCrms 1 
,
A c2
2R
2
2  2
....(A)
max  33 % when 100% modulation is taking into account.
Note: The calculation of modulation efficiency as derived is applicable
for sinsoidal signals only.
 2 
I 2t  IC2 1  a  or
2

2

Generally,  
m 2 (t)

A c2  m 2 (t)
2
Where, m (t) = power of message signal

If the modulating signal is square wave then
2
PT = PC +
 8.65 2 
or  = 
 1 =81.2%
 7.5 

For the second part we have,
2
A m
A
A2m
= 1 + m = 1+
= PC ( 1 + µ2)
A2C
PC 2
2
P
2
C
It  Ic 1 
2
or PT since for square wave rms value is equal to its peak value

I 
2  t  1
 Ic 
 7.5 1 
2
2
(0.75) 2
 8.489 A
2
If the modulating signal is triangular wave then
 µ2 
 since for triangular wave rms value is equal
PT = PC 1 




to
Vm
3
where Vm is the peak value
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
,
When the message contains more than one frequency, it is
called multi-tone modulation.

2 2
2
PT  Pc 1  1  2  3  ........
2
2
2

Where, 1 
A m1
Ac
, 2 
A m2
Ac
, 3 
A m3
Ac



PERSONAL REMARK :

....(i)
and so on
and equation (i) reduces to PT = PC (1 + µeffe.)
Where, µeffe. =
,

  

   .......



Baseband communication is the communication that does not uses
modulation, while carrier communication uses modulation
,
GENERATION OF AM WAVE
Generation of AM waves
Using non-linear circuits
Using linear time variant circuits
For example : switching or
using non linear charcteristics
chopper modulator, collector
devices such as transistors,
modulator, drain modulator.
diodes, FETs etc.
+
+
+
m(t)
vi (t)
AC cos ct
–
–
ideal
diode
L
C vo (t)
R
For example : square law
modulator, Balanced modulator
–
BPF
Figure : simple diode switching
modulator
 For an input voltage vi (t) = AC
cos ct + m(t) where AC >> |m(t)|
non linear equation is given by
y (t) = ax(t) + b x2(t)
Where x(t) = input of non-linear
y (t) = output of non-linear
element
 v i (t) for c(t)  0
Therefore v0(t) = 
for c(t)  0
0
 Mathematically v0(t) can
Tuned to f c
Nonlinear
+
Device
+
m(t)
vi (t)
be expressed as
A c cos c t
vo(t) =[Ac cos ct + m(t)] gp(t)
–
V1
R
L
C v(t)
o
–
BPF
Figure : square law modulator
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
where gp(t) is a periodic pulse train
Square law modulator used for
of duty cycle 50% and period
very small amplitude signal
PERSONAL REMARK :

V1(t) = a Vi(t) + b V2i (t)
gp(t) =
 2

 
(–1) n –1
2n – 1
n 1

where Vi(t) = m(t) + AC cosct
cos [2 fc (2n – 1)t]
or gp(t) =
Now V0(t) = a [Accosct + m(t)]
 2
 cos (2  fc t)
 
2b


or V0(t)= a Ac   a m(t) cosct


+ odd harmonic terms.
Now, v0(t) =
Ac

+ b [Ac cosct + m (t) ]2
4


  Acm(t)


cos 2  fc t + unwanted terms.
AM wave
a m(t) + b m2(t) + bA2c cos2(ct)
removed by means of BPF
unwanted terms
After passing through BPF
tuned to c
We get,
 2b

V0(t) = a Ac  
m(t) cosct
a


Note :

Diode modulator circuit does not provide amplification and
hence, it can be used for Low power application only

However amplifying devices like : BJT, FET etc. can
provide amplification. A very popular circuit used for this
purpose is called collector modulation uses class C amplifier
or drain modulator.
AM DEMODULATION
Detection of original signal i.e. message signal or modulating signal
from the modulated signal is called demodulation or detection.
Square law Detectors or Non-linear Detectors
AM Demodulators
,

Envelop detectors or Linear Detectors
Square Law Detectors
used for low level amplitude modulated signals (say below 1V) so
that the operating region of device characteristics is restricted to
non-linear region. This circuit is similar to square law (non-linear)
modulator. The only difference is in filter circuits.
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
Diode, operating in non-linear region
AM
modulated
wave
i
R
PERSONAL REMARK :

V0=output
C
+ –
vd
,
L.P.F
The circuit arrangement of square law detector is shown.The diode,
is operating in non-linear region.The distorted diode current is given
by non-linear(square law) relation, i = a vi(t)+ b v2i(t)
....(A)
where vi(t) is the input modulated wave voltage i.e.
vi(t) = AC [1+  coswmt]coswct
,
The d.c. source Vd is used to adjust the operating point. This portion
is limited to non-linear region due to which the lower half portion of
the current waveform is compressed. This causes envelop distortion.

,
Envelop Detector or Linear Detector
In envelop detector diode is operating in linear region therefore it is
also called linear detector, as shown below.
Diode, operating in linear region
AM
modulated
wave
C V0=output
RL
Tuned transformer
,
When the modulated carrier at the input of the detector is  1V, the
operation takes place in the linear region of the diode characteristic.
,
The AM wave has a time varying amplitude called as the envelop
of the AM wave. The envelop consists of the baseband signal m(t).
Therefore, the baseband signal can be recovered from an AM wave
by detecting the envelop. By using the envelop detector, the
detection is less costly and simple.
,
Envelop detector is most popular in commercial receiver circuits
since it is very simple and cheaper.
NOTE : The baseband signal is preserved in the envelop only if   1
(i.e. modulation index is less than or equal to 1).
,
Assume that the Rs is the source resistance and rf is the forward
resistance of diode then charging time constant
i.e.
,
(RS + rf) <<
1
fc
....(A)
Assume (RS + rf) << RL Discharging time RLC >>
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....(i)
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
and
RL C <<
PERSONAL REMARK :
1
fm
....(ii)

Combining (i) and (ii) we get
,
In an envelop detector the RC time constant of the diode
should be greater than period of the carrier signal and less
than the period lowest modulating signal i.e.,

1
< RLC <
....(B)
fc
fm
Where, RL C = discharging time constant of diode
fm = highest frequency of modulating signal m(t) & c = 2fc
Where, fc = frequency of carrier wave
or in other words we can say charging time constant (RsC)
should be very-very low and discharging time constant (RLC)
should be very-very high for proper detection of the
modulating signal.
The ripple can be reduced by increasing the time constant RC so
that capacitor discharges very little between the positive peaks
,

1 
 i.e. R L C 
 making RC too large, however would make it
c 

impossible for the capacitor voltage to follow the envelop thus
producing diagonal clipping.
Distortion in Envelope Detector Caused by the Wrong time
Constant as shown
,
Vi(t)
Vi(t)
t
C
(a)
RL
(b)
V0(t)
V0(t)
Called Clipping
Distortion
t
t
(c) Correct RLC
V0(t)
V0(t)
(d) RLC too large
Spikes produced at
the output with low
time constant
t
(e) RLC too small
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,
The required condition for the detector output is to follow
PERSONAL REMARK :

1  2
1 R  1
LC
m
2
c
Where, RLC = time constant of diode
m = 2 fm
µ = modulation index
For   1 the envelop does not preserve the baseband signal, rather,,
the envelop at all times is
,
the baseband signal recovered from the envelop is distorted. This
type of distortion is known as envelop distortion. An AM signal with
  1 is known as over modulated signal.
NOTE : Envelop detection is an extremely simple and
inexpensive operation which does not require generation of
a local carrier for the demodulation.Square law detectors does
not require local carrier for the demodulation.
The envelop of AM has the information about m(t) only if the AM
signal AC [1 + m(t)] cos ct satisfies the condition Ac [1 + m(t)] > 0
for all t.
Am(max)
Envelop |AC+m(t)|
Am(min)
(a)
<1
(b)
 =1
Over modulated
signal
 >1
(c)
,
An over modulated signal can’t be demodulated by a square law
demodutlator and envelope detector.
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,
Overmodulation (i.e.,   1 ) is never applied in the case of envelop
detector method. However, an overmodulated signal can be recovered
using a costly as well as complex technique i.e., synchronous
detection.
,
Experimentally modulation index can be expressed as
,

PERSONAL REMARK :

A m ( max )  A m ( min )
A m ( max )  A m ( min )
Resulting depth of modulation i.e., degree of modulation after
transmitting through circuit.
0

Where,
1  4 Q2  2
 0 = initial depth of modulation
Q = quality factor
fm
 = f
c
,
TYPES OF AM GENERATION
The device which is used to generate an amplitude modulated (AM)
wave is known as Amplitude Modulator.
,
Low-Level AM
Methods of AM Generation
,
High-Level AM
Square law diode modulation and switching modulation are examples
,
of Low level modulation & high level modulation respectively.
(i)
Using linear time variant circuit, for example : switching or
chopper modulator, collector modulator, drain modulator etc.
(ii)
Using non-linear devices such as transistors, diodes, FETs.
Switching modulator can be obtained by a ring modulator used for
,
AM-SC (amplitude modulated suppress-carrier) generation.
The diode modulator circuit does not provide amplification, and hence
,
it can be used for low power application.
For high power amplification we need amplifying devices like
transistors,FET's etc. Each one of them can be used for generating
amplitude modulation by varying gain parameters ( h fe , gm ,  etc. ) in
accordance with modulating signal. The collector modulation method
is an example of High-Level modulation.
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,
Usually class-C amplifier configuration is used for amplification in
PERSONAL REMARK :

order to get high efficiency.
,
In brief, AM generation using non-linear circuits is given below :
m(t)
+
+
V1
nonlinear
device V2
BPF
AM signal
V0(t)
Ac cos ct
V1( t )  m( t )  A c cos  c t
V2 ( t )  a V1( t )  b V12 ( t )
since non-linear

device have

voltage characteristics like


2
V
o (t)  a V1 (t)  b V 1 (t)

Note : Here modulation index, µ =
,





2b
A
a m
Advantage of a Balanced Modulator over a Simple non-linear
Circuit
In simple non-linear circuits, the undesired non-linear terms i.e.,
harmonics are eliminated by a BPF (bandpass filter). Hence in the
case of non-linear modulator circuit, bandpass filter must be carefully
designed. But in a balanced modulator, the undesired non-linear terms
are automatically balanced out, and at the output we get only the
desired term, so filter design is not too much complex.
,
Square law detectors are used for detecting low level modulated
signals (below 1 volt) so that operating region of device characteristic
is restricted to non-linear region.
,
The only difference between the modulator and demodulator is the
output filter. In the modulator, output is passed through a bandpass
filter tuned to fc, whereas in the demodulator the multiplier output is
passed through a LPF. Therefore, all the modulators can be used as
demodulators provided that the BPF at the output are replaced by
low-pass filter (LPF) of bandwidth B.
,
For demodulation, the receiver must generate a carrier in phase and
frequency synchronism with the incoming carrier. These modulators
are called synchronism or coherent or homodyne demodulators.
,
Usually Band Pass filter (BPF) is a parallel combination of R, L
and C.
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,
Costa’s receiver has two synchronous detector inphase coherent
detector or I-channel and quadrature phase coherent detector or Q-
PERSONAL REMARK :

channel.
,
Quadrature multiplexing is an effective method of transmitting two
message signals within the same bandwidth, and usually used in
colour television chrominance signals, which carry the information
about colours.
,
One important component of Costas receiver is a voltage controlled
oscillator (VCO) and its frequency can be adjusted by an error control
d.c. signal.
,
Ring modulator or chopper-type balanced modulator is referred to
as a double-balanced modulator as it is balanced with respect to the
baseband signal as well as the carrier.
,
Switching modulator is single balanced modulator as it is balanced
with respect to the carrier only.
,
Summary of Different Possible Amplitude Modulated System,
with   1 (i.e., 100 % modulation) is given below
System
Pt
(Transmitted
Power)
Ps
(Saved
Power)
(i) AM-DSB/FC
or
AM-FC
(ii) AM-DSB/SC
or
DSB-SC
(iii) AM-SSB/FC
or
SSB-FC
(iv) AM-SSB/SC
or
SSB-SC

PC

Pc


PC


PC

Where,
BW
Circuit
Complexity
–
%Saving power
PT – Pt where, P =  P
T
C

PT
 0%
2m
Min,
PC
 67%
2m
 100%
Pc


PC

 16%
m
 33%
 83%
m
Max,
 33%
 100%
Pt = Transmitted power
PT = Total power
Pc = Carrier power =
A c2
2R
Ps = Saved power
BW = Bandwidth
 = Efficiency
Which of the following analog modulation scheme requires the
minimum transmitted power and minimum channel bandwidth?
(GATE-EC-2004)
(a) VSB
(b) DSB-SC (c) SSB
(d)
AM
Sol.(c) SSB anlog modulation scheme requires minimum transmitted power
and minimum channel Bandwidth.
Ex.
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
MIXER
,
PERSONAL REMARK :

Mixer is non-linear device which generates the sum and difference
frequencies or in other words mixer is a device which is used to
change the carrier frequency of a modulated signal to some
intermediate frequency which is usually less than the carrier
frequency.
V1
cos 2  f Lt
Oscillator
s (t) = m (t) cos 2 fct
V1(t) =
m(t)
[cos 2  (fC + fL) t + cos 2  (fC – fL) t]
2
Where fL = fC – fI , fI is intermediate frequency.
V1(t) =
m (t)
[cos 2 (2fC – fI) t + cos 2 fI t]
2
After passing through BPF, tuned to fI
0
f
fI
2f C –f I
2f C
2 fC + fI
(i)
When fL is fC + fI , the operation is called up-conversion
(ii)
When fL is fC – fI then it is called down-conversion
,
Mixer is also called frequency converter or translator.
,
Usually a detector circuit consist of a half wave rectifier followed
by a Low Pass Filter (L.P.F.).
Ex.
Consider a system shown in the figure. Let X(f) and Y(f) denote the
Fourier transforms of x(t) and y(t) respectively. The ideal HPF has
the cutoff frequency 10 kHz..
[GATE-EC-2004]
HPF
10 kHz
13 kHz
X(f)
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
The positive frequencies where Y(f) has spectral peaks are
(a) 1 kHz and 24 kHz
(b) 2 kHz and 24 kHz
(c) 1 kHz and 14 kHz
(d) 2 kHz and 14 kHz
Sol.(b) Let the modulating signal, x(t) with frequency, fm
PERSONAL REMARK :

Output after balance modulator = 10  fm
Output after HPF with cut-off frequency, 10KHz = 10 + fm
Output after next balance modulator
,
= 13  (10 +fm) = 23 + fm and 3  fm
Double-Sideband Suppressed Carrier (DSB-SC) Modulation
In AM the power required to transmit the carrier is very high when
compare to the sidebands. So the modulation efficiency is very less.
Always the power in the sideband should be as high as possible. To
increase the modulation efficiency the carrier is suppressed and only
the sidebands are transmitted.
s (t) = Ac m (t) cos 2fct + Ac cos 2fct
(time domain equation of AM)
s (t) = Ac m (t) cos 2fct
(time domain equation of DSB carrier is suppressed
i.e., DSB - SC)
s (t) = m (t) c (t)
s (f) =
Ac
[M (f – fc) + M (f + fc)]
2
(frequency domain equation)
Ac S(f)
2
1 M(f)
–fm
fm  –fc –fm –fc –fc +fm
f c+ f m fc
fc+ f m

B.W. = 2w
= 2 × (Highest frequency component of the message)
Power required to transmit a DSB wave is very less as
compared to AM but the bandwidth is same as AM.
Single-tone Modulation of DSB-SC
m(t) = Am cos 2fmt
ACA M
s(t)  m(t) c(t)
4
–fc –fm –fc+f m
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or s(t) = Am Ac cos 2fc t cos 2fm t
s(t) 
Ac Am
2
PUSB =
PERSONAL REMARK :

[cos2(fc – fm) t + cos2(fc + fm)t]
A c2 A 2m
A2 A2
& Pt = c m
8
4
% Power saving 
% Power saving 
Power saved
 100
Total power
Pc
2

 100
Pc (1   2 / 2)
2  2
or % Power saving  1  AM
,
GENERATION OF DSB-SC SIGNALS
Two methods, which are most widely used are :

(i)
Balanced modulator (Non-linear device)
(ii)
Ring Modulator or Switching Modulator (Linear device)
Balanced Modulator
,
Figure shows the block diagram of balanced modulator
,
A relatively simple method for generating DSB-SC AM signal is to
use two conventional AM modulators.
m(t)
A C[1+m(t)] cos ct
AM
modulator
+

–
Carrier
–m(t)
DSB = 2 A m(t) cos  t
C
c
signal
AC cos ct
AM
modulator
AC[1– m(t)] cos ct
Figure: Block Diagram of Balanced Modulator
,
In a balanced modulator two non-linear devices (For example :
Diodes, BJT's ,FET's etc) are connected in the balanced mode so as
to suppress the carrier wave
,
The circuit arrangement of balanced modulator using two
diodes as non-linear elements is shown below D1
+
+
+
VA
–
I1
m(t)
modulating
signal m(t)
cosct
–
+
+
–
–
C
V 0(t)
DSB-SC
wave
I2
+
L
–
m(t)
VB
R
R
L
C
–
D2
BPF centred with ( c)
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
,
From above figure
PERSONAL REMARK :
Ex.
VA = m(t) + cosct
so
VB = –m(t) + cosct
And the current I1 and I2 obtained as
I 1 = aVA + b VA2 = a [m(t) + cosct] + b [m(t) + cosct]2
and
and
What would be the value of
gain k in figure below to
yield the suppressed carried
DSB signal?
[IES-EE-2001:10 Marks]
+
I2 = aVB + b VB2 = a [–m(t) + cosct] + b [–m(t) + cosct]2
x(t)
k
,
2
aV
+
+
A cosc t
+

V
Vo
V0 = I1 R – I2 R = R [I1 – I2] = 2a m(t) + 4bR m(t) cos c t
The output of a BPF centred around  c is given by output
V= 4bR m(t) cosct
or

V0 = K m(t) cosct
(which is desired DSB-SC wave)
V
bV22
Sol. From the given figure we
observe that the signals V1
and v2 are expressed
Diode-Bridge Modulator
V1  k[x(t)  A cos  c t] and
The DSB-SC wave can be obtained by multiplying the message signal
V 2 [ x ( t ) A co s  c t ]
m(t) with any periodic signal c(t) of the fundamental frequency fC.
The fourier series expression is
V 0 = aV12 bV 22
= ak 2 [x(t) + Acos  c t] 2

c(t) =

b[x(t) Acos  c t] 2
C n cos (n ct + n)
n0

Hence, m(t) c(t) =
 C n m(t) cos (n  t +  )
c
n
.
n0
The spectrum of the product m(t)c(t) is
a
the spectrum M() shifted to  c, 
c,  c ...... If this signal is passed
D1
D3
through a bandpass filter of band width
2B Hz and tuned to c, the desired
modulated signal C1 m(t) cos (ct +1) is
d
c
D4
D2
obtained.
The figure shown below is of a electronic
b
switch, the diode-bridge modulator,
Diode-bridge
electronic switch
or V0= ak2[x2(t) + A2 cos2  ct
+ 2Ax(t)cos  ct]  b[x2(t) +
A2 cos2  c t  2Ax(t)cos  ct]
or V0 = ak2[x2(t) + A2 cos2  ct +
2A x(t) cos  ct]  b[x2(t) +
A2 cos2  ct  2Ax(t)cos  ct]
or V0 = (ak2  b)x2(t) +A2
(ak2  b) A2 cos2  ct +
2A x(t) cos  ct(K2+b)
For DSB  SC (Double
Sideband Suppressed
Carrier System) to
generate the first two term
should be zero.
i.e. ak2  b = 0
or k 
driven by a sinusoid A cos c t to produce
b
a
Ans.
the switching action.

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,
During positive half cycle of the carrier, the terminal c is positive
PERSONAL REMARK :

than d, all the diodes are ON closing the terminals a & b. During
next half cycle, terminal d is positive with respect to c and all four
diodes are open, opening the termminals a and b.
,
The input to BPF is m(t) during positive half cycle and is zero during
negative half cycle. The switching on and off of m(t) repeats for
each cycle of the carrier, resulting in the switched signal m(t) c(t).



,
The fourier series for carrier signal used as a switching purpose is
given by
c(t) =
 2


 (cos ct –
cos 3ct +
cos 5ct ......... )
 


m (t) c(t) =

2


m(t) + [m(t) cos ct –
m(t) cos ct +
m(t)




cos 5ct – ...... ]
2
m(t) cos ct

Ring modulator or Chopper type Balanced Modulator
Ring modulator uses square wave as a carrier.
Since 4 diodes are connected in the form of ring that's why switching
modulator is called ring modulator.
After passing through BPF, Y(t) =

,
,
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TECHGURU PUBLICATIONS (A Unit of TECHGURU EDUCATIONALS Pvt. Ltd.)
CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
Figure shows the circuit arrangement of Ring Modulator
D1
a

c
+
+
D4
m(t)
PERSONAL REMARK :

D2
–
b
d
D3
+
–
,
A cos 
The diodes are used as a switching device. The carrier signal is such
,
that its amplitude is Ac > |m(t)|max and c > m
During Positive half-cycles of the carrier, diodes D1 and D3 conduct
and, D2 and D4 are open. Hence, terminal a is connected to c, and
,
terminal b is connected to d.
During negative half cycle of the carrier, diodes D1 and D3 are open,
and D2 and D4 are conducting, thus connecting terminal a to d and
,
terminal b to c.
The output is proportional to m(t) during the positive half cycle and
to –m(t) during the negative half cycle.
m(t)
t (modulating signal)
c(t)
t (carrier signal)
s(t)
,
t (modulated signal)
m(t) is multiplied by a square pulse train c(t). The fourier series for
c(t) is given by
c(t) 
4  (1) n
cos[2fc(2n  1)t]

 n 1 (2n  1)
s (t)  m (t) c (t)
or s (t) 
4
m(t)



n  1
( 1)n1
2n  1
cos [2fc t (2n – 1)]
So, frequency component fm  fc (2n – 1) will be present where
n = 1, 2, 3, ......
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or
s(t) = (4/) m(t) [cos 2f c t – (1/3) cos 6f c t + (1/5) cos
2 (5fc) t – ......]
By passing the output of ring modulator through a BPF with centre
frequency fc and bandwidth 2, we get DSB signal.

s(t) =
m(t) cos2  fc t

or
,
s(t) = K m(t) cos2  fc t  which is required DSB-SC wave
This circuit is referred to as a double balanced modulator as it is
balanced with respect to the baseband signal as well as the carrier.
SYNCHRONOUS OR COHERENT OR HOMODYNE
DETECTION
,
PERSONAL REMARK :

Ex. Which one of the following is
used for the detection of AMDSB-SC signal ?
(a) Ratio detector
(b) Foster-Seeley discriminator
(c) Product demodulator
(d) Balanced-slope detector
(DRDO-EC-2007)
Sol.(c) Product demodulator is used
for the detection of AMDSB-SC signal
Local oscillator signal must be exactly coherent or synchronized with
the carrier wave at the transmitter both in phase and frequency.
Synchronization Techniques
Pilot Carrier
Costa's Receiver
(For synchronous Detection
of DSB-SC or AM-SC wave)
This system has two synchronous detectors
(i) I-phase or inphase coherent detector
(which is inphase with transmitted carriers)
(ii) Q-phase (Quadrative phase coherent detector)
(which is in phase quadrature with the carrier.
Here the two detectors constitute a negative
feedback system which synchronizes the
local carrier with the transmitted carrier
Product
Modulator
LPF
A small amount of carrier signal
known as pilot carrier is transferred
along with the modulated signal
from the transmitter
This pilot carrier is a separated at the
receiver by an appropriate filter, is
amplified and is used to phase
lock the locally generated carrier
at the receiver
1
2 m(t)cos
I-channel
Cos (ct+ )
90ºphase
shifter

Sin(ct+ )
Product
Modulator
,
Demodulated
output
phase
discriminator
VCO
m(t) cosct
c
Q-channel
LPF

m(t)sin c

Phase discriminator provides a dc control signal which may be used
to correct local oscillator phase error. The local oscillator is a VCO
whose frequency can be adjusted by an error control dc signal.
Limitation : The costa's receiver ceases no phase control when
there is no modulation i.e. m(t) = 0
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,
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
DEMODULATION OF DSB SIGNALS
PERSONAL REMARK :

Most widely used methods are Synchronous detection or coherent
detection
Receving
Antenna
s'(t)= m(t)cos2 ct
DSB-SC
m(t)cosct

m(t)

LPF
modulating
signal
cosct
(locally generated carrier)
(t) c o
s c t .
s'(t) = m


D S B .S C .
or S'(t) =
cos c t

Locally generated
carrier signal

m(t)
m(t)
m(t) [1 + cos2c t] =
+
cos 2 c t

2
2
and S'() =



M() +
M ( + 2c ) + M ( – c)



S'()
After passing through LPF.


m(t)
or s'(t) =
2
Spectrum of S'()
M(0)

M(0)



M(0)
2c
–2c
m
m
LPF
Effect of phase and frequency Errors in Synchronous detection
One thing should be always kept in mind that the frequency and
phase of the locally generated carrier signal and the carrier signal at
the transmitter must be identical. This means that the local oscillator
signal must be exactly synchronized with the carrier signal at the
transmitter both in frequency and phase otherwise the detected signal
would get distorted and /or attenuated
Receiver
DSBSC Product
m(t)cosct Demodulator
s'(t)
LPF
modulating
signal
cos{(c+ ) t+ } locally generated carrier
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s'(t) = m(t) cosct. cos [(c  ) t   )]
s'(t) =
PERSONAL REMARK :


m(t) [cos{t  }  cos c  ) t   }]

After LPF s'(t) =

m(t) cos [  t +  ]


This part distort th e signal
Now, Let us consider the three cases
(i)
when and  = 0
Here, s'(t) =
(ii)

m(t) 
 No distortion

When  = 0 but   0
so, s'(t) =

m(t) cos  
 No distortion, only attenuation

when  = 90º s'(t) = 0 
 This is known as quadrature
null effect Because the output
signal is zero when the local
carrier is in phase quadrature with
the carrier
(iii)
When  = 0 and   0
s'(t) =

m(t) cos (  )t is time dependent and produce distortion

(iv)
When   0 and   0
Here we get an attenuated and distorted signal
,
SINGLE SIDEBAND (SSB) MODULATION
SSB-SC wave with single tone modulating signal
Let m(t) = cos mt
cos (c –m) t = cos mt cos ct + sin mt sin ct
cos (c +m) t = cos mt cos ct – sin mt sin ct
....(A)
....(B)
(A) and (B) can be expressed as –
s(t)SSB = cos mt cos ct  sin mt sin ct
Note: + sign represents the lower side band
– sign represents the upper side band
....(C)


we can write sin mt = cos  m t – 
2

Now equation (C) can be written as
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
s(t)SSB = m(t) cos ct  mh (t) sin ct
PERSONAL REMARK :

Note : Where mh(t) is a signal obtained by shifting the phase
 
of every component present in m(t) by  –  .
 2
HILBERT TRANSFORM
,
Here the name "Transform is some what misleading because there
is no change of domain is involved (as in the case of Fourier, Laplace
and Z-transform)
,
Hilbert transform of m(t) is obtained by phase shifting the every
,
frequency component present in m(t) by –

.
2
A delay of /2 at all frequencies at negative frequencies the
spectrum of signal multiplied by + j and at positive frequencies
the spectrum of signal is multiplied by –j.
This is equivalent to spectrum of signal is multiplied by –j sgn(f)
F.T.
i.e. If m(t)  M(f)
,
F.T.
then mh(t)  –j sgn (f) M(f)
Thus the operation of Hilbert transform is equivalent to
convolution integral i.e. filtering. In fact Hilbert transform is
a simple filter. This filter is called a quadrature filter,
,
emphasizing it role in providing a 90º phase shift.
Hilbert transform of m(t) can be defined as :
mh(t) =

1
m(t) *

t
,
m(t)
or
M(f)
or
mh(t) =



2
(– phase shifter)

–
m()
d
t–
mh(t)
or
Mh(f)
and the inverse Hilbert transform is defined as
m(t) = –



–
m h () d
t–

 – j sgn (f)
t
,
Time domain of sgn (t) is given by
,
The transfer function of Hilbert transform H (f) = – j sgn f
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Where, sgn f =
,
 1

 0

 – 
PERSONAL REMARK :
for f  0

at f  0
for f  0
Hilbert transform may be viewed as a linear filter with impulse
response h(t) =
,
1
and frequency respone H(f) = –j sgn f
πt
Figure shows magnitude and phase spectrum of H(f) = –j sgn f
H(f)
sgn(f )

2
1
f
–1
Magnitude Spectrum
–
f

2
Phase Spectrum
The transfer function is expressed as - H(f) = |H (f)| ej  (f)
 (f) 



–


for f  0 (i.e. for negative frequency)
2

for f  0 (i.e. for positive frequency)
2
1
and H (f) = F  
π t
 j ,
 e 2 f 0


f 0
= –j sgn (f) =  0
 – j ,
e 2 f  0

f 0
 j,


–j ,
0
f

0
or H (f) = 
= e 2 sgn (f )

– j, f  0
The response Mh() of the system with transfer function H() is
related to input M() as
Mh() = H() M()
Where m(t)  M() and mh(t)  Mh()
Applications of Hilbert Transform
(i)
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
(ii)
Design of minimum phase type filters
(iii)
Representation of Band pass signals
PERSONAL REMARK :

Properties of Hilbert Transform
(i)
A signal m(t) and its hilbert transform mh(t) have the same
energy density spectrum

Energy spectra of m(t) =


 | M () |



| –j sgn  M () | d =

–

d
–

Energy spectra of mh(t) =


=




 | M h () |

d
–

 | –j sgn  |

| M () | d
–
(ii)
A signal m(t) and its Hilbert transform mh(t) have the same
autocorrelation function
(iii)
A signal m(t) and mh(t) are mutually orthogonal

i.e.
–  m(t) m h (t) dt  0
By parseval theorem


*
 m (t) m h (t) dt   M (f) M h (f) df
–
–


=

*
M (f) j sgn(f) M (f) df = j
2
 sgn f | M (f)|
df  0
–
–
Since, sgn (f) is an odd function so integral is zero.
(iv)
If mh(t) the Hilbert transform of m(t), then the Hilbert
transform of mh(t) is – m(t)
(v)
For non-overlapping spectra mh(t) ch(t) = m(t) ch(t) e.g. Hilbert
transform of m(t) cos ct is m(t) sin ct
(vi)
Hilbert transform of sin 2 f0t = – cos 2 f0t
(vii)
H. T. of e j2π t 0t is = –j sgn (2 f0) e j2π t 0t
(viii) Mh(f) = (–j sgn f) M(f), |Mh(f)| = |M(f)|
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
Concept of Pre-Envelop of Analytic Signal
PERSONAL REMARK :

Pre-envelop of signal m(t) called complex values signal is
mp(t) = m(t) + jmh(t) where, m(t) is called the real part and
mh(t) is called the imaginary part. Envelop of the signal m(t) is the
magnitude of its pre-envelop. i.e. |mp(t)| = Envelop of m(t).
Thus, the envelop is the trace of the positive peaks of carrier (i.e. in
modulated signal)
In order to reduce the bandwidth requirement to transmit the signal
SSB modulation is used. In this technique only one sideband is
transmitted (either USB or LSB). So the bandwidth and power
requirement to transmit the signal is reduced.
S(t) = m (t) Ac cos 2fc t = Am Ac cos 2fm t cos 2 fct
S(t) =
S(t) =
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Ac Am
Ac Am
cos 2(fc + fm) t +
cos 2 (fc – fm) t
2
2
Ac Am
cos 2(fc + fm) t
2
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Ac Am
cos 2(fc – fm) t
2
S(t) =
Ac Am
cos 2(fc  fm) t
2
or S(t) =
,
PERSONAL REMARK :
S(t) =

(If LSB is transmitted)
Ac Am
[cos2fct cos 2fmt  sin 2 fc t sin 2 fmt]
2
The generalized equation of AM-SSB signal
S(t) =
Ac
[m(t) cos 2fc t  mh (t) sin 2 fc t]
2
Transmitted Power, Pt 
2
A c2 A m
8
,
P
Pc  µ 2 c
2
Pc  PUSB
4 = 4 2
Power saving, Ps =
=
2(2   )
Pt
Pc (1  µ 2 /2)
,
or Ps = 1 
AM
2
GENERATION OF SSB SIGNALS
Most widely used methods are :
(i)
Frequency Discrimination Method / Selective Filtering Method
(ii)
Phase Discrimination Method
(i)
Frequency Discrimination Method
The output of a bandpass filter is a DSB signal. If the DSB signal is
passed through a
bandpass filter, the
upper sideband or
lower sideband is
suppressed.
A c cos 2  fC t
If the passband is
,
from fC to fC + W, we will get the USB.
In filter or frequency discrimination method we need a sharp cut-off
bandpass filter which is practically impossible to be realized. Such
filter which separate the desired (usually USB) sideband from the
lower one (i.e. LSB) because the USB and LSB have very small
,
frequency difference. (because fm is very small)
Filter method is used for speech communication where lowest spectral
component is 70Hz, and it can be taken as 300 Hz without affecting
the intelligibility of the speech.
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
,
Filter method is not useful for video communication where baseband
PERSONAL REMARK :

starts from as low as d.c.
,
Need High degree of selectivity (quality factor, Q range lying
between 1000 to 2000)
(ii) Phase Discrimination Method or Phasing Method
,
In this method, the time domain description of SSB-SC is used.
,
A lower sideband SSB-SC signal is given by expression
 SSB(t) = m(t) cosct  mh(t) sinct  as shown by using block
diagram
,
Basic Requirements of Phase Discrimination or Phasing
method

Each baseband modulator need to be carefully balanced in
order to suppress the carrier

Phase shifting is possible by using Hilbert transform of m(t).

Each modulator should have equal sensitivity to the baseband
signal

The carrier phase shifting network must provide an exact 90º
phase shift at the carrier frequency.
,
Demodulation of SSB Signals
Coherent / Synchronous
Detection
Demodulation of SSB Signals
Carrier Reinsertion Method
(1)
Coherent / Synchronous (Homodyne Detection)
V1
V2
Ac cos 2  f c t
s (t) 
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A
m ( t ) cos 2  fc t  c mh( t ) sin 2  fc t
2
2
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V1(t) 
V2 (t) 
A 2c
4
1 cos4 f t
c
m(t) 
Ac
mh (t) sin
4
PERSONAL REMARK :
4fct
 Detection of SSB Signals
with a Carrier (SSB + C)
2
c
A
m(t)
4
We now consider SSB singals
Consider the locally generated signals as A c cos ( 2  fc t   )
with an additional carrier
(SSB + C). Such a signal can
be expressed as
2
C
A
(cos m(t)  m h (t) sin )
4
V2 (t ) 
S(SSB + C)(t) = Acos ct + [m (t)
cos c t + mh(t) sinct]
A2
 = 0 , V 2 (t) = c m (t) i.e. Perfect replica of message
4
  we get highly distorted signal
0
  90 0 , V2 ( t )  
and m(t) can be recovered by
synchronous
detection
[multiplying S (SSB + C)(t) by
cos C t] if the carrier
component A cos ct can be
extracted (by narrowband
filtering of)
S (SSB + C) (t)
alternatively, if the carrier
amplitude A is large enough,
m(t)
can
also
be
(approximately) recovered
from S(SSB + C)(t) by envelope
or rectifier detection. This can
be shown be rewriting as
A c2
mh( t )
4
Note :Quadrature null effect in the case of SSB, is a major
advantage over DSB.
(ii) Carrier Reinsertion Method ( i.e. Pilot Carrier)
The major advantage of the SSB-SC modulation is that it reduces
the bandwidth requirement to half as compared to DSB-SC
,
modulation.
,
But, SSB-SC signal are relatively difficult to generate due to difficulty
in isolating the desired sidebands. The required filter must have a
very sharp cut-off characteristic, particularly when the baseband
signal contains extremly low frequencies (i.e. used in television
S(SSB + C)(t) = [A + m(t)]cos ct + mh(t)
sinct = E(t)cos (ct + )
and telegraphic signals). Under such circumstances, it becomes
where, E(t) is the envelope of
very difficult to isolate one sideband from the other. Hence SSB
S(SSB + C)(t) is given by
scheme becomes unsuitable for handling such types of signals.Refer
E(t)  {[A  m(t)]2  m h2 (t)}1/ 2
right hand side for detailed discussion.
 2m(t) m 2 (t) m 2h (t) 1/ 2

 A 1 



A
A2
A 2 
This difficulty overcome by scheme known as Vestigial Sideband
(VSB) Modulation.
VESTIGIAL SIDEBAND (VEB) MODULATION SYSTEMS
,

In VSB modulation the desired sideband is allowed to pass completely,
whereas just a small portion (called trace or vestige) of the
undesired sideband is also allowed.
Generation of VSB modulation signals is easier than conventional.
Am, DSB-SC and SSB signals. The bandwidth requirement in VSB
modulation signal is slightly higher (approximately 25%) the SSB
signals but considerable less than DSB-SC signals.
VSB is used in television for transmission of picture signals i.e.
VSB is used for video signal transmission in commercial television
broadcasting.
,
,
,

VSB is a compromise between DSB-SC and SSB-SC signals.
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Classroom & Online Test Series
Foundation Batches also for 2nd & 3rd Year sturdents
If A >> |m(t)|, then in general
A >> |mh(t)|, and the terms
m2(t)/A2 and m2h(t)/A2 can be
ignored.
Thus, E(t)

 2m(t) 1/ 2
A 1 


A 

Using Taylor series expansion
and discarding hiher order
terms [because m(t)/A <<1],
we get
 m(t) 
E(t)  A 1 
  A  m(t)

A 

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110
TECHGURU CLASSES for ENGINEERS (Your Dedication + Our Guidance = Sure Success)
CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
,
Figure shows the frequency spectrum of VSB signal
PERSONAL REMARK :

It is evident that for a large carrier,
the SSB + C can be demodulated by
an envelope detector.
VSB
In AM, envelope detection requires
the condition A > |m(t)|, whereas for
SSB + C, the condition is A >> |m(t)|.
Bandwidth of the VSB signal BW = fc + fv  fc + fm = fm + fv
where, fm = Bandwidth of the message fv = width of the VSB
Filter method
,
VSB Generation
Phase-Discrimination method
(i)
,
Generation and Detection of VSB Signal
Filiter Method : A VSB-SC signal can be genereated by passing
DSB-SC signal through an appropriate filter as in figure 1(a). The
system is similar to DSB-SC except that the filter characteristic should
be appropriate. The filter characteristic desired for VSB can be
derived by analysing the demodulation technique of the VSB-SC
signal which is nothing but the synchronous dectection shown in fig.
1(b)
Characteristics of the filter with a transfer function H(  ) shown in
figure 2(a) that may generate a VSB-SC signal from a DSB-SC
signal. A DSB-SC signal has a spectrum given by.
1
1
F(   c )  F(   c )
2
2
The output of the filter H(  ) will be given by
SDSB ( ) 
SVSBSC ( ) 
f (t)
1
H( )[F(   c )  F(   c )]
2
cos 
c t
VSB-SC
signal
H( )
filter
Product
modulator
Product
modulator
....(i)
VSB-SC
signal
(a)
y(t)
LPF
y0 (t) = f (t)
(b)
cos
c t
Figure : 1(a) VSB-SC Modulator (filter method)
1(b) VSB-SC Demodulator Synchronous
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CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
This signal is passed through a product modulator for synchronous
detection as shown in figure 1(b). The output of this product modulator
denoted by ed(t) will be given as
PERSONAL REMARK :

1
y d (t) S VSB SC (t) cos  c t = [SDSB SC (c )SDSBSC (c )]
2
substituting the value of SVSB SC () from (1) we get
1
y d (t)  [{F(  2  c )  F(  c )  F(  )}H (  c ) 
4
{F(  )  F(  )  F( 2  c )}H (  c )]
The signal ed(t) is passed through alow pass and and, hence, the
components centered around 2 c are filtered out. Thus, the
output of LPF of the synchronius detector will be gives as
y o (t) 
1
F( ){H(   c )  H(   c )}
4
....(ii)
For getting a distortionless reception, the output e0(t) should be
given as, y 0 (t)  C1F( )
where,C1is a constant
....(iii)
when comparing equation (iii) with equation (ii) we get the following
condition for a frequency range |  | <  m (since the baseband is
limited to  m)
H(   c )  H(   0 )  C(cons tant ) |  | <  m ....(iv)
The terms H(  +  c) and H(    c) represent H(  ) shifted by  c and +  c, respectively, as frequency range |  |<  m as shown
in figure 2. It is obvious from figure 2 that H(  +  c) + H(    c)
will be constant over |  |<  m only if the cut-off characteristic of
filter H(  ) has a complementary symmetry (odd symmetry) around
the carrier frequency.
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Correspondance
Study Material
Classroom & Online Test Series
Foundation Batches also for 2nd & 3rd Year sturdents
Regular & Weekend Batches
Interview Guidance
112
TECHGURU CLASSES for ENGINEERS (Your Dedication + Our Guidance = Sure Success)
CHAPTER - 4 (AMPLITUDE MODULATION) : COMMUNICATION ENGG .
,
Table given below shows the modulators and demodulators
used by various AM systems.
S.No.
System
1.
DSB-SC
2.
DSB+FC
or AM
3.
SSB-SC
4.
VSB-SC
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PERSONAL REMARK :

(Very Important)
Modulators
Demodulators
(i) Multiplier Modulator
(ii) Non-linear Modulator
(i) Synchronous Detection
(iii) Switching Modulator
(ii) Switching demodulator
(a) Diode Bridge Modulator
(iii) Ring demodulator
(b) Ring Modulator
(iv) Balanced Modulator
(i) Rectifier detector or
(i) Switching Modulator
Square Law detector
(ii) Balanced Modulator
(ii) Envelope detector or
Linear detector
(i) Frequency discriminator
(i) Synchronous detection
(ii) Phase discriminator
(ii) Envelope detection
(iii) Weaver's method
(i) Filter Method
(i) Synchronous detection
(ii) Phase discriminator
(ii) Envelope detection
GORAKHPUR
9919526958
ALLAHABAD
AGRA
9919751941
9451056682
PATNA
9919751941
NOIDA
SUMMER CRASH COURSE ONLINE TEST SERIES
9919751941 WINTER CRASH COURSE OFF-LINE TEST SERIES
113