Analog Communication about amplitude modulation

Analog
Communications
SUBJECT CODE:17EC3404
B TECH II YEAR 4TH SEM
Dr. K. Shri Ramtej,
Assistant Professor,
ECE, VRSEC
1

Signal
 A signal is an electromagnetic or electrical current that is used for carrying data
from one system to another.
 In electronics, a signal is a time-varying voltage/current that is an
electromagnetic wave which carries information.
 There are two main types of signals used in electronics: analog and digital
signals.
 Analog signals are continuous in both values and time.
 Unlike analog signals, digital signals are not continuous, but signals are discrete
in value and time.
2

Signal
 An analog signal is time-varying and generally bound to a range (e.g. +12V to -
12V), but there is an infinite number of values within that continuous range.
 Analog signals are often calculated responses to changes in light, sound,
temperature, position, pressure, etc.
 When plotted on a voltage vs. time graph, an analog signal should produce a
smooth and continuous curve. There should not be any discrete value changes
3

Signal
 A digital signal is a signal that represents data as a sequence of discrete values.
 A digital signal can only take on one value from a finite set of possible values at
a given time.
 When plotted on a voltage vs. time graph, digital signals are one of two values,
and are usually between 0V and VCC.
 Communication is simply the process of exchanging information.
4

Communication System
 Communication is simply the process of exchanging information.
 Transmitter converts information into a signal that is suitable for transmission
over a medium.
5

Modulation
 Modulation is a process of mixing a signal with a sinusoid to produce a new
signal.
 This new signal, will have certain benefits over an un-modulated signal.
 Mixing of low frequency signal with high frequency carrier signal is called
modulation.
 Low frequency signals cannot be transmitted for longer distances.
 So we modify the carrier signal with respect to modulating (message) signal.
 Modulating Signal: Message signal
 Carrier Signal: Signal which carries message signal.
 Modulated Signal: The resultant signal after modulation.
6

Need for Modulation
1. Reducing the height of antenna
 Usually the size of antenna is around /4.
 For voice signal ranging from 300 Hz to 3.4 KHz, = =
×
×
= 10 =
100 km. So the height of antenna becomes 25 km which is not practically
possible.
 If we modulate the signal to higher frequency (1MHz), =
×
×
= 300 .
So antenna size becomes 300/4 = 75 m, which can be installed easily.
7

Need for Modulation
2. Multiplexing
 If 3 users are transmitting voice signals simultaneously, all the signals get
mixed together and a receiver can not separate them from each other.
 If we modulate the 3 voice signals on to 3 different carrier signals, they will
not interfere with each other.
 This process is called Frequency Division Multiplexing (FDM).
 Multiplexing is a process in which two or more signals can be transmitted
over the same communication channel simultaneously.
8

Need for Modulation
3. Increase the Range of Communication
 Low frequency signals can not travel long distance when they are transmitted
as they get heavily attenuated .
 The attenuation reduces with increase in frequency of the transmitted signal,
and they travel longer distance .
 The modulation process increases the frequency of the signal to be
transmitted. Therefore, it increases the range of communication..
9

Types of Modulation
 Consider a carrier signal = cos(2 + ).
 is the amplitude of the carrier.
 is the frequency of the carrier.
 is the phase of the carrier.
 Modulation is the process of varying the characteristic of a carrier signal in
accordance with the modulating (message) signal.
 Amplitude Modulation
 Frequency Modulation
 Phase Modulation
10

Amplitude Modulation (AM)
 Consider a carrier signal = cos(2 ).
 Amplitude Modulation is defined as a process in which the amplitude of
carrier wave is varied linearly with message signal .
Time-Domain Description of AM
 The standard form of AM wave is defined by
! = 1 + "# ( ) cos(2 )
 where "# is a constant called amplitude sensitivity of the modulator.
 The amplitude of time function multiplying cos(2 ) is called the envelope
of the AM wave.
11

 The amplitude of time function multiplying cos(2 ) is called the envelope
of AM wave, denoted by
$ = 1 + "# ( )
 The maximum absolute value of "# ( ) multiplied by 100 is referred to as the
percentage modulation.
 If "# ( ) < 1, Under modulated
 If "# ( ) = 1, Critically modulated
 If "# ( ) > 1, Over modulated
12

 = 1, "# =
(
, = cos 2 ) , ) =
(
$ = 1 + "# ( ) = 1 +
1
2
cos
! = 1 +
1
2
cos cos(2 )
14

 = 1, "# =
(
, = cos 2 ) , ) =
(
$ = 1 + "# ( ) = 1 +
3
2
cos
! = 1 +
3
2
cos cos(2 )
15

 If "# ( ) > 1, modulated wave will suffer from envelope distortion as it is
over modulated.
 So percentage modulation should be less than 100%, to avoid envelope
distortion.
18

Fourier Transform
 FT{1} = *
 FT{cos 2 }=FT
(
+,-(. /0
+ +-(. /0
=
(
* − + * +
 FT{ ( )} = 2( )
 FT{ ( ) cos 2 }=
(
2 − + 2 +
19

Frequency-Domain Description of AM
! = 1 + "# ( ) cos 2
! = cos 2 + "# ( ) cos 2
 To determine frequency description of this AM wave, take Fourier transform on
both sides.
3 =
2
* − + * + +
"#
2
2 − + 2 +
 2( ) is the FT of ( ) and ( ) is band-limited to the interval −4 ≤ ≤ 4
 > 4
20

21
3
=
2
* − + * +
+
"#
2
2 − + 2 +

 The spectrum consists of two delta functions weighted by factor /2 occurring
at ± and two versions of the baseband spectrum translated in the frequency by
± and scaled in amplitude by "# /2
 For positive frequencies, the portion of spectrum lying above carrier frequency
is called upper sideband and the symmetric portion below is called lower
sideband.
 The condition > 4 ensures that the sidebands do not overlap. Otherwise the
modulated wave exhibits spectral overlap and therefore frequency distortion.
 For positive frequencies, the highest frequency component of AM wave is
+ 4 and lowest frequency component is − 4.
 22

 The difference between these two frequencies defines transmission bandwidth
B of AM wave, which is exactly twice the message bandwidth W.
 B=2W
 This spectrum of the AM wave is full i.e., the carrier, the upper sideband, and
the lower sideband are all completely represented.
 Hence this form of amplitude modulation is treated as standard.
23

Single-Tone modulation of AM
 Consider a modulating wave m = )cos(2 ) ).
 The AM wave is described by
! = 1 + "# )cos(2 ) ) cos 2
! = 1 + 7 cos(2 ) ) cos 2
 where 7 = "# ) is called modulation factor or modulation index.
 To avoid envelope distortion due to over modulation, the modulation factor 7
must be kept below unity.
 Let )#8 and )9: be the maximum and minimum values of the envelope of
the modulated wave.
24

)#8
)9:
=
(1 + 7)
(1 − 7)
 That is
7 =
)#8 − )9:
)#8 + )9:
! = 1 + 7 cos(2 ) ) cos 2
! = cos 2 + 7 cos(2 ) )cos 2
 Using the relation cos(A)cos(B) =
(
[cos(A+B)+cos(A-B)]
! = cos 2 +
1
2
7 cos 2 + ) +
1
2
7 cos 2 − )
25

! = cos 2 +
1
2
7 cos 2 + ) +
1
2
7 cos 2 − )
 FT of s(t) is
3 =
2
* − + * + +
7
4
* − − ) + * + + )
+
7
4
* − + ) + * + − )
 Thus the spectrum of an AM wave, for special case of sinusoidal modulation,
consists of delta functions at ± , ± ) and − ± ).
26

27

Power Calculation in AM
! = cos 2 +
1
2
7 cos 2 + ) +
1
2
7 cos 2 − )
 Power = ;
<)=><)= =
?@AB
C
D
=
?E
(
(
D
=
?E
C
(D
=
?E
C
(
when R=1.
 Carrier Power, F =
G/
C
(
 Upper Sideband Power, FHIJ =
G/K/( C
(
=
G/
C
KC
L
=
M/KC
N
 Lower Sideband Power, FOIJ =
G/K/( C
(
=
G/
C
KC
L
=
M/KC
N
 Total power, F0 = F + FHIJ + FOIJ = F +
M/KC
N
+
M/KC
N
= F +
M/KC
(
28

Power Calculation in AM
 Total power, F0 = F 1 +
KC
(
=
G/
C
(
1 +
KC
(
 Transmission Efficiency, P =
QR0#S =9TUV#:T WRXU<
QR0#S 0<#:=)900UT WRXU<
=
M/
YC
C
M/ Z
YC
C
=
KC
(ZKC
 Let F0 = 3004, 7 = 1 then 300 = F 1 +
(
=
(
F
 i.e., F = 2004, FIJ = F0 − F = 1004
 So 2004 of the power is wasted to transmit carrier. 2/3rd of power is lost in
transmitting carrier and only 1/3rd of power is used to transmit sidebands.
29

Generation of AM Waves
Square Law Modulator
 It requires 3 features:
 a means of summing the carrier and modulating waves,
 a nonlinear element, and
 a band pass filter for extracting the desired modulation products.
30

 Semiconductor diodes and transistors are the most common nonlinear devices
used for implementing square law modulators.
 The filtering requirement is usually satisfied by using a single or double tuned
filter.
 The nonlinear device can be modeled as, [( = $ [ + $([(
( )
 where $ and $( are constants.
 The input voltage [ consists of the
carrier wave plus the modulated wave
i.e., [ = + cos 2
31

 [( = $ [ + cos 2 ] + $([ + cos 2 ](
 [( = $ + $ cos 2 + $(
( + $(
( ^!( 2 + 2$( ( ) cos 2
 [( = $ 1 +
(#C
#_
( ) cos 2 + $ + $(
(
+ $(
(
^!(
2
 The first term is the desired AM wave with amplitude sensitivity "# = 2$(/$ .
 The remaining 3 terms are unwanted and are removed by appropriate filtering.
32

Switching Modulator
 It is assumed that carrier wave applied to diode is larger in amplitude.
 We assume that diode acts as an ideal switch, it is short circuited (zero
impedance) when it is forward biased and is open circuited (infinite impedance)
when it is reverse biased.
33

Detection of AM Waves
 The process of detection or demodulation means recovering the message signal
from an incoming modulated wave.
 Detection is the inverse of modulation.
Square Law Detector
 A square law detector is obtained by using a square law modulator for the
purpose of detection.
 The nonlinear device can be modeled as, [( = $ [ + $([(
( )
 The input to the detector is AM wave given by
[ = 1 + "# ( ) cos 2
42

Square Law Detector
 Substituting [ in [( , we get
[( = $ 1 + "# ( ) cos 2 + $( 1 + "# ( ) cos 2 (
[( = $ 1 + "# ( ) cos 2
+$(
(
1 + 2"# + "#
( (( )
1 + cos 4
2
 The desired signal, $(
("# is due to the $([(
( ) term, hence the
description square law detector.
 This component can be extracted by means of a low pass filter.
 This is not the only contribution within the baseband spectrum, because
$(
("#
( (( )/2 will give rise to a plurality of similar frequency components.
43

Square Law Detector
 The ratio of wanted signal to distortion is equal to
#CG/
Cà) 0
#CG/
Cà
C)C(0)/(
=
(
à) 0
.
 To make this ratio large, we choose "# small compared to unity.
44

Envelope Detector
 An envelope detector is a simple yet highly effective device that is well suited
for demodulation of a narrowband AM wave (carrier frequency is large
compared with message bandwidth), for which percentage modulation is less
than 100%.
 Ideally an envelope detector produces an output signal that follows the envelope
of the input signal exactly.
 Envelope detector consists of a diode and
a resistor capacitor filter.
45

Envelope Detector
 On the +ve half cycle of input signal, the diode is forward biased and capacitor
charges up rapidly to the peak value of input signal.
 When input signal falls below this value, the diode becomes reverse biased and
the capacitor discharges slowly through the load resistor Rl.
 The discharging process continues until the next +ve half cycle.
 When the input signal becomes greater than the voltage across the capacitor, the
diode conducts again and the process is repeated.
 We assume that the diode is ideal and the envelope detector is supplied by a
voltage source of internal impedance Rs.
46

Envelope Detector
 The charging time constant b=c must be short compared with the carrier period,
1/ , that is
b=c ≪
1
 Hence, capacitor charges rapidly and thereby follows the applied voltage up to
the positive peak when the diode is conducting.
 On the other hand, the discharging time constant bSc must be long enough to
ensure that the capacitor discharges slowly through the load resistor bS between
positive peaks of carrier wave, but not so long that capacitor voltage will not
discharge at maximum rate of change of the modulating wave, that is
1
≪ bSc ≪
1
4
47

Envelope Detector
 where W is the message bandwidth.
 The result is that the capacitor voltage or the detector output is very nearly same
as the envelope of AM wave.
 The detector output usually has a small ripple at carrier frequency, which is
removed by low pass filtering.
48

Applications of AM
 In radio broadcasting, a central transmitter is used to radiate message signals for
reception at a large number of remote points.
 AM broadcasting is radio broadcasting using amplitude modulation (AM)
transmissions.
 One of the most important factors which promoted the use of AM in radio
broadcasting is the simple circuitry required at the receiver’s end.
 A simple diode circuit is enough at the receiver’s end to properly receive the
modulated signal and get the original message.
52

Applications of AM
 Since, while broadcasting, there are a large number of receivers which are the
common masses of public, it is essential that circuitry involved be simple and
compact so that everyone can accommodate and use it properly.
 Amplitude modulation serves this purpose perfectly as explained above and
hence is used for broadcasting.
53

Double Sideband Suppressed Carrier
(DSB-SC)
 The spectrum of standard AM wave is full i.e., the carrier, the upper sideband,
and the lower sideband are all completely represented.
 Hence it is called as Double Sideband with Full Carrier.
 But 2/3rd of power is lost in transmitting carrier and only 1/3rd of power is used
to transmit sidebands. i.e., Transmission efficiency is only 33.33% when 7=1.
QR0#S 0<#:=)900UT WRXU<
=
KC
(ZKC
 This is the main drawback of standard AM wave.
 To overcome this drawback, we can suppress the carrier component from the
modulated wave resulting in Double Sideband Suppressed Carrier modulation.
54

Double Sideband Suppressed Carrier
(DSB-SC)
 Thus by suppressing the carrier, we obtain a modulated wave that is
proportional to the product of carrier wave and message signal.
Time-Domain Description of DSB-SC
 DSB-SC wave can be expressed as
! = ( )
! = cos 2 ( )
 This modulated wave undergoes a phase reversal whenever the message signal
crosses zero.
 Hence the envelope of DSB-SC modulated wave is different from the message
signal.
55

Time-Domain Description of DSB-SC
56

Frequency-Domain Description of DSB-SC
 By taking the Fourier transform on both sides of time-domain signal, !
! = cos 2 ( )
3 =
2
2 − + 2 +
 where 3 is the FT of modulated wave, and 2( ) is the FT of message signal
 When message signal is limited to the interval −4 ≪ ≪ 4, the modulation
process simply translates the spectrum of baseband signal by ± .
57

Frequency-Domain Description of DSB-SC
58
 The transmission bandwidth required
by DSB-SC modulation is same as that
for standard AM, i.e., 2W.
 However, the carrier is suppressed in
DSB-SC as there are no delta functions
at ± .

Generation of DSB-SC Waves
59
 A DSB-SC wave consists simply the product of the message signal and the
carrier wave.
 A device for achieving this requirement is called a product modulator.
 We have two forms of product modulator namely balanced modulator and ring
modulator.

Balanced Modulator
60
 A balanced modulator consists of two standard amplitude modulators arranged
in a balanced configuration so as to suppress the carrier wave.
 We assume that the two modulators are identical,
except for the sign reversal of the modulating
wave applied to the input of one of them.

Balanced Modulator
61
 Thus the outputs of two modulators may be expressed as
! = 1 + "# ( ) cos 2
!( = 1 − "# ( ) cos 2
 Subtracting !( from ! , we obtain
! = !( − ! = 2"# cos 2 ( )
 Hence, except for the scaling factor 2"#, the balanced
modulator output is equal to the product of modulating
wave and carrier, as required.

Ring Modulator
62
 One of the most useful product modulators that is well suited for generating a
DSB-SC modulated wave is the ring modulator.
 It is also known as lattice or double-balanced modulator.
 The four diodes form a ring in which they all point in the same way.
 The diodes are controlled by a square wave carrier of frequency fc, which is
applied by means of two center-tapped transformers.
 We assume that the diodes are ideal and the
transformers are perfectly balanced.

Ring Modulator
63
 When the carrier supply is positive, the outer diodes are switched ON,
presenting zero impedance, where as the inner diodes are switched OFF,
presenting infinite impedance, so that the modulator multiplies the message
signal m(t) by +1.
 When the carrier supply is negative, the situation becomes reversed
and the modulator multiplies the message signal m(t) by -1.
 Thus a ring modulator is a product modulator for a square wave carrier
and the message signal.

Ring Modulator
64
 Thus a ring modulator is a product modulator for a
square wave carrier and the message signal.
 The square wave carrier can be expressed by a Fourier
series as
 The ring modulator output is therefore
 We can see that there is no output from modulator at carrier frequency.

Coherent Detection of DSB-SC Waves
65
 The message signal is recovered from a DSB-SC wave s(t) by first multiplying
s(t) with a locally generated sinusoidal wave and then low pass filtering the
product.
 It is assumed that the local oscillator output is exactly coherent or synchronized,
in both frequency and phase with the carrier wave c(t) used in the product
modulator to generate s(t).
 This method of demodulation is known as
coherent detection or synchronous detection.

66
 Let the signal generated from local oscillator is having same frequency and
phase, measured with respect to the carrier wave c(t).
 Then the local oscillator signal can be denoted by cos 2 assuming =1
for convenience.
 The output of product modulator is given by
[ = cos 2 !( )
[ = cos 2 cos 2 ( )
[ =
cos 2 + 2 + cos 2 − 2
2
( )
[ =
cos 4 + 1
2
( )

67
[ =
2
+
2
cos 4 ( )
 The low pass filter removes unwanted term in the product modulator output.
 The final output is therefore given by
[ =
2
 The demodulated signal [ is therefore proportional to when local
oscillator is perfectly synchronized.

Effect of phase drift in Coherent Detector
68
 Let the signal generated from local oscillator is having same frequency but
arbitrary phase difference , measured with respect to the carrier wave c(t).
 Then the local oscillator signal can be denoted by cos 2 + assuming
=1 for convenience.
 The output of product modulator is given by
[ = cos 2 + !( )
[ = cos 2 + cos 2 ( )
[ =
cos 2 + + 2 + cos 2 + − 2
2
( )
[ =
cos 4 + + cos
2
( )

69
[ =
2
cos +
2
cos 4 + ( )
 The low pass filter removes unwanted term in the product modulator output.
 The final output is therefore given by
[ =
2
cos
 The demodulated signal [ is therefore proportional to when the phase
error is constant.
 The amplitude of this demodulated is maximum when = 0, and is minimum
(zero) when = ± /2.

70
 The zero demodulated signal which occurs for = ± /2, represents the
quadrature null effect of the coherent detector.
 Thus the phase error in the local oscillator causes the detector output to be
attenuated by a factor equal to cos .
 As long as the phase error is constant, the detector output provides an
undistorted version of the original message signal ( ).
 In practice, phase error varies randomly with time because of random variations
in the communication channel, which is undesirable.
 Therefore, circuitry must be provided in the receiver to maintain the local
oscillator in perfect synchronism, in both frequency and phase, with the carrier
wave used to generate DSB-SC wave in the transmitter.

71
 The resulting increase in receiver complexity is the price that must be paid for
suppressing the carrier wave to save transmitter power.

Single Tone Modulation of DSB-SC Wave
72
 Consider a sinusoidal modulating wave m = )cos(2 ) ).
 The corresponding DSB-SC wave is given by
! = = )cos(2 ) ) cos 2
! =
)
2
cos 2 + ) +
)
2
cos 2 − )
 Assuming perfect synchronism between the local oscillator and carrier wave in
coherent detector, the product modulator output is
[ = cos 2
)
2
cos 2 + ) +
)
2
cos 2 − )

Single Tone Modulation of DSB-SC Wave
73
[ =
)
4
cos 2 2 + ) +
)
4
cos 2 )
+
)
2
cos 2 2 − ) +
)
4
cos 2 )
 The first two terms are produced by upper side frequency, and last two terms
are produced by lower side frequency.
 The first and third terms are removed by low pass filter.
 The coherent detector output hence reproduces the original message signal.
 The detector output has two equal terms, one derived from upper side frequency
and the other from lower side frequency.
 Hence for transmission of information, only one side frequency is necessary.

Costas Loop
74
 In coherent detection, the signal generated by the local oscillator should be
coherent to or perfectly synchronized with the transmitter carrier.
 Detection is also possible if we transmit the carrier component with modulated
signal, which is nothing but the standard amplitude modulation.
 But DSB-SC signal has no such component.
 Costas loop has capability to generate a coherent carrier at the receiver and
therefore used for demodulation of DSB-SC signals.

Costas Loop
75
 One method of obtaining a
practical synchronous receiving
system, suitable for use with
DSB-SC modulated waves, is to
use Costas Loop.
 This receiver consists of two
coherent detectors supplied with
same input signal i.e., incoming
DSB-SC modulated wave but with individual local oscillator signals that are in
phase quadrature to each other.

Costas Loop
76
 The detector in the upper path is referred to as the in-phase coherent detector
or I-channel, and the lower path is referred to as quadrature-phase coherent
detector or Q-channel.
 These two detectors are coupled to form a negative feedback system designed
in such a way to maintain the local oscillator synchronous with the carrier
wave.
 To understand the operation of this receiver, suppose that the local oscillator
signal is of the same phase as the carrier wave cos 2 used to generate
incoming DSB-SC wave.
 Under these conditions, I-channel output contains desired demodulated signal
m(t) as
G/
(
cos =
G/
(
( ) when = 0.

Costas Loop
77
 Whereas, Q-channel output is zero owing to quadrature null effect of Q-channel
as
G/
(
sin = 0 when = 0.
 Now if the local oscillator phase drifts from its proper value by a small amount
radians, the I-channel output will be
G/
(
cos and some signal will be
appearing at Q-channel output which is equal to
G/
(
sin . sin ≃ .
 For small values of , cos ≃ 1 and sin ≃ .
 This Q-channel output will have the same polarity as the I-channel output for
one direction of local oscillator phase drift and opposite polarity for opposite
direction of local oscillator phase drift.

Costas Loop
78
 The I and Q-channel outputs are combined in a phase discriminator (which
consists a multiplier followed by a low pass filter).
 Thus, the output of the multiplier in the phase discriminator is
G/
(
×
G/
(
=
G/
C
N
(( ).
 The low-pass filter, which has a very low cutoff frequency, gives a dc voltage
proportional to at its output since variations in will be very slow compared
to variations in (( ).
 Hence a dc control signal proportional to the phase error is obtained at the
discriminator output.
 Hence the receiver automatically corrects for local oscillator phase errors.

Numerical
79
 A 400 Watt carrier is modulated to a depth of 75 percent. Calculate the total
power in AM wave.
 Consider the AM signal s(t) = [Ac + m(t)]cos500t where the modulating signal
is given by m(t) = 3 cos50t + 5 cos150t. Let the modulation index be 0.8. Find
amplitude of the carrier, carrier power and transmission efficiency.

 Consider a modulating wave m = )cos(2 ) ).
! = 1 + "# )cos(2 ) ) cos 2
! = 1 + 7 cos(2 ) ) cos 2
G/
C
(
, Upper Sideband Power, FHIJ =
M/KC
N
 Lower Sideband Power, FOIJ =
M/KC
N
, Total power, F0 = F 1 +
KC
(
QR0#S 0<#:=)900UT WRXU<
=
KC
(ZKC
80

Multi-Tone modulation of AM
 = ) cos 2 ) + )(cos(2 )( )
! = 1 + "# ) cos 2 ) + "# )(cos(2 )( ) cos 2
! = 1 + 7 cos 2 ) + 7( cos 2 )( cos 2
 where 7 = "# ) , 7( = "# )(.
 Effective modulation index, 70 = 7(
+ 7(
(
G/
C
(
, Total power, F0 = F 1 +
Ki
C
(
Ki
C
(ZKi
C
81

Numerical
82
 An AM transmitter has an unmodulated carrier power of 10 kW. It can be
modulated by a sinusoidal modulating voltage to a maximum depth of 40%,
without overloading. If the maximum modulation index is reduced to 30%,
what is the extent up to which the unmodulated carrier power can be increased
without overloading?

Numerical
83
 An AM transmitter has an unmodulated carrier power of 10 kW. It can be
modulated by a sinusoidal modulating voltage to a maximum depth of 40%,
without overloading. If the maximum modulation index is reduced to 30%,
what is the extent up to which the unmodulated carrier power can be increased
without overloading?

Numerical
84
 Calculate the percentage power saving when the carrier and one of the
sidebands are suppressed in an AM wave modulated to a depth of (i) 100%, and
(ii) 50%.

Noise in Analog Modulation
86
 To carryout noise analysis of analog modulation systems, a parameter called
output signal-to-noise ratio is used.
 Output signal-to-noise ratio is defined as the ratio of the average power of the
message signal to the average power of the noise, both measured at the receiver
output. It is denoted as
 (3jb)k=
#lU<#mU WRXU< R )U==#mU =9m:#S #0 0nU <U U9lU< Ro0Wo0
#lU<#mU WRXU< R :R9=U #0 0nU <U U9lU< Ro0Wo0
 Output signal-to-noise ratio alone is not sufficient when we have to compare
different modulation systems and hence a baseband transmission model is used.

87
 In a baseband transmission model, two assumptions are made:
1. The transmitted or modulated message signal power is fixed.
2. The baseband low-pass filter passes the message signal, and rejects out-of-band
noise.
 Channel signal-to-noise ratio is defined as
 (3jb)p=
#lU<#mU WRXU< R )RToS#0UT =9m:#S
#lU<#mU WRXU< R :R9=U )U#=o<UT 9: )U==#mU V#:TX9T0n

88
 Channel signal-to-noise ratio is independent of the type of modulation or
demodulation used.
 We can normalize the noise performance of a specific modulation-demodulation
system by dividing the output signal-to-noise ratio of the system by the channel
signal-to-noise ratio.
qrstu+ ^ +ur =
(3jb)k
(3jb)p
 The noise performance of the receiver is better if figure of merit value is high.

AM Receiver Model
89
 Channel noise is usually modeled as white noise, whose mean is zero and
whose power spectral density is constant.
 Channel noise is denoted by v( ) and its power spectral density is j /2
defined for both positive and negative frequencies.
 In other words j is the average noise power per unit bandwidth measured at
the front end of the receiver.

AM Receiver Model
90
 The received signal consists of an amplitude modulated signal component !( )
corrupted by the channel noise v( ).
 To limit the degrading effect of noise component v( ) on the signal component
!( ), the received signal is passed through IF filter whose bandwidth is just
large enough to accommodate !( ).
 The IF filter is usually tuned so that its midband frequency is same as the carrier
frequency of the modulated signal !( ).

AM Receiver Model
91
 The composite signal w( ), at the IF filter output is defined by
w = ! + x
 where x( ) is a band-limited version of the white noise v( ).
 x( ) is the sample function of a noise process j( ) with the following power
spectral density:

Signal-to-Noise Ratios for Coherent
Reception
92
 Noise analysis is done by evaluating the output and channel signal-to-noise
ratios for an AM receiver using coherent detection, with an incoming DSB-SC
modulated wave.
 The use of coherent detection requires multiplication of the IF filter output w( )
by a locally generated sinusoidal wave cos 2 and then low-pass filtering
the product.

Reception
93
 For coherent detection, the local oscillator should be synchronized both in
frequency and phase with the transmitter carrier.
 Consider a DSB-SC wave ! = cos 2 ( )
 where cos 2 is the carrier wave and ( ) is the message signal.
 Typically, the carrier frequency is greater than the message bandwidth 4.
 The average power of DSB-SC modulated wave is
y cos 2 ( ) (
=
G/
C
(
F, where P is the average power of message
signal m(t).
 The transmission bandwidth of B of DSB-SC modulated wave is equal to twice
the message bandwidth 4.

Reception
94
 With a noise power spectral density of j /2, defined for both positive and
negative frequencies, the average noise power in the message bandwidth =
24 ×
z{
(
= 4j .
 The channel signal-to-noise ratio is therefore
 (3jb)p=
#lU<#mU WRXU< R )RToS#0UT =9m:#S
#lU<#mU WRXU< R :R9=U )U#=o<UT 9: )U==#mU V#:TX9T0n
=
|/
C
C
M
}z{
=
G/
CM
(}z{
 Now we determine the output signal-to-noise ratio of the system. The total
signal at coherent detector input may be expressed as
 w = ! + x
= cos 2 + x~ cos 2 − x•( ) sin 2

Reception
95
 w = ! + x
= cos 2 + x~ cos 2 − x•( ) sin 2
 where x~ and x• are the in-phase and quadrature components of x ,
with respect to the carrier cos 2 respectively.
 The output of the product modulator component of coherent detector is
 [ = w cos 2
= ^!( 2 + x~ ^!( 2 − x•( ) sin 2 cos 2
= [ + x~ ] ^!( 2 − x•( ) sin 2 cos 2
= [ + x~ ]
[1 + cos 4 ]
2
− x•( )
sin 4
2

Reception
96
 [ = [ + x~ ]
[ Z€•‚ N. /0 ]
(
− x•( )
‚ƒ„ N. /0
(
=
1
2
+
1
2
x~ +
1
2
+ x~ cos 4 −
1
2
x•( ) sin 4
 The low pass filter in coherent detector removes the high frequency components
of [ , and the receiver output is
 … =
(
+
(
x~
 The message m(t) and in-phase noise component x~ of narrowband noise n(t)
appear additively at the receiver output.
 The quadrature component x•( ) of the noise n(t) is completely rejected by the
coherent detector.

Reception
97
 The message signal component at the receiver output = /2.
 Hence average power of message signal at the receiver output is
y /2 ( = (F/4, P is the average power of message signal m(t).
 The noise component at the receiver output = x~ /2.
 Hence average power of noise at the
receiver output is
y x~ /2 ( = y x~
( /4
= 24j /4 = 4j /2

Reception
98
 (3jb)k=
#lU<#mU WRXU< R )U==#mU =9m:#S #0 0nU <U U9lU< Ro0Wo0
#lU<#mU WRXU< R :R9=U #0 0nU <U U9lU< Ro0Wo0
=
G/
CM/N
}z{/(
=
G/
CM
(}z{
 Figure of merit =
(IzD)†
(IzD)‡
= 1

Noise in AM Receivers using Envelope
Detection
100
 In a standard amplitude modulated (AM) wave both the side bands and the
carrier are transmitted.
! = 1 + "# ( ) cos(2 )
 The average power in the modulated signal ! = (
(1 + "#
(
F)/2, where P is
the average power of message signal.
 With average noise power in the message bandwidth = 4j , the channel
signal-to-noise ratio is
(3jb)p=
((1 + "#
(F)/2
4j
=
((1 + "#
(F)
24j

Detection
101
 The received signal x(t) at the envelope detector input consists of modulated
signal s(t) and narrow band noise n(t).
 w = ! + x
= 1 + "# ( ) cos 2 + x~ cos 2 − x• sin 2
= + "# ( ) + x~ cos 2 − x• sin 2
 The envelope detector output is given by
 … = +x[+ˆ^‰+ ^ w = + "# ( ) + x~
( + x•
(
( )
 As ideal envelope detector is totally insensitive to phase variations in x(t).
 This expression of y(t) is complex and needs to be simplified.

Detection
102
 When the average carrier power is large compared with the average noise
power, so that the receiver is operating satisfactorily, then the signal term
1 + "# ( ) will be large compared with the noise terms x~ and x• .
 Then we may approximate the output as
 …( ) ≃ + "# ( ) + x~
 The presence of the dc term or constant term in the envelope detector output
is due to demodulation of transmitted carrier wave and it can be removed
simply by means of a blocking capacitor. Hence output SNR is given by
(3jb)k≃
y "# ( ) (
y x~
( ≃
("#
(F
24j

Detection
103
(IzD)†
(IzD)‡
=
|/
CŠa
C‹
CŒ•{
|/
C(_ŽŠa
C‹)
CŒ•{
=
`a
CM
Z`a
CM
 This expression is valid only if:
 The noise at the receiver input is small compared to the signal
 The amplitude sensitivity "# is adjusted for a percentage modulation less than or
equal to 100%.
 The figure of merit of DSB-SC receiver using coherent detection is always
unity.
 The figure of merit of AM receiver using envelope detection is always less than
unity.

Detection
104
 This means that the noise performance of DSB-SC receiver is always better
than the AM receiver.
 This is due to the wastage of transmitted power that results from transmitting
the carrier as a component of AM wave.
Single-Tone Modulation
 Consider a modulating wave = )cos(2 ) ).
 The corresponding AM wave is ! = 1 + 7 cos(2 ) ) cos 2
 The average power of message signal is F = )
( /2.

Detection
105
à
CM
Zà
CM
=
à
CGA
C /(
Zà
CGA
C /(
=
KC
(ZKC.
 When 7 = 1, which corresponds to 100% modulation, we get a figure of merit
equal to 1/3.
 This means that, other factors being equal, this AM system must transmit 3
times as much average power as a suppressed carrier system in order to achieve
the same quality of noise performance.

Analog Communication about amplitude modulation

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