unit-5noise-230123162705-a69a9f8d (1).pptx

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DEPARTMENT OF ELECTRONICS AND COMMUNICATION
ENGINEERING
SUBJECT NAME: ANALOG COMMUNICATIONS
FACULTY NAME: Dr. M.NARESH
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ANALOG COMMUNICATIONS
COURSE OBJECTIVES:
1. To Analyze the Analog communication system requirements
2.To understand the Generation and Detection of various analog modulation
techniques
3.To Analyze the noise performance of analog modulation techniques
4. To understand AM and FM Receivers.
5. To Understand the Pulse modulation techniques
COURSE OUTCOMES:
CO1: Understand analog communication system
CO2: Compare and analyze analog modulation techniques
CO3: Calculate noise performance of analog modulation techniques
CO4: Design AM and FM receivers
CO5: Differentiate between pulse modulation techniques & continuous
modulation techniques.
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SYLLABUS
UNIT I- Linear Modulation schemes: Need for modulation,
conventional Amplitude Modulation (AM). Double side band
suppressed carrier (DSB –SC)modulation ,Hilbert transform,
properties of Hilbert transform. Pre-envelop. Complex envelope
representation of band pass signals, In-phase and Quadrature
component representation of band pass signals. Low pass
representation of band pass systems. Single side band (SSB)
modulation and Vestigial-sideband (VSB) modulation. Modulation
and demodulation of all the modulation schemes, COSTAS loop.
UNIT II- Angle modulation schemes: Frequency Modulation (FM)
and Phase modulation (PM), Concept of instantaneous phase and
frequency. Types of FM modulation: Narrow band FM and wide
band FM. FM spectrum in terms of Bessel functions. Direct and
indirect (Armstrong's) methods of FM generation. Balanced
discriminator, Foster–Seeley discriminator ,Zero crossing detector
and Ratio detector for FM demodulation. Amplitude Limiter in FM.
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UNIT IV- Analog pulse modulation schemes: Sampling of
continuous time signals. Sampling of low pass and band pass signals.
Types of sampling. Pulse Amplitude Modulation (PAM) generation
and demodulation. Pulse time modulation schemes: PWM and PPM
generation and detection. Time Division Multiplexing.
UNIT III- Transmitters and Receivers: Classification of
transmitters. High level and low level AM transmitters. FM
transmitters. Principle of operation of Tuned radio frequency (TRF)
and super heterodyne receivers. Selection of RF amplifier. Choice of
Intermediate frequency. Image frequency and its rejection ratio
Receiver characteristics: Sensitivity, Selectivity, Fidelity, Double
spotting, Automatic Gain Control.
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UNIT V- Noise Sources and types: Atmospheric noise, Shot noise
and thermal noise. Noise temperature. Noise in two-port network:
noise figure, equivalent noise temperature and noise bandwidth.
Noise figure and equivalent noise temperature of cascade stages.
Narrow band noise representation. S/N ratio and Figure of merit
calculations in AM, DSB-SC, SSB and FM systems, Pre-Emphasis and
De-Emphasis

TEXT BOOKS /REFERENCES
TEXT BOOKS:
1. Simon Haykin, “Communication Systems,” 2/e, Wiley India, 2011.,
2. B.P. Lathi, Zhi Ding, “Modern Digital and Analog Communication
Systems”, 4/e, Oxford University Press, 2016
3. P.Ramakrishna Rao, “Analog Communication,” 1/e, TMH, 2011.
REFERENCES:
1.Taub, Schilling, “Principles of Communication Systems”
, Tata
McGraw‐Hill, 4th Edition, 2013.
2. John G. Proakis, Masond, Salehi, “Fundamentals of Communication
Systems”, PEA, 1st Edition,2006
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LESSON PLAN:
UNIT V- Noise Sources and types
S. No. Topic(S)
No.
of Hrs
Relevant
COs
Text Book/
Reference
Book
1. Noise Sources and types: Atmospheric noise, Shot
noise and thermal noise
1 CO3 T1,T2,T3
2. Noise temperature. Noise in two-port network:
noise figure, equivalent noise temperature and noise
bandwidth. Noise figure and equivalent noise
temperature of cascade stages
1 CO3 T1,T2,T3
3. Narrow band noise representation. 1 CO3 T1,T2,T3
4. S/N ratio and Figure of merit calculations in AM,
DSB-SC, SSB and FM systems,
3 CO3 T1,T2,T3
5. Pre-Emphasis and De-Emphasis, 1
Total 07
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PRE-REQUISITES FOR THIS COURSE:
PTSP III-SEM
ES215EC :SS IV-SEM
3-Credits
3-Credits
EXTERNAL SOURCES FOR ADDITIONAL LEARNING:
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Description Proposed Actions Relevance With POs
Relevance
With PSOs
Modulation &
Demodulation of all
Techniques including
multiplexing .
Communication Lab PO3, PO4, PO5 PSO2
CONTENT BEYOND SYLLABUS:
S. No. Topic Relevance with POs and
PSOs
1. Advanced Communication system PSO1

INTRODUCTION:
Initially Noise Definition and Types of noises, Noise temperature are discussed.
Then Noise in two port Network-Noise figure, equivalent temperature ,Noise
bandwidth are discussed. Then noise figure and noise temperature of cascaded
stages are calculated .finally students will calculate S/N ratio and Figure of merit
calculations for AM ,DSB-SC,SSB-SC and FM systems. Finally Pre-emphasis and De-
emphasis concepts are also discussed.
UNIT V- NOISE
Discuss the different types of Noises and noise source, Narrowband Noise In phase and
quadrature phase components and its Properties.
Analyze the Noise in DSB and SSB System, Noise in AM System, Noise in Angle
Modulation System, Pre-emphasis and de-emphasis circuits
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CONTENTS:
1. Noise sources and types:
- Atmosphericnoise,
- Shot noise
- Thermal noise.
2. Noise temperature, noise in two-port network: noise figure, equivalent noise temperature,
noise bandwidth, Noise figure and equivalent noise temperature of cascade stages.
3. Narrow band noise representation.
4. S/N ratio and figure of merit calculations in: AM, DSB-SC, SSB and FM systems
5. Pre-emphasis and de-emphasis
OUTCOMES:
Analyze the Noise in DSB and SSB System, Noise in AM System, Noise in Angle Modulation
System, Pre-emphasis and de-emphasis circuits
UNIT V- NOISE
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CONTENTS:
1. Noise sources and types:
- Atmospheric noise,
- Shot noise
- Thermal noise.
OUTCOMES:
MODULE-1
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Noise is an unwanted signal which interferes with the original message signal and corrupts the
parameters of the message signal. This alteration in the communication process, leads to the
message getting altered. It is most likely to be entered at the channel or the receiver.
5.1. Noise sources and types
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The noise signal can be understood by taking a look at the following example.
Most common examples of noise are −
•Hiss sound in radio receivers
•Buzz sound amidst of telephone
conversations
•Flicker in television receivers, etc.

Types of noise:
There are two main ways in which noise is produced. One is through some external source , other is
created by an internal source.
External source: This noise is produced by the external sources which may occur in the medium or
channel of communication, usually. This noise cannot be completely eliminated. The best way is to
avoid the noise from affecting the signal.
Most common examples of this type of noise are −
Atmospheric noise (due to irregularities in the atmosphere). Extra-terrestrial noise, such as solar
noise and cosmic noise, Industrial noise.
Internal source:
This noise is produced by the receiver components while functioning. The components in the circuits,
due to continuous functioning, may produce few types of noise. This noise is quantifiable. A proper
receiver design may lower the effect of this internal noise.
Most common examples of this type of noise are −
• Thermal agitation noise (johnson noise or electrical noise).
• Shot noise (due to the random movement of electrons and holes).
• Transit-time noise (during transition).
•Miscellaneous noise is another type of noise which includes flicker, resistance effect and mixer
generated noise, etc.
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Atmospheric noise or static is caused by lighting discharges in thunderstorms and other
natural electrical disturbances occurring in the atmosphere. These electrical impulses are
random in nature. Hence the energy is spread over the complete frequency spectrum used for
radio communication.
Extraterrestrial noise:
(I)solar noise: This is the electrical noise emanating from the sun. Under quite conditions, there is a
steady radiation of noise from the sun.
This results because sun is a large body at a very high temperature (exceeding 6000°C on the
surface), and radiates electrical energy in the form of noise over a very wide frequency spectrum
including the spectrum used for radio communication.
The intensity produced by the sun varies with time. In fact, the sun has a repeating 11-year noise
cycle. During the peak of the cycle, the sun produces some amount of noise that causes tremendous
radio signal interference, making many frequencies unusable for communications.
(Ii)Galatic noise (or)cosmic noise: Distant stars are also suns and have high temperatures. These
stars, therefore, radiate noise in the same way as our sun. The noise received from these distant stars
is thermal noise (or black body noise) and is distributing almost uniformly over the entire sky. We
also receive noise from the center of our own galaxy (the milky way) from other distant galaxies and
from other virtual point sources such as quasars and pulsars.
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iii. Man-made noise (industrial noise) is meant the electrical noise produced by such sources as
automobiles and aircraft ignition, electrical motors and switch gears, leakage from high voltage lines,
fluorescent lights, and numerous other heavy electrical machines. Such noises are produced by the
arc discharge taking place during operation of these machines.
Such man-made noise is most intensive in industrial and densely populated areas. Man-made noise
in such areas far exceeds all other sources of noise in the frequency range extending from about 1
MHz to 600 MHz
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INTERNALNOISE:
i. Thermal noise conductors contain a large number of free electrons and ions strongly bound
by molecular forces. The ions vibrate randomly about their normal (average) positions,
however, this vibration being a function of the temperature. Continuous collisions between the
electrons and the vibrating ions take place.
Thus there is a continuous transfer of energy between the ions and electrons. This is the
source of resistance in a conductor. The movement of free electrons constitutes a current
which is purely random in nature and over a long time averages zero. There is a random
motion of the electrons which give rise to noise voltage called thermal noise. Thus noise
generated in any resistance due to random motion of electrons is called thermal noise or
white or johnson noise relate the noise power generated by a resistor to be proportional to
its absolute temperature.

Thermal Noise: Noise power is also proportional to the bandwidth over which it is measured.
Pn𝖺 T
Pn𝖺 B
Pn = KTB
where Pn = maximum noise power output of a resistor.
K = boltzmann’s constant= 1.38 x10^-23 joules / kelvin.
T = absolute temperature,
B = bandwidth over which noise is measured
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Thermal noise is often referred to as ‘white
noise’ because it has a uniform ‘spectral density
This thermal noise may be represented by an equivalent
circuit as shown

Shot Noise:
Shot noise was originally used to describe noise due to random fluctuations in electron emission from
cathodes in vacuum tubes (called shot noise by analogy with lead shot).
Shot noise also occurs in semiconductors due to the liberation of charge carriers.
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For pn junctions the mean square shot noise currentis
Where I is the direct current as the Pn junction (amps) saturation current
(amps)
• “Io” is the electron charge = 1.6 x 10-19coulombs
• B is the effective noise bandwidth(Hz)
• Shot noise is found to have a uniform spectral density as for “thermal noise”

CONTENTS:
5.2. Noise temperature, noise in two-port network: noise figure, equivalent noise
temperature, noise bandwidth, Noise figure and equivalent noise temperature of
cascade stages.
OUTCOMES:
Discuss the Noise temperature, noise bandwidth and Noise figure
MODULE-2
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Two-Port Network:
5.2.Noise Figure &Equivalent Noise Temp .of 2-port Network
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10
i
i
o
o
(SNR)
NoisePower
input.Noise.Powert N
(SignaltoNoiseRatio)
The signal to noise ratio is givenby Signal power to Noise power
SNR 
Signal.Power
Noise.Power
10log(
signalpower
)
(SignaltoNoiseRatio) 
input.signal.power

Si

output.signal.power

So
output.Noise.Powert N
So
(SNR)i
Si
N
i
NoiseFigure 
(SNR)0

No

(i) for noise less system sno=sni
therefore noise figure=1
(ii) for noisy system sno>sni noise figure is nf>1
total noise power density at the output is the sum of the noise power density(sno) due to the input
source sni and noise power density contributed by the system sns
(sno)= sni+ sns
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Therefore Noise figure is
SNI SNI SNI
S S  S S
NF  No
 NI Ns
1 Ns
Noise Figure in terms of Noise Temperature
The noise figure in terms of equivalent input noise temperature can be expressed
NF 1
Ts
T
Ts=Noise temperature of the system
T=Noise temperature of the source
Tc T(NF 1)

Noise figure in cascaded stages:
let the two stage amplifier connected in cascade. Then the overall noise figure of the
cascade connection in terms of the noise figure of the individual amplifier or 2-ports
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.
Actual.output.noise.power
GNi Noise.output.power.if .the.amplifier.in
(i)NF 
GNiNo

Available gain G
Available input noise power KT(Δf)
Available Output Noise Power NF.G.KT.(S Δf)
Power
Gain(G1)
NF=F1
Power
Gain(G2)
NF=F2
(F1-1)KT(Δf)
KT(Δf)
(F2-1)KT(Δf)
F1.KT(Δf)G1G2
+
(F2-1)KT(Δf)G2

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1
1
Actual.Output.Noise.Power
Output.Noise.Power.assuming.the.amplifier
G
NOISE FIGURE IN CASCADED STAGES:
Overall.Noise.Figure(NF) 
NF  F 
(F21)
Overall.Noise.Figure(NF) 
F1KT(f )G1G2  F21 KT(f )G2
KT(f )G1G2
It may be extended to any no of amplifiers connected in cascade
1
1 1 2 1 2 3
G G .G G .G .G
(F41)
NF  F 
(F21)

(F31)

Quadrant noise temperature of cascaded amplifiers
Individual stages have equivalent noise temperature To1,To2,To3,….and available power gains
G1,G2,G3,….Let the Room temperature be T.If the equivalent noise temperature of cascaded
connection is say Te. Te Te1 Te2 Te3
To To G1To G1G2To
1 1  
Te 
Te1

Te2

Te3
G1 G1G2

CONTENTS:
5.3. Narrow band noise representation.
OUTCOMES:
MODULE-3
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5.3. Narrow band Noise Representation
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



c 
c
c 
c
2
1
SSB  SC : m (t)  A m(t).cos w t  m (t).sin w t
^
BPF Detector output
NARROW BAND NOISE REPRESENTATION:
SINGLE –SIDE BAND SUPPRESSED CARRIER (SSB-SC):
The front end of the receiver will be designed to have a bandwidth just equal to the bandwidth of the
transmitted signal
k.mc(t)
+
nw(t)

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
S  K 2
M 2
(t)
R
2 4
1 1
2 4
1 1
4
2
2 2 ^
2 2 2
2
2 2 2 ^ 2
c
R c
c
c
c
R C
S  . k .A m (t)  . k .A m (t)



1 2  
S  k A m (t).cos w t  2.m(t).m (t).sin w t.cos w t  m (t).sin wct

m 2
(t )  m ^ 2
(t )
Since the Hilbert transform does not alter the power
where AR  K.Ac
c i c q c
c R
R
2
2
1 1 ^
y(t)  A m(t).cosw t  A m (t).sin w t  n (t)cosw t n (t)sin w t
y(t)  Kmc (t)  n(t)
n(t)  ni (t).coswct nq (t).sin wct

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After LPF (with cuttoff frequency ‘w’ Hz)
2 2
2
2 2 2
2 2 2 2 2
4 4
R i
R i
R i
n
T T
D ..S S B
A 2
Z n 2
( f ) A m ( f )
S R
(
S
)
N
   w
. (t)
 w ( f ) 
1
A m (t )(1 
C o s 2 w c t
)  n (t )(1 
C o s 2 w c t
)

1
A m (t )(
1

C o s 2 w c t
)  n (t )(
1

C o s 2 w c t
)

1
A m ( t ) 
1
n (t)
 1 
2
 1 
  R   R
 (
S
)
N
  4    4   
S R
 
 1 
2
  i
 2 


D
C
(
S
)
(
S
)
N


F i g u r eo fM e rit  N   1
c i c q c
R
c
R
4
2
1 1
2 ^ 2
z(t)  A m(t).cos w t  A m (t).sin 2w t  n (t).cos w t  n (t).sin 2w t
.In detector/synchronous detector y(t) is multiplied by coswct and LPF:
z(t)  y(t).cos wct

. Consider detector is synchronous detector , Then the modulated or transmitted signal is
given by :
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c c c
m (t)  A m(t)cosw t DSBSC..signal
2
R
Then received signal is K.mi(t)
.mi t K.Ac .m(t).cos wct
K.mi t AR .m(t) cos wct
Re ceived.signal.power(SR )  K m (t)
2 2

1
m2
(t)A 2
..............DSBSC  BW  2w
Input.to.the.det ector  y(t)  AR m(t) cos wct  n(t)
 ARm(t) cos wct  ni (t) cos wct  nq (t) sin wct
 AR m(t)  ni (t)cos wct  nq (t)sin wct
The..synchronous det ector..multiplies.y(t).by.coswct

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  2
2 2 2
2
R i c q c c
R i R i c q c
R i
The..output.of .LPF.is
 A m(t) n (t) cos w t  n (t)sin w t.cosw t

1
A m(t)  n (t)
1
A m(t)  n (t)Cos2w t 
1
n (t)sin 2w t
W(t) 
1
A m(t)  n (t)
Z t yt.coswct
 ARm(t)  ni (t)cos wct  nq (t)sin wct.coswct
2 2
c R R
D i T
A m (t) S S
n 2
(t)  2W
 S 
  
 
 N 

CONTENTS:
5.4. S/N ratio and figure of merit calculations in: DSB-SC, SSB
OUTCOME:
Analyze the Noise in DSB and SSB System,
MODULE-4
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S/N Ratio and Figure of Merit Calculations in DSB-SC
DSB-SC signal =Ac m(t)cos2π fc t
Input of the receiver Si(t)= Ac m(t)cos2π fc t+ Ni(t)
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    2
c c
Si t  (A .m t cos2 f t)
Mean square value of the signal
Input band pass Noise can be
Ni (t)  ni (t)cos2 fct  nq (t)sin 2 fct
Ni  n 2
(t)  n 2
(t)  n 2
(t)
i q I
At Demodulator/Detector :DSB-SC signal is multiplied by carrier signal Cos2πfct
=Ac m(t). Cos2f ct. Cos2f ct
  2
c
c
 f t
 m t cos 2

Ac
2
m(t)1 cos4 f t
Output of LPF:
2
Sot
Acm(t)
2
A2
m2
(t)
Si  c
Input signal Power

.
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The output Signal Power:
   
2
2
2
i c q c c
q
2
i
c c
i i c q c
n (t)
n (t)
 f t.cos2 f t
sin 4 f t
no (t)  n(t)cos2 fct
 n (t)cos 2 f t  n (t)sin 2
 1 cos4 f t 

1
n (t)  n (t)cos 4 f t n (t)sin 4 f t
After LPF
1
2
4 4
4
o o i I
I
No t ni (t)
N  n 2
(t) 
1
n 2
(t) 
1
N
No

1
8
2
2
2
A 2
.m 2
(t )
c
o
S o ( t )  c





 
 
 

 
 A . m ( t ) 
S ( t )   
Figure of Merit:
i
S  N
SNRi
SNR
N 1
S 1
O
1
Ni 4
o

Si 4
o


.Single Sideband Suppressed carrier(SSB-SC):
S/N Ratio and Figure of Merit Calculations in SSB-SC
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 
A
c
c
m(t).cos2f t  m(t).sin 2f t
2 
SSB  SC :
m(t).cos 2
A
c
c
c 
2 
 f t  m(t).s

 in 2f t  n(t)
c 
Input of the Receiver + Noise
4
1 ^ 2
2 A2
i

 c


4  2 2
c 
A2 
1
m (t)  m (t)  m (t)
S 


Input signal Power is 2

At Input of Demodulator or Detector
A
c
c
c
c
d f t
f t .cos 2
m(t).cos 2 
^




 2

 f t m(t).sin 2
S (t) 
A
A c
c c
c
^
4
4
f t]  m(t).sin 4f t
m(t).[1 cos 2


S/N Ratio and Figure of Merit Calculations in SSB-SC
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After LPF:
4
Ac
o
S (t)  .m(t)

2
Output signal Power of the Demodulator:
2
.m (t)
A
S  c
16
o
i

1
S
4
So

1
Si 4
Figure of Merit:
 i   i 
 o    i   1
 
N
S

 So 
 N 
 Si   No 
 N 
 So 

CONTENTS:
5.4. S/N ratio and figure of merit calculations in: AM systems
OUTCOME:
Analyze the Noise in AM System
MODULE-5
MATRUSRI
ENGINEERING COLLEGE

.In a conventional amplitude modulated (AM)wave both sidebands and the carrier are transmitted.
The received signal has the term :
S(t)=Ac(1+Kam(t))cos2 fct
Envelope Detector/Envelope Detection:
It consists of simply a non linear device followed by a LPF.
Si(t)= Ac(1+Kam(t))cos2 fct + ni(t)
Noise In Amplitude Modulation (AM) Scheme
MATRUSRI
ENGINEERING COLLEGE
2 2
2
c
i a
The mean square signal power Si and noise Power Ni
A 2
S  [1 k m (t)]
To compute the mean square power, so and noise power No at the output of the demodulator,

.
MATRUSRI
ENGINEERING COLLEGE
  
  
2 2 2
i c a c I c Q c
c a I Q
Q
c a I
n (t)
(t)]
S t A 1 K mtcos2 f t  n (t)cos2 f t n (t)sin 2 f t
Si t [Ac 1 Kamt nI (t)]cos2 fct  nQ (t)sin 2 fct
k  C(t).cos(2 fct (t))
1
where....C(t)  [[A 1 K m t  n (t)] n (t)
 
(t)  tan1



[A 1 K m t  n 
The output of the envelope detector is obviously C(t).we shall now consider two cases:
a)small noise case
b) Large noise case
Ac(1+Kam(t)) >> n(t)
n(t) >> Ac(1+Kam(t))

. a) small noise case: Ac(1+Kam(t)) >> n(t)
In this case Ac(1+Kam(t)) >> n(t)
Therefore Ac(1+Kam(t)) >> nI(t) or nQ(t)
The envelope equation can be approximated under this condition
MATRUSRI
ENGINEERING COLLEGE
         
 
1
2
1
2
c a c a I
c a
t ]
2n (t)
nI (t)
2


E t  [{A 1 K m t }  2 A 1 K m t . n
 Ac 1 Kam t [1 I

Ac 1 Kamt

 Ac 1 Kamt[1
A 1 K mt
 Ac 1 Kamt nI (t)
Ni(t)
Nq(t)
Phasor diagram for small noise Ψ(t)

5.4. Noise In Amplitude Modulation (AM) Scheme
MATRUSRI
ENGINEERING COLLEGE
a) small noise case: Ac(1+Kam(t)) >> n(t)
E(t)  Ac 1 Kamt nI (t)
And Ψ(t)=0
It is evident that the useful signal at the output of the demodulator
So(t)=Ka Ac m(t)
ni(t)=nI(t)
 
2 2 2
a c
So  K A m t
o I i
N  n 2
(t)  N
 
 
 
 
2 2 2
2 2
2 2 2
2 2
 a c  a
 a 
 a 
K A m t 2K m t
Ac
2
 S 
 o

 No   
 Si  1 K m t
1 K m t
 N 
 i 
When µ=K A
a m is the modulation index. Now the avg power of the modulating signal is
2
2 m
2
A
m (t) 
 
2 2
2
2
a
a m
m
2
a m
a
N 2K 2
A 2
N
 S   2 A 2

 o
 2K m

 o   
 
 S   A 2
 2  K A
1 K
 i
  
 
 i 
When µ=K A =1 which corresponds to 100%
a m
modulation The max improvement in S/N that
can be achieved by 2/3

5.4 Noise In Amplitude Modulation (AM) Scheme
MATRUSRI
ENGINEERING COLLEGE
b) Large noise case : n(t) >> Ac(1+Kam(t)):
In this case n(t) >> Ac(1+Kam(t))
ni(t) and nq(t) >> Ac(1+Kam(t))
under this condition the envelope of the second signal given by:
          
      
   
2 2
1
2
2
1
2
2 2
1
2
I Q I c a
I c a
I Q
nQ t
1
cos[(t)]]2
et R(t)[1
R(t)  [n t  n t ]
e t  [n t  n t  2n t A 1 K m t ]
(t)  tan1
(
nI t)
e t  [R (t)  2n t A 1 K m t ]
(Ac 1 Kamt
R(t)
R(t)
cos[(t)]]
et R(t)[1
(Ac 1 Kamt
et R(t)  (Ac 1 Kamtcos[(t)]
et R(t)  (Ac cos(t))  AcKam tcos[(t)]
e t R(t)  (Ac cos(t))  AcKam tcos[(t)]
E(t) can be further simplified as:

MATRUSRI
ENGINEERING COLLEGE
2 2
2
c
i a
.
B) COHERENT DETECTION:
If synchronous or coherent detector is used for demodulation of AM , it can be shown that the
same improvement in the S/N ratio will be obtained in the large noise as well as in the small
noise case:
A 2
S  [1 k m (t)]
i i
N  n 2
(t)
 
 

 
2 2
2
d c a c I c q c c
q
2
I
d c a c c c
n (t)
n (t)
sin 4 f t
S (t)  A 1 K m t )cos 2  f t  n (t)sin 2 f t.cos2 f t
 f t) 
The synchronous detector output:
Sd (t) [(Ac1 Kamtcos2 fct nI (t)cos2 fct  nq (t)sin 2 fct]cos2 fct
 f t  n (t)cos 2
S (t)  A 1 K m(t) (1 cos4 f t)  (1 cos4

MATRUSRI
ENGINEERING COLLEGE
After LPF 2 2
4 4
c
4
o a
A 2
K m (t)
n 2
(t) 1
S 
No  I
 Ni
 2 2
2
2
2
2
3
m
2
a m
a
A 2
2K 2
A 2
 S   2 A 2

 o
  2K m

 N
a
o  
   a m

2 2
 2   2
 S   A 2
 2  K A
1 K
 i
  

 Ni  
 So 
 N 
when.....  1.....  o  
 Si 
 N 
m (t)  m
2
 i 

CONTENTS:
5.4. S/N ratio and figure of merit calculations in: FM systems
OUTCOME:
Analyze the Noise in Angle Modulation System
MODULE-6
MATRUSRI
ENGINEERING COLLEGE

5.4 Noise in FM receivers
MATRUSRI
ENGINEERING COLLEGE
BPF
Frequency
discriminator
Post Detection
filter(LPF)
.Noise in FM Receiver:
FM
Noise
The angle modulated carrier is generalized form S(t)  Accos(2 fct (t))
Message is bandlimited to W hz
The channel noise at the input of the demodulator is a bandpass noise with power spectral
density sn(f) and band limited to 2( Δf+fm)
Where Ac=unmodulated carrier component
fc=carrier frequency
Ø(t)= Instantaneous phase angle
Ø(t)=Kp.m(t)………………..for PM
Ø(t)=2πKf. ∫m(t).dt……….for FM

.The noise can be expressed
n(t)  ni (t)cos wct  nq (t)sin wct
n(t)  R(t).cos(2 fct (t))
MATRUSRI
ENGINEERING COLLEGE
2 2
q
q
(t)  tan1
 nI (t) 

R(t)  nI (t)  n (t)

 n (t


) 
Where
Resultant
The signal present at the input of FM demodulator can be written as
Si t Accos(2 fct  2K f . mt.dt)  n(t)
Si t Accos(2 fct  2K f . mt.dt)  R(t).cos(2 fct (t))
R(t)
 (t)  (t) (t) (t)
This can be represented by
phasor diagram

 The relative phase Ψ(t) is
t (t)  tan1  R(t)sin[(t) (t)] 
 A  R(t)cos[(t) (t)]
 c 
Where
Ø(t)=2πKf. ∫m(t).dt
MATRUSRI
ENGINEERING COLLEGE
t
(t)  (t) 
R(t)
[(t) (t)]
For the sake of simplicity we assume that the amp of un-modulated carrier is very large so that the
carrier to noise ratio is measured at the discriminator input is large compared to unity
Under this condition the relative phase Ψ(t) of the resultant phasor can be
sin
Ac
(t)  2K f . mtdt  2K f .  mt.dt
0
d
2 dx
The output of the discriminator can be written as
S (t) 
1 d(t)
Sd (t)  K f .m(t)  nd (t) Where nd(t) is the noise defined as
1
c
d
2 A dt
n (t) 
d
R(t)sin[(t) (t)]

MATRUSRI
ENGINEERING COLLEGE
L
. inear filter transfer function
The assumption further simplifies
1
c
d
d
[R(t)sin(t)]
2 A dt
n (t) 
Further written as 1
c
d s
d
[n (t)]
2 A dt
n (t) 
The discriminator output is given by kfm(t)+nd(t), when this signal is passed through LPF, the
final demodulator signal output becomes:
so(t)=kfm(t)
mean square signal power is f
So  k 2
m2
(t)
j2 f jf
2 Ac Ac
H( f )  
The PSD of the quadrature component of the bandpass noise and noise output of the
demodulator is:
N nq
c
f 2
Snq ( f )
A 2
S f  H(f)
2
S ( f )
SN f 

MATRUSRI
ENGINEERING COLLEGE
  2
nd c
A
BT

 f 2
 
f 
2
S f 
0otherwise

 
0 f
BT
2 2
BT

f
The average noise power is obtained by
integrating the PSD
η
Where
2
w
o
c
f df
A
No
3A 2

c w
N 

2w3
2 
The average signal power present at the input of the demodulator:
2
c
2
A
Si 
The average noise power at the demodulator input is Ni  2T
 So 
6Kf 2
m2
(t)BT
W 3
 N 
 o  
 S 
 i

 Ni 

.
MATRUSRI
ENGINEERING COLLEGE
Signal to noise ratio at the demodulator output is given by
2W 3
 S  3Kf 2
A 2
m2
(t)
 o
  c
 No 
The signal output of the Envelope detector is given
It is interesting to compare S/N ratio at the demodulator output for FM and AM
If there signal m(t) were transmitting using AM
2
o a c
o I i w
S  k 2
A 2
m2
(t)
N  n (t)  N  2
The S/N at the AM demodulator o/p can be written as:
FM
A
fm fm
 So 
 No   k A 
2
 k 
2
 f 
2
   3  3 2
 
f c
 3
f m
  3 
 Si       fm 
 Ni 
 AM
For comparison we also consider
AM under most favorable condition i. e
AM with 100% modulation
In this case the amp of m(t)
becomes same as that of the carrier i.e Ac
Ka=1/Ac=1/Am AM being
amplitude of message
a
f
F M
w 2
k 2
3 k 2

 o 
 N o  A M
 S 
 
N
 0 
 S o 
2W
k2
m2
(t).B

 o   a
 No AM
 S 

.
MATRUSRI
ENGINEERING COLLEGE
Threshold in FM:
The threshold effect in FM is much more pronounced then in Am
The FM signal at the demodulator input can be expressed as:
Si t Ac.Cos(2 fct (t))  n(t)
t
(t)  2kf m(t)dt
0
n(t)  ni (t)Cos(2 fct) nq (t)Sin(2 fct)
n(t)  R(t)Cos(2 fct (t))
Where
The above equation can be written as : Si t Ac.Cos(2 fct (t))  R(t)Cos(2 fct (t))
The phasor diagram representing the equation
Si t Ac.Cos(2 fct (t))  (t)
Ac sin((t) (t))
where.....(t)  tan1
R(t)  Ac cos((t) (t))

MATRUSRI
ENGINEERING COLLEGE
For large noise case:
R(t)>>Ac the equation can be expressed as
c
R(t)
Ac
R(t)
1  A sin((t) (t)) 
(t)  tan  
 
(t)  tan1
sin((t) (t))
The output of the FM Demodulator is given by
d c
d c
dt
dt dt
S (t) 
d
(2 f t (t)  (t))
S (t)  2 f 
d(t)

d(t)

CONTENTS:
5.5. Pre-emphasis and de-emphasis
OUTCOME:
Understand the concepts of Pre-emphasis and de-emphasis .
MODULE-7
MATRUSRI
ENGINEERING COLLEGE

Pre-emphasis & De-emphasis:
MATRUSRI
ENGINEERING COLLEGE
Pre-emphasis: The Boosting of the amplitude of high frequency modulating signal at
FM transmitteris called Pre-emphasis
3dB Low cut-off frequency for the pre-emphasis circuit cab be computed by
Fc=1/2πR2C

. De-emphasis:
MATRUSRI
ENGINEERING COLLEGE
The Artifically Boosted High frequency signal in the process of pre-emphasis
at FM tranmitter are brought to their original amplitude levels using using
de-emphasis circuit at the FM Receiver

1. (A)What are external and internal noises?
(B)Define signal to noise ratio, noise figure and equivalent noise temperature
2.Explain using phasor diagram the effect of noise on FM.
3.Calculate the system noise of a receiver that has a bandwidth of 6 mhz and an input noise
temperature of 250K to the antenna. The equivalent noise resistance of receiver is 75 ohms, the
antenna has a resistance of 72 ohms. Assume to=2900 k.
4. Explain pre-emphasis and de emphasis in FM systems?
5. Explain noise in angle modulation systems?
Assignment Question
MATRUSRI
ENGINEERING COLLEGE

Short answer questions
Questions & Answers
MATRUSRI
ENGINEERING COLLEGE
S.NO QUESTION
Blooms
Taxonomy
Level
Course
Outcome
1. Classify the different noises in communication system. CO5
2 Define the noise figure and noise temperature. CO5
3. What is meant by Pre-emphasis and De-emphasis? CO5
4. Explain thermal noise and Shot noise? CO5
5. Explain Equivalent noise temperature in cascaded stages? CO5

Long answer questions
Questions & Answers
MATRUSRI
ENGINEERING COLLEGE
S.NO QUESTION
Blooms
Taxonomy
Level
Course
Outcome
1. Define the Terms:
(a) Thermal Noise (b) Shot noise (c) Noise temperature (d) Noise
Figure CO5
2. Derive the figure of merit Expressions for AM, CO5
3. Derive the figure of merit Expressions for DSBSC and SSBSC CO5
4. Derive the expression for figure of merit of FM system. CO5
5. A mixer stage has a noise figure of 25 dB and a stage before it is an
amplifier with a noise figure of 7 dB and an available power gain of
15 db. Find out the overall noise figure referred to input.
CO5

THE-END
MATRUSRI
ENGINEERING COLLEGE

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