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EC8491 COMMUNICATION THEORY
UNIT I
AMPLITUDE MODULATION
Amplitude Modulation- DSBSC, DSBFC, SSB, VSB - Modulation index, Spectra, Power relations
and Bandwidth – AM Generation – Square law and Switching modulator, DSBSC Generation –
Balanced and Ring Modulator, SSB Generation – Filter, Phase Shift and Third Methods, VSB
Generation – Filter Method, Hilbert Transform, Pre-envelope & complex envelope –comparison of
different AM techniques, Superheterodyne Receiver
UNIT II ANGLE MODULATION
Phase and frequency modulation, Narrow Band and Wide band FM – Modulation index, Spectra,
Power relations and Transmission Bandwidth - FM modulation –Direct and Indirect methods, FM
Demodulation – FM to AM conversion, FM Discriminator - PLL as FM Demodulator.
UNIT III RANDOM PROCESS
Random variables, Random Process, Stationary Processes, Mean, Correlation & Covariance
functions, Power Spectral Density, Ergodic Processes, Gaussian Process, Transmission of a Random
Process Through a LTI filter.
UNIT IV NOISE CHARACTERIZATION
Noise sources – Noise figure, noise temperature and noise bandwidth – Noise in cascaded systems.
Representation of Narrow band noise –In-phase and quadrature, Envelope and Phase – Noise
performance analysis in AM & FM systems – Threshold effect, Pre-emphasis and de-emphasis for
FM.
UNIT V SAMPLING & QUANTIZATION
Low pass sampling – Aliasing- Signal Reconstruction-Quantization - Uniform & non-uniform
quantization - quantization noise - Logarithmic Companding –PAM, PPM, PWM, PCM – TDM,
FDM.
TEXT BOOKS:
1. J.G.Proakis, M.Salehi, ―Fundamentals of Communication Systems‖, Pearson Education 2014.
(UNIT I-IV
2. Simon Haykin, ―Communication Systems‖, 4th Edition, Wiley, 2014.(UNIT I-V)
REFERENCES:
1. B.P.Lathi, ―Modern Digital and Analog Communication Systems‖, 3rd Edition, Oxford
University Press, 2007.
2. D.Roody, J.Coolen, ―Electronic Communications, 4th edition PHI 2006
3. A.Papoulis, ―Probability, Random variables and Stochastic Processes‖, McGraw Hill, 3rd
edition, 1991.
4. B.Sklar, ―Digital Communications Fundamentals and Applications‖, 2nd Edition Pearson
Education 2007
5. H P Hsu, Schaum Outline Series - ―Analog and Digital Communications‖ TMH 2006
6. Couch.L., "Modern Communication Systems", Pearson, 2001.
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EC8491
ENGINEERING COLLEGES
2016 – 17 Even Semester
IMPORTANT QUESTIONS & ANSWERS (IQA)
Department of ECE
SUBJECT CODE:
EC 6402
SUBJECT NAME: COMMUNICATION THEORY
Regulation: 2013
Year and Semester: II/IV
Prepared by
Sl. No.
1
2
3
4
5
6
Name of the Faculty
Designation
DEPARTMENT OF ECE
Mr. V. Parvathinathan
AP
SUBJECT CODE : EC8491
Affiliating College
SCADCET
SUBJECT NAME : COMMUNICATION THEORY
REGULATION :2017
YEAR : II
Verified by DLI, CLI an d Approved by SEM
the Centralized
Monitoring Team dated
:IV
EC8491
EC8491
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COMMUNICATION THEORY
LTPC
3003
1. Aim and Objective of the Subject
The student should be made
 To introduce the concepts of various analog modulations and their spectral
characteristics.
 To understand the properties of random process.
 To know the effect of noise on communication systems.
 To study the limits set by Information Theory.
2. Need and Importance for Study of the Subject
The student will be able to understand the working of simple communication
systems
3. Industry Connectivity and Latest Developments
Industry Connectivity:
 The following companies (Industries) are linked to communication systems:
BSNL, TATA Communications
Latest Developments:
 LIFI if fast data transfer in networking.
 New revolution in 5G, 6G in all the smart phones, smart televisions, etc.
 Network on chip.
 AM and FM Modulation Schemes.
 LTE were introduced almost in all the home appliances.
4. Industrial Visit (Planned if any):
-Nil-
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EC8491
SCAD GROUP OF INSTITUTIONS
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
Detailed Lesson Plan
Name of the Subject & Code: EC8491 COMMUNICATION THEORY
Name of the Faculty:
1. Mr. Parvathinathan V, AP/ECE, SCADCET
TEXT BOOKS:
1. J. G. Proakis, M. Salehi, “Fundamentals of Communication Systems”, Pearson
Education 2006.
2. S. Haykin, “Digital Communications”, John Wiley, 2005.
REFERENCES:
1. B. P. Lathi, “Modern Digital and Analog Communication Systems”, 3rd Edition, Oxford
University Press, 2007.
2. B. Sklar, “Digital Communications Fundamentals and Applications”, 2nd Edition
Pearson Education 2007
3. H P Hsu, Schaum Outline Series - “Analog and Digital Communications” TMH 2006
4. Couch.L., "Modern Communication Systems", Pearson, 2001.
TOPIC
TOPIC NAME
No. of
Cumulative
Books
Periods
Hour
Referred
1
1
R1,T1
2
Introduction to Communication
Systems
Generation of Amplitude modulation
1
2
T1, T2
3
Demodulation of AM
1
3
T1, T2
4
Double side band suppressed carrier
modulation
Double side band suppressed carrier
demodulation
Single side band suppressed carrier
modulation
1
4
T1, T2
1
5
T1
1
6
T1
NO.
1
5
6
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7
8
9
Single side band suppressed carrier
demodulation
Vestige side band modulation &
demodulation
Comparison of AM modulation
1
7
T1
1
8
T1
1
9
T1
systems
10.
Super heterodyne Receiver
1
10
T1
12
Phase Modulation
1
11
T1
13
Frequency Modulation
1
12
T1
14
Single tone FM
1
13
T1
15
Narrow band FM
1
14
T1
16
Wide band FM
1
15
T1
17
Generation of FM
2
17
T1
18
Demodulation of FM
2
19
T1
19
Transmission Bandwidth of FM
1
20
T1
20
Review
1
21
T1
of
probability,
random
process
21
Central limit Theorem
1
22
T1
22
Stationary Processes
1
23
T1
23
Mean, Correlation
1
24
T1
& Covariance functions
24
Power Spectral Density
1
25
T1
25
Ergodic Processes
1
26
T1
26
Gaussian Process
1
27
T1
27
Transmission of a Random Process
1
28
T1
Through a LTI filter
28
Noise sources and types
1
29
T1
29
Noise figure and noise temperature
1
30
T1
30
Noise in cascaded systems
1
31
T1
31
Narrow band noise
1
32
T1
32
PSD of in-phase and quadrature
1
33
T1
noise
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33
Noise performance in AM systems
3
34
T1
34
Noise performance in FM systems
1
35
T1
35
Pre-emphasis and de-emphasis
1
36
T1
36
Capture effect and threshold effect
1
37
T1
34
Introduction to Information
1
38
T2
35
Entropy & Average information
1
39
T2
36
Discrete Memory less channels &
1
40
T2
Channel Capacity
37
Hartley - Shannon law
1
41
T2
38
Source coding
2
43
T2
theorem
39
Huffman coding
2
45
T2
40
Shannon - Fano codes
2
47
T2
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INDEX
S.
NO.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
TABLE OF CONTENT
TITLE
AMPLITUDE MODULATION
PART A
PART B
Super heterodyne Receiver
DSBSC
Amplitude Modulation
Envelope Detector
Filter and phase shift method
Weaver method
Comparison of AM
PART C
Hilbert Transform
VSB
Problem
2. ANGLE MODULATION
PART A
PART B
Comparison of NBFM & WBFM
Generation of FM-Direct method
Generation of FM-Indirect method
FM detector
Foster –Seeley discriminator
NBFM & WBFM
PART C
Comparison of AM and FM
Problems
Single tone FM
3. RANDOM PROCESS
PART A
PART B
Differentiate SSS with WSS
Ergodicity Principle
Power spectral density
Central limit theorem
Covariance and auto correlation function
PART C
Problems
PAGE NO.
1
3
6
9
11
12
14
14
15
16
18
19
21
22
23
23
25
27
31
32
33
36
37
39
41
43
44
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4. NOISE CHARACTERIZATION
28
29
30
31
32
33
34
35
36
37
38
39
40
41
PART A
PART B
Noises
Pre-emphasis & De-emphasis
NB Noise
Figure of merit of FM system
Noise performance of AM receiver using envelope detection
PART C
Problems
5. INFORMATION THEORY
PART A
PART B
Shannon laws
Rate distortion theory
Huffman Theory
Mutual Information
Problem
PART C
Problems
Previous Year Question Papers
51
52
56
58
64
71
75
77
78
79
81
83
85
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UNIT I
AMPLITUDE MODULATION
PART A
1. Define modulation and what are the types of analog modulation?
Modulation is a process by which some characteristics of high frequency carrier
signal is varied in accordance with the instantaneous value of the modulating signal.
Types:

Amplitude modulation.

Angle Modulation

Frequency modulation

Phase modulation.
2. What is the need for modulation and what are the degrees of modulation? (or)
What are the advantages of converting low frequency signal in to high
frequency signal?
(
MAY/JUNE 2013)
Needs for modulation:

Ease of transmission

Multiplexing

Reduced noise

Narrow bandwidth

Frequency assignment

Reduce the equipments limitations
Degrees of modulation
 Under modulation, m<1
 Critical modulation, m=1

Over modulation m>1
3. Define Heterodyning. (APRIL/MAY 2015)
Heterodyning means the translating or shifting in frequency. By heterodyning the
incoming signal at ωRF with the local oscillator frequency ωLO, the message is
translated to an intermediate frequency ωIF, which is equal to either the sum or the
difference of ωRF and ωIF.
4. What are the advantages of converting low frequency signal in to high
frequency signal? (or) What are the advantages of modulation? (NOV/DEC
2016)
 Reduction in the height of antenna
 Avoids mixing of signals
 Increases the range of communication
 Multiplexing is possible
 Improves quality of reception
5. How to calculate the average power of a periodic signal? (MAY/JUNE 2016)
For a periodic signal, its average normalized power is equal to the power over one
period.
𝑃 = 1 𝑇 𝑥(𝑡) 2 𝑑𝑡
5. What is Super Heterodyne Receiver?
The super heterodyne receiver converts all incoming RF frequencies to a fixed
lower frequency, called intermediate frequency (IF). This IF is then amplitude and
detected to get the original signal.
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6. What is single tone and multi tone modulation?
If modulation is performed for a message signal with more than one frequency
component then the modulation is called multi tone modulation.
If modulation is performed for a message signal with one frequency component
then the modulation is called single tone modulation.
7. Compare bandwidth and power requirement for AM with DSB-SC and SSBSC? (MAY/JUNE 2013)
S.
No
1
2
3
AM signal
DSB-SC
SSB-SC
Bandwidth = 2fm
Contains
USB,
Carrier
Bandwidth = 2fm
Bandwidth = fm
LSB,
Contains USB,LSB
USB,LSB
Power required is less er required is less
More Power is required for than
than
Transmission
that of AM.
AM &DSB-SC
8. Define Demodulation.
Demodulation or detection is the process by which modulating voltage is
recovered from the modulated signal. It is the reverse process of modulation. The
devices used for demodulation or detection are called demodulators or detectors. For
amplitude modulation, detectors or demodulators are categorized as,
 Square-law detectors
 Envelope detectors
9. What are the advantages of VSB-AM? (APRIL/MAY 2011)

It has bandwidth greater than SSB but less than DSB system.

Power transmission greater than DSB but less than SSB system.

No low frequency component lost. Hence it avoids phase distortion.
10. Define SSB-SC and DSB-SC

SSB-SC stands for Single Side Band Suppressed Carrier

When only one sideband is transmitted, the modulation is referred to as Single
side band modulation. It is also called as SSB or SSB-SC.
DSB-SC:
After modulation, the process of transmitting the sidebands (USB, LSB) alone
and suppressing the carrier is called as Double Side Band-Suppressed Carrier.
11. Define Coherent Detection (APRIL/MAY 2013)
During Demodulation carrier is exactly coherent or synchronized in both the
frequency and phase, with the original carrier wave used to generate the DSB-SC
wave. This method of detection is called as coherent detection or synchronous
detection.
12.What is image frequency? (NOV/DEC-2014)
The local oscillator frequency (fo), input signal frequency (fs) and intermediate
frequency (fi) are related as f0 – fs=fi that is f0=fs+fi .If some other frequency
fsi=fs+2fi appear at the input of mixer, it produces fi at the output of mixer.This
interferes with the desired IF,since it is same as IF.The frequency is called image
frequency. Thus image image frequency gets converted to IF range and it is amplified
by IF amplifier.
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13. Draw the frequency spectrum of VSB. Where it is used?(APRIL/MAY 2015)
VSB is used for TV transmission, since low frequencies near f c represents picture
details. They are unaffected by VSB.
14.A transmitter radiates 9 kW without modulation and 10.125 kW after modulation.
Determine depth of modulation. (APR/MAY 2013)
Depth of modulation:
Therefore,
=1.125-1
=0.125
ma2=0.125X2
=0.250
ma=0.50
15. Suggest a modulation scheme for the broadcast video transmission and
justify.
(NOV/DEC 2016)
Vestigial Sideband modulation (VSB) is used for video transmission for the
following reasons:
1. Video signal exhibits a large bandwidth and significant low-frequency content
which suggests the use of VSB.
2. The circuitry for demodulation in the receiver should be simple and therefore
cheap.
PART-B
1.Explain With Block Diagram Super Heterodyne Receiver? (April/May 2015,
MAY/JUNE 2016)
In a broadcasting system whether it is based on amplitude modulation or
frequency modulation, the receiver not only have the task of demodulating the
modulated signal, but it is also required to perform some other system functions.
Carrier frequency tuning, the purpose of which is to select the desired signal
(i.e.) desired radio or TV station) Filtering, which is required to separate the desire
signal from other modulation signals that may be picked up along the way.
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Amplification, which is intended to compensate for the loss of signal power incurred in
the course of transmission.
R.F Section
The incoming amplitude modulated wave is picked up by the receiving antenna and is
fed to the RF section. The RF section consists of a pre selector and an RF Amplifier.
The pre selector is a band pass filter with an adjustable centre frequency that is tuned
to the desired carrier frequency of the incoming signal. The main use of the preselected
is to provide sufficient band limiting to prevent undesired ratio in frequency signal or
image signal. The effectiveness of suppressing unwanted image signals increases as
the number of selective stages in the RF section increases and as the ratio of
intermediate to signal frequency increases. R.F amplifiers are used for better
selectivity.
Fig. 1 Super Heterodyne Receiver
Frequency Changer
The combination of mixer and local oscillator provides a heterodyning function
whereby the incoming signal is converted to a predetermined fixed intermediate
frequency, usually lower than the incoming carrier frequency. This frequency translation
is achieved without disturbing the relation of the sidebands to the carrier. The result of
heterodyning is to produced an intermediate frequency carrier defined by fIF = flo –fRF
Where fLO is the frequency of the local oscillator and fRF is the carrier
frequency of the incoming RF signal. Since the output of the frequency his neither the
original input frequency not the final baseband frequency, it is called as intermediate
frequency. Sometimes the frequency changer circuits are referred to as the first
detector, in which case the demodulator i s called as second detector.
IF Section
The IF section consists of one or more stages of turned amplification
with
a
bandwidth corresponding to that required for the particular type of modulation that the
receiver intended to handle. The IF section provides most of the amplification purpose
of which is to recover the baseband or message signal.
If coherent detection is used, then a coherent signal source must be provided
in the receiver.
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Audio Amplifiers
The final stage of the super heterodyne receiver consists of one or more audio
amplifiers which is used for the power amplification of the recovered message signal.
Image frequency and its rejection ratio
In a super heterodyne receiver, the mixer will develop and intermediate
frequency output when the input signal frequency is greater or less than the local
oscillator frequency by an amount equal to intermediate frequency.
Amplitude Limiter
The basic difference between AM and FM super heterodyne receiver lies in the
use of an FM Demodulator such as limiter frequency discriminator. In FM system
the message signal is transmitted by the instantaneous value of carrier signal & its
amplitude remain constant. Therefore any variation of the carriers amplitude at the
receiver input must result from noise or interference. An amplitude limiter following the
IF section is used to remove amplitude variations by clipping the modulated wave is
rounded by a band pass filter that suppresses harmonics of the carrier frequency. Thus
the filter output is again sinusoidal, with an amplitude that in practically independent of
the carrier amplitude of the receiver input. The Fig shows basic block diagram of FM
super heterodyne receiver.
Performance Parameters of Receivers
The performance of a Radio receiver is measured on the basic of its selectivity,
sensitivity, fidelity and image frequency rejection selectivity.
Selectivity
The selectivity is the ability of the receiver to select a signal of a desired
frequency while rejecting all others. The selectivity of the receiver is obtained partially
by RF amplifier and mainly by IF amplifiers. The selectivity shows the attenuation that
the receiver offers to signals at frequencies near to the one to which it is tuned. Fig.
shows the typical selectivity curve of the receiver. The selectivity depends upon tuned
LC circuits used in RF and IF stages, fr is the resonating (tuned) frequency and Q is
quality factor of these LC Circuits, As shown in Fig. bandwidth should be narrow for
better selectivity. Hence Q of the coil should be high.
Sensitivity
The ability of the receiver to pick up weak signals and simplify them is called
sensitivity. It is often defined in terms of the voltage that must be applied to the receiver
input terminals to give the standard output power, measured at the output terminals.
As the gain of the receiver is increased, sensitivity is also increased. The
sensitivity is expressed in micro volts or decibels. Fig.shows the typical sensitivity curve
of a receiver. As shown in the Fig., the sensitivity is decreased (i.e., voltage is
increased) at high frequencies.
Fidelity
Fidelity is a measure of the ability of a communication system to produce at the
output of the receiver, an exact replica of the original source information. This may also
be defined as the degree to which the system accurately reproduces at the output, the
essential characteristics of signals that are impressed upon the input.
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Signal to noise Ratio
Signal to noise Ratio may be defined as the ratio of signal power to noise power
at the receiver output. A good receiver should have high signal to noise ratio (SNR)
which indicates negligible noise present at the output.
Image Frequency Rejection
We know that local oscillator frequency is made higher than the signal frequency
such that f0 – fs = fi . Here fi is IF. That is f0 = fs + fi. The IF stage passes only fi . If the
frequency fi = fs +2fi appears at the input of the mixer, then the mixer will produce
different frequency equal to fi . This is equal to IF. The frequency fsi is called image
frequency and is defined as the signal frequency plus twice the IF. The image
frequency is converted in the IF stage and it is also amplified by IF amplifiers. This is
the effect of two stations being received simultaneously. The image frequency rejection
is done by tuned circuit in the RF stage. It depends upon the selectivity of the RF stage.
The image rejection should be done before the RF stage.
2.With The Help Of Neat Diagram Explain The Generation Of DSB-SC Using
Balanced Modulator And Ring Modulator. (Nov/Dec 2010, MAY/JUNE
2016,NOV/DEC 2016)
In DSB – SC, the transmitted wave consists of only upper and lower sidebands.
Transmitted power is saved here through the suppression of the carrier wave because
it does not contain any useful information, but the channel bandwidth required is the
same as before.
Expression for DSB –SC:
Let the modulating signal,
The carrier signal
Comparing equation (1.57) and (1.58) the carrier terms Vc sin ωct is missing and only
upper and lower sidebands are present.
Fig.2 Spectrum of DSB-SC
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In this fig, the carrier term fc is suppressed. It contains only two sideband terms having
the frequency of (fc – fm) and (fc + fm).
Generation of DSB – SC – AM
There are two ways of generating DSB – SC – AM such as ,
(i) Balanced modulator,
(ii) Ring modulator.
Balanced Modulator
The circuit that is very commonly used for DSB – SC generation.
In balanced modulator, two non-linear devices are connected in the balanced mode, so
as to suppress the carrier wave. It is assumed that the two transistors are identical and
the circuit is symmetrical. Since the operation is confined in non-linear region of its
transfer characteristics.
Fig.3 Balanced modulator
modulating voltage across the two windings of a centre-tap transformer is equal,
The and
opposite in phase,
i.e., Vm = V'm
Ring Modulator (or) Diode Balanced
Modulator Introduction:
The one of the most popular method of generating a DSB – SC wave is ring modulator.
The circuit employs diodes as non-linear devices and the carrier signal is
connected between centre taps of the input and output transformers.
There is no need for a band pass filter at the output. The four diodes are controlled by a
carrier Vc(t) of frequency fc
The carrier signal acts as a switching signal to alternate the polarity of the
modulating signals at the carrier frequency. For better understanding of the operation,
assume that the modulating input is zero. Only carrier signal is present.
Fig. 4 Diode Balanced modulator
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Positive Half Cycle of Carrier:
Diodes D1 and D2 are form ward biased. AT this time D3 and D4 are reverse
biased and act like open circuits. The current divides equally in the upper and lower
portions of the primary winding of T12 .
The current in the upper part of the winding produces a magnetic field that is
equal and opposite to the magnetic field produced by the current in the lower half of the
secondary. Therefore, these magnetic fields cancel each other out and no output is
induced in the secondary. Thus the carrier is effectively suppressed.
Negative Half Cycle of Carrier:
When the polarity of the carrier reverses. Diodes D1 and D2 are reverse biased
and diodes D3 and D4 conduct. Again the current flows in the secondary winding of Tr1
and the primary winding of Tr2.
The equal and opposite magnetic fields produced in Tr2 cancel each other out
and thus result in zero carrier output. The carrier is effectively balanced out.
Principle of Operation:
When both the carrier and the modulating signals are present, during positive
half cycle of the carrier, diodes D1 and D2 conduct, while diodes D3 and D4 does not
conduct.
During negative half cycle of the carrier voltage diodes D3 and D4 conduct and
D1 and D2 does not conduct.
Fig. 5. Graphical representation of DSB-SC signals
Phase Reversal
When polarity of the modulating signal changes, the result is a 180 phase
reversal.
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At the time, during the positive half cycle of the carrier, diodes D3 and D4 are in
forward bias and the negative half cycle of the carrier, diodes D1 and D2 are in reverse
bias. Consider the modulating signal Vm (t) and carrier signal Vc (t) , such that,
The equation (1.76) shows that the output is free from the carrier and other
higher order terms, and it contains upper and lower sidebands only.
The ring modulator circuit is also known as double balanced modulator because
comparing to balanced modulator here two more diodes are used.
Advantages:
1. DSB –SC is more efficient in transmitted power as compared to DSBFC .
2. DSB –SC has better signal to noise ratio as compared to single side band (SSB)
transmission.
Disadvantage:
Even though the carrier is suppressed the bandwidth of DSBSC remains same
as DSBFC.
3.i). Define amplitude modulation. How an amplitude modulated signal can be
generated using a non linear modulator circuit.(NOV/DEC 2012,NOV/DEC 2016)
Amplitude modulation:
Amplitude modulation is the process by which amplitude of the carrier signal is
varied in accordance with the instantaneous value of the modulating signal,but
frequency and phase remains constant.
Non linear modulator circuits:
A simple diode can be used as a non linear modulator by restricting its
operation to non linear operation of its characteristics.
The undesired frequency terms are filtered out by a band pass filter.
The methods for generation of AM waves using non linear property are broadly
divided into two types
(a)square law modulator
(b)Balance modulator
(a)Square law modulators:
Any device operated in non linear region of its output characteristics is capable
of producing amplitude modulated waves when the carrier and modulating signals are
fed at the input. Thus a transistor, a triode tube,a diode etc. may be used as the square
law modulator. A square law modulator circuit consists of the following:
(i) A non linear device
(ii) A bandpass filter
(iii)A carrier source and modulating signal
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Fig.6 The square law modulator
Consider a non linear device to which a carrier c(t)= A cos(2Π fct) and an information
signal m(t) are fed simultaneously as shown in figure1. The total input to the device at
any instant is
As the level of the input is small very small, the output can be considered up to square of the
input
Taking Fourier transform on both sides we get,
Therefore the square law device output Vo consists of the dc component at f=0
The information signal ranging from 0 to W Hz and its second harmonics
Signal at fc and 2fc Frequency band centered at fc with a deviation of ± W Hz.
The required AM signal with a carrier frequency fc can be separated using a
bandpass filter at the output of the square law device. The filter should have a
lower cutoff frequency ranging between 2W and (fc - W) and upper cut-off
frequency between (fc+W) and 2fc Therefore the filter output is
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The output AM signal is free from distortion and attenuation only when(f c-W)2W or
fc<3W
3 ii)Draw An Envelope Detector Circuit Used For The Demodulation Of Am And
Its Operation. (MAY/JUNE 2012,MAY/JUNE 2013,APRIL/MAY 2010,APRIL/MAY
2015)
Diode Detector or Envelope Detector
The most commonly used AM detector is simple diode detector as the shown in
Fig. The AM signal at fixed IF is applied to the transformer primary. The signal at
secondary is half wave rectified by diode D. This diode is the detector diode. The
resistance R is load resistance to rectifier and C is the filter capacitor. In the positive
half cycle of AM signal diode conducts and currents flows through R, whereas in
negative half cycle, the diode is reverse biased and no current flows. Therefore only
positive half of the AM wave appears across resistance R as shown in figure. The
capacitor across capital R provides low impedance at the carrier frequency and much
higher impedance at the modulating frequency. Therefore capacitor reconstructs the
original modulating signal as shown in figure and high frequency carrier is removed.
Fig 7 Diode detector
Negative peak clipping in diode detector:
This is the distortion that occurs in the output of diode detector because of
unequal ac and dc load impedances of the diode. The modulation index is
defined as Em /Ec.
Fig.8 Diode detector waveforms
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Therefore it can also be defined as Im /Ic with
Im =
and Ic =
Here
is audio diode load impedance and
is the dc diode resistance. The
audio load resistance of the diode is smaller than the dc resistance. Hence the AF
current
is larger, in proportion to dc current. This makes the modulation index in the
demodulated wave relatively higher than that of modulated wave applied at the detector
input. This introduces the distortion due to over modulation in the detector signal for
modulation index near 100%. This is illustrated in Fig. In the figure observe that the
negative peak of the detected signal takes place because of over modulation effect
taking place in detector.
Diagonal Clipping in Diode Detector
As the modulating frequency is increased, the diode ac load impedance, Zm does not
remain purely resistive. It does have reactive component also. At high modulation
depths, the current changes so fast that the time constant of the load does not follow
the changes. Hence the current decays slowly as shown in fig. The output voltage
follows the discharge law of RC circuit. This introduces distortion in the detected signal
and it is called diagonal peak clipping.
Fig.9 Diagonal peak clipping
4.(i) Explain The Filter Method And Phase Shift Method To Produce SSB.
SSB – SC – AM waves can by generated in two ways.
1.
Frequency discrimination (or) Filler method
2.
Phase discrimination method.
Phase discrimination method itself can be divided into two types.
1.
Phase shift method.
2.
Modified phase shift (or) weaver's method.
Suppression of Unwanted Sideband
In the previous subsection we studied the techniques to suppress the carrier. To
generate single sideband suppressed carrier (SSBSC), we have to suppress the carrier
as well as one of the
sidebands. In this section let us consider the techniques to suppress one of the
sidebands. These techniques are
(i) filter method,
(ii) phase shift method and
(iii) The 'third' method.
Filter Method to Produce SSB
Fig.shows the block diagram of filter method to suppress one sideband. As
shown in the block diagram, the balanced modulator produces DSB output. This DSB
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signal contains both the sideband. The filter must have a flat pass band and extremely
high attenuation outside the pass band. In order to have this type of response the Q of
the tuned circuits must be very high. The required value of Q factor increases as the
difference between modulating frequency and carrier frequency increases. Carrier
frequency is usually same as the transmitter frequency increases. Carrier frequency is
usually same as the transmitter frequency. For higher transmitting frequencies them
required value of Q is so high that there is no practical way of achieving it. In such
situation, initial modulation is carried out at a low frequency carrier say 100 kHz by the
balanced modulator. Then the filter suppresses one of the sidebands. The frequency of
the SSB signal generated at output of filter is very low as compared to the transmitter
frequency. The frequency is boosted up to the transmitter frequency by the balanced
mixer and crystal oscillator. This process of frequency booting is also called as up
conversion. The SSB signal having frequency equal to the transmitter frequency is then
amplified by the linear amplifiers.
Fig.10 Filter method to suppress sideband
Phase Shift Method to Generate SSB
Fig. 11shows the block diagram of phase shift method to generate SSB. The carrier
signal is shifted by 90 and applied to the balanced modulator M1. The modulating signal is
also directly applied to the balanced modulator M2. The modulating signal is phase shifted
by 90 and applied to balanced modulator M2. Both the modulators produce an output
consisting of only sidebands. The upper balanced modulator (M1 ) generates upper
sideband and lower sideband, but upper sideband is shifted by +90 whereas lower
sideband is shifted by -90.The output of balanced modulators are added by the summing
amplifier. Since upper sidebands of both the modulators are phase shifted by +900, they
are in phase and add to produce double amplitude signal. But lower sideband of the
balanced modulator s are (+90 , -90 ) 180 out of phase and hence cancel each other.
Thus the output of summing amplifier contains only upper sideband SSB signal. The carrier
is already suppressed by balanced modulators.
Fig.11 phase shift method to generate SSB
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4 (ii) How SSB Can Be Generated Using Weaver’s
Method.(MAY/JUNE 2012) Weaver's Method or Third Method of
SSB Generation
Principle: It uses two carriers: One is audio subcarrier at frequency fo and other is RF
carrier at frequency fc .
Block diagram and operation
Fig. 1.30 shows the block diagram of weaver's method.
The input to the modulator is s(t) = cos( 2
fmt). It is the modulating signal of
frequency fm.
Fig.12 Block diagram of weaver's method
5. Write The Comparison Of Amplitude Modulation Systems.(MAY/JUNE 2012)
Description AM with carrier DSB – SC – AM SSB – SC on
AM
Band width
2fm
Power
Saving for
Sinusoid al
33.33%
Power
Saving for
33.33%
non Sinusoidal
Generation
methods Easier to generate
Detection
methods
Simple
&
Inexpensive
2fm
fm
VSB - AM
fm <BW<2fm
66.66%
83.3%
75%
50%
75%
75%
Not difficult
Difficult
More difficult Difficult.
But
to
easier to generate
generate
than SSB-SC
More difficult
Difficult
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PART C
1. Explain Hilbert Transform With An Example. (APRIL/MAY 2015)
Hilbert Transform
If every frequency components of a signal f(t) is shifted by (-π/2) the resultant signal fh
(t) is the Hilbert transform of f(t).
Fig.13 phase shifting system
A signal f(t) is passed through a phase shift system H(ω) and the output fh (t) shown in
fig.
The characteristics of the of the system specified as follows:
i)
The magnitude frequency components present in f(t) remains unchanged when it is
passed through the system that is H(ω) = 1 and
ii) The
phase of the positive frequency components if shifted by -π/2 . Since the phase
spectrum (ω) has an odd symmetry, the phase of the negative frequency components
is shifted by π/2. H(ω) and (ω) are plotted in Fig by continuous and dotted lines
respectively.
Fig.14 Transfer function -π/2 phase shifter
Properties of Hilbert transform
Hilbert transform has the following properties
1. A signal f(t) and its Hilbert transform have the same magnitude spectrum.
2 A signal f(t) and its Hilbert transform sh(t) have the same energy density spectrum.
3 If the Hilbert transform of fh(t) is –f(t), then fh(t) is Hilbert transform of s(t) that is if
Where H denotes the Hilbert transform.
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4. A signal f(t) and its Hilbert transform fh(t) are mutually orthogonal over the time
interval (-∞,∞) that is
5. A signal f(t) and its Hilbert transform fh(t) have the same auto correlation function.
Some useful Hilbert transform.
Application of Hilbert transform pair
 Generation of SSB signal
 Design of minimum phase type filters
 Representation of band pass signals.
2. With suitable block diagrams and equations show how will you
generate VSB signals (NOV/DEC 2013)
Generation of VSB signals:
A vestigial-sideband system is a compromise between DSB and SSB It inherits
the advantages of DSB and SSB but avoids their SSB. It inherits the advantages of
DSB and SSB but avoids their disadvantages.
VSB signals are relatively easy to generate and their bandwidth is VSB signals
are relatively easy to generate and their bandwidth is only slightly (typically 25 percent)
greater than that of SSB signals.
In VSB, instead of rejecting one sideband completely as in SSB, a gradual cutoff of one sideband is accepted. All of the one sideband is transmitted and a small
amount (vestige) of the other sideband is transmitted The filter is allowed to have a
nonzero transition band.
The roll-off characteristic of the filter is such that the partial suppression of the
transmitted sideband in the neighborhood of the carrier is exactly compensated for by
the partial transmission of the carrier is exactly compensated for by the partial
transmission of the corresponding part of the suppressed sideband.
Our goal is to determine the particular H( f ) required to produce a modulated
signal s( t) with desired spectral characteristics such with desired spectral
characteristics, such that the original baseband signal m( t) may be recovered from s(
t) by coherent detection.
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Fig. 15 Filtering scheme of the generation of VSB modulated wave
Fig. 16 Spectrum of VSB SC
Amplitude response of VSB filter:
To obtain baseband signal m(t) at coherent detector output, we require V o(f) to be
a scaled version of M(f),Therefore we can write
Now equation(a) can be written as
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UNIT 2 ANGLE MODULATION
PART A
1. What do you understand by narrowband FM?
When the modulation index is less than 1, the angle modulated systems are
called low index. The bandwidth requirement of low index systems is approximately
twice of the modulating.
2. Define frequency modulation and modulation index of frequency modulation and
phase modulation? (MAY/JUNE 2013) (NOV/DEC 2016)
Frequency modulation:
Frequency modulation is defined as the process by which the frequency of the
carrier wave is varied in accordance with the instantaneous amplitude of the
modulating or message signal.
Modulation index of frequency modulation.
It is defined as the ratio of maximum frequency deviation to the modulating
β = δf/fm
Phase modulation:
Phase modulation is defined as the process of changing the phase of the carrier
signal in accordance with the instantaneous amplitude of the message signal.
3. What are the types of Frequency Modulation?
Based on the modulation index FM can be divided into types. They are Narrow
band FM and Wide band FM. If the modulation index is greater than one then it is wide
band FM and if the modulation index is less than one then it is Narrow band FM
4. What is the basic difference between an AM signal and a narrowband FM signal?
In the case of sinusoidal modulation, the basic difference between an AM signal
and a narrowband FM signal is that the algebraic sign of the lower side frequency in
the narrow band FM is reversed.
5. What are the two methods of producing an FM wave?
Basically there are two methods of producing an FM wave. They are,
i) Direct method: In this method the transmitter originates a wave whose
frequency varies as function of the modulating source. It is used for the generation of
NBFM
ii) Indirect method: In this method the transmitter originates a wave whose phase is a
function of the modulation. Normally it is used for the generation of WBFM where
WBFM is generated from NBFM.
6. Compare WBFM and NBFM. (APRIL/MAY 2011,2015) (NOV/DEC-2013)
S.NO
WBFM
NBFM
1
Modulation index is greater than 1 Modulation index less
than 1
2
Frequency deviation 75 KHz
Frequency deviation 5
KHz
3
Bandwidth 15 times NBFM
Bandwidth 2fm
4
Noise is more suppressed
Less suppression of noise
5
Used in broadcasting
Used in mobile
communication
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7.Define phase deviation and frequency Deviation? APRIL/MAY 2014)
Phase deviation:
The maximum phase deviation of the total angle from the carrier angle is called
phase deviation.
Frequency Deviation:
The maximum departure of the instantaneous frequency from the carrier
frequency is called frequency deviation.
8. State the Carson’s rule.(APRIL/MAY 2015, NOV/DEC 2015)
An approximate rule for the transmission bandwidth of an FM Signal generated
by a single tone-modulating signal of frequency f m (max) is defined as
∴
BW=2[δ + fm(max)]
9.What is the use of crystal controlled oscillator?
The crystal-controlled oscillator always produces a constant carrier frequency
thereby enhancing frequency stability.
10.How will you generate message from frequency-modulated signals?
First the frequency-modulated signals are converted into corresponding
amplitude-modulated signal using frequency dependent circuits. Then the original
signal is recovered from this AM signal.
11.What are the disadvantages of balanced slope detector?

Amplitude limiting cannot be provided

Linearity is not sufficient

It is difficult to align because of three different frequency to which various tuned
circuits to be tuned.

The tuned circuit is not purely band limited.
12. What are the applications of phase locked loop (PLL)?
(NOV/DEC 2013)
Phase locked loops are used for various purposes in AM and FM
communication.
(i)Automatic frequency correction in FM transmitter uses PLL to
keep carrier frequency constant. (ii)PLL is used direct FM Transmitter to generate
WBFM signals.
(iii) PLL is also used in FM demodulators.
13.Differentiate phase and frequency modulation.
S.No Phase Modulation(PM)
1 Phase of the carrier varies as per
amplitude variations of modulating
signal.
2 Instantaneous phase deviation,
ϕ(t ) = k Em(t )
Frequency Modulation (FM)
Frequency of the carrier varies as per
amplitude variations of modulating
signals.
Instantaneous frequency deviation,
∆ (t ) = k Em(t )
3
Modulation index = k Em
Modulation index = k Em
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14.A 80 MHz carrier is frequency modulated by a sinusoidal signal of 1V
amplitude and the frequency sensitivity is 100 Hz/V. Find the approximate
bandwidth of the FM waveform if the modulating signal has a frequency of 10
kHz. (APR/MAY 2010)
Ans: Frequency Sensitivity = 100 Hz/ volt.
Amplitude of modulating signal = 1V
Hence maximum frequency deviation, δ =100 Hz / volt ×1V= 100 kHz
Frequency of modulating signal, fm = 10kHz
∴
BW = 2 [δ + fm (max)]= 2 [100 +10×103 ]
BW = 20.2 kHz
15. What is the need for Pre-emphasis? (MAY/JUNE 2016,NOV/DEC 2016)
Pre emphasis is a process used to boost the input frequency range which is
most susceptible to noise.
PART B
Write The Comparison Of Wideband And Narrowband FM (NOV/DEC 2011,
MAY/JUNE 2013 )
1.
SI. Parameter
No Characteristics
1. Modulation index
2. Maximum
deviation
3. Range of
modulating
Frequency
4. Bandwidth
5. Maximum
modulation
6. Pre-emphasis and
De-emphasis
7. Noise
Wideband
FM
Greater than
1
75 KHz
Narrowband FM
30 Hz to 15
KHz
30 Hz to 3 KHz
Less than (or) slightly
greater than 1
5 KHz
Large, about 15 times higher Small. Approximately same
than BW of narrow band
as that of AM. BW=2fm
FM.
BM=2(ΔF+F
m)
5 to 2500
Slightly greater than 1
Needed
Needed
Noise is more suppressed
Less suppressing of noise
8. Applications
Entertainment broadcasting
FM mobile communication
9. Side bands
Spectrum contains infinite
number of side bands and
carrier
Spectrum contains two
sidebands and carrier.
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2.Explain With Diagram The Generation Of FM Using Direct Method. (APRIL/MAY
2015, NOV/DEC 2016)
Direct FM
Direct FM can be obtained by using FET and varactor diode. These methods
are discussed next.
(i).FET Reactance Modulator
Fig shows the basic circuit of FET reactance modulator. It behaves as
reactance across terminals A-B. The terminals A-B of the circuit may be connected
across the tuned circuit of the oscillator to get FM output. The varying voltage
(modulating voltage) V, across terminals A-B changes reactance of the FET. This
change in reactance can be inductive or capacitive.
Fig.1 FET reactance modulator
(ii).Frequency Modulation using varactor Diode
All the diodes exhibit small junction capacitance in the reverse biased condition.
The varactor diodes are specially designed to optimize this characteristic. The junction
capacitance of the varactor diode changes as the reverse bias across it is varied. The
variations in capacitance of this diode are wide and linear. The varactor diodes provide
the junction capacitance in the range of 1 to 200 pF. Fig shows how varactor diode
can be used to generate FM. L1 and C1 form the tank circuit of the carrier oscillator.
The capacitance of the varactor diode depends upon the fixed bias set by R1 and R2
and the AF modulating signal. Either R1 or Rs is made variable so that the center
carrier frequency can be adjusted over a narrow range. The Radio Frequency Choke
(RFC) has high reactance at the carrier frequency to prevent the carrier signal from
getting into the modulating signal circuits. At positive going modulating signal adds to
the reverse bias applied to the varactor diode D, which decreases its capacitance and
increases the carrier frequency. A negative going modulating signal subtracts from
bias, increasing the capacitance, which decreases the carrier frequency.
Fig.2 Varactor diode for FM generation
The frequency of the LC oscillator changes due to temperature effects. Hence crystals
are used in FM generators to provide frequency stability.
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3. Explain Indirect Method Of Generating FM Signal (APRIL/MAY
2015,NOV/DEC2016,MAY/JUNE 2016)
Indirect method (Armstrong method)
In this method of FM generation, the modulating signal is integrated and it is
phase
modulated by crystal oscillator to get narrow band FM signal which later passed on to
a frequency multiplier to get a wideband FM signal. The block diagram of an
Armstrong method is shown in Fig
Fig.3 Block diagram of Armstrong method for generating wideband FM signal
Fig.4 Block diagram of Frequency multiplier
Advantages:
i)
FM is generated from PM indirectly.
ii)
Modulation takes place at low carrier frequency.
4.(i). Explain The Function Of Any Two FM Detector Circuit.(MAY/JUNE
2014,NOV/DEC 2016)
The FM receivers also super heterodyne receivers. But they have different
types of demodulators or detectors. FM receivers have amplitude limiters which are
absent in AM receivers. The AGC system of FM receivers is different than that of AM
receivers. RF amplifiers, mixers, local oscillators IF amplifiers, audio amplifiers etc. all
are present in FM receivers
The detection of FM is totally different compared to AM. The FM detector should be
able to produce the signal whose amplitude is proportional to the deviation in the
frequency of signal. Thus the job FM detector is almost similar to frequency to voltage
convertor. Here we will discuss these types of FM detectors. Slope detectors, phase
discriminator and ratio detector.
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Round – Travis detector or balanced slope detector (frequency Discriminator)
Fig.5 shows the circuit of balanced slope detector. It consist of two identical
circuit connected back to back . The FM signal is applied to the turned LC circuit. Two
turned LC circuits are connected in series . The inductance of this secondary turned
LC circuit is coupled with inductance of the primary (or input side) LC circuit . Thus it
forms a turned transformer. In fig., the upper turned circuit is shown as T1 and lower
turned circuit is shown as T2. The input side LC circuit is turned to fc, carrier
frequency. T1 tuned to fc- , which represents the minimum frequency of FM signal.
The input FM signal is coupled to T1 and T2 180 out of phase. The secondary side
tuned circuits (T1 and T2) are connected to diodes D1 and D2 with RC loads. The total
output
is equal to difference between
and , since they subtract
Fig. shows
the characteristic of the balanced slope detector. It shows
with respect to input
frequency.
Fig.5 Balanced Slope detector
Fig.6 Characteristic of balanced slope detector, or 'S' curve
Frequency Discriminator
Fig.shows the block diagram of a frequency discriminator which is based on the
principle of slope detection.
There are two slope circuits in Fig. Their transfer functions are as follows:
Fig.7 frequency discriminator
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4.(ii) With The Phasor Representation Explain The Foster Seeley Discriminator
And Ratio Detector. (APRIL/MAY 2015,MAY/JUN 2016, NOV/DEC 2016)
Foster-Seeley Discriminator (Phase Discriminator)
The phase shift between the primary and secondary voltages of the tuned transformer
is a
function of frequency. It can be shown that the secondary voltage lags primary voltage by
90 degree at the carrier center frequency. The carrier frequency
) is the resonance
(or tuned) frequency of the transformer. Foster-Seeley discriminator utilizes this
principle for FM detection. Fig shows the circuit diagram of basic Foster-Seeley
discriminator. In the figure observe that capacitor C3 passes all the frequencies of FM.
Fig. 8 Foster-Seeley discriminator
The output of upper rectifier is V01 and lower rectifier is V02. The net output
V0=V01-V02. Since V01 │VD1│ and V02 |VD2| output V0 | V01| |VD1|.Thus
the net output depends upon the difference between magnitudes of VD1and VD2 .
At the centre frequency both VD1and VD2 will be equal, since V2 will have 90
phase shift with V1. Fig.shows how VD1and VD2 are generated from V1 and V2. It
shows that |VD1|=|VD2|. Hence the net output of the discriminator will be zero. Now
consider the situation when input frequency increases above fc. Hence the phase shift
between V1 and V2 reduces. Therefore |VD1| is greater than |VD2|. This is shown by
vector addition in Fig.. Hence the net output V0=V01-V02 will be positive. Thus the
increase in frequency increases output voltage. Now consider the situation when
frequency reduces below fc. This makes |VD1| less than |VD2|.
This is shown is Fig.8 Hence the output V0=V01-V02 will be negative. Thus the
Foster- Seeley discriminator produces output depending upon the phase shift, The
linearity of the output depends upon the linearity between frequency and induced
phase shift. The characteristic of the Foster-Seeley discriminator (i.e. S-curve) is
similar to that shown in Fig.8 with more linearity in the operation. Phase shift between
V1 and V2.
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Ratio Detector:
Ratio detector can be obtained by slight modifications in the Foster -Seeley
discriminator. Fig. shows the circuit diagram of ratio detector .As shown in diagram
the diode D2 is reversed, and output is taken from different points. The polarity of
voltage in the lower capacitor is reversed, since connections of diode D2 are
reversed. Hence the voltages V01 and V02 across two capacitors add. We know that
when V01 increases, V02 decreases and vice-versa as we have seen in FosterSeeley circuit. Since V‟0 is sum of V01 and V02, it remains constant.
Fig. 9 Ratio Detector
Advantages:
1) As compared to Foster – Seeley circuit, this circuit does not respond to amplitude
variations.
2) The output is bipolar (i.e., positive as well as negative).
Disadvantages:
1) Ratio detector does not tolerate variation in signal strength over performed period.
2) It requires an ACC signal.
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PART C
1. Compare Am and FM in detail.
AM
FM
AM stands for Amplitude
Modulation
AM method of audio transmission
was first successfully carried out in
the mid 1870s.
In AM, a radio wave known as the
"carrier" or "carrier wave" is
modulated in amplitude by the
signal that is to be transmitted. The
frequency and phase remain the
same.
AM has poorer sound quality
compared with FM, but is cheaper
and can be transmitted over long
distances. It has a lower bandwidth
so it can have more stations
available in any frequency range.
AM radio ranges from 535 to 1705
KHz (OR) Up to 1200 bits per
second.
Twice the highest modulating
frequency. In AM radio
broadcasting, the modulating
signal has bandwidth of 15kHz,
and hence the bandwidth of an
amplitude-modulated signal is
30kHz.
Equidistant
FM stands for Frequency Modulation
Complexity
Transmitter and receiver are
simple but syncronization is
needed in case of SSBSC AM
carrier.
Noise
AM is more susceptible to noise
because noise affects amplitude,
which is where information is
"stored" in an AM signal.
Transmitter and receiver are more
complex as variation of modulating
signal has to beconverted and
detected from corresponding
variation in frequencies.(i.e. voltage
to frequency and frequency to
voltage conversion has to be done).
FM is less susceptible to noise
because information in an FM signal
is transmitted through varying the
frequency, and not the amplitude.
Stands for
Origin
Modulating differences
Pros and cons
Frequency Range
Bandwidth Requirements
Zero crossing in
modulated signal
FM radio was developed in the
United states in the 1930s, mainly
by Edwin Armstrong.
In FM, a radio wave known as the
"carrier" or "carrier wave" is
modulated in frequency by the signal
that is to be transmitted. The
amplitude and phase remain the
same.
FM is less prone to interference than
AM. However, FM signals are
impacted by physical barriers. FM
has better sound quality due to
higher bandwidth.
FM radio ranges in a higher
spectrum from 88 to 108 MHz. (OR)
1200 to 2400 bits per second.
Twice the sum of the modulating
signal frequency and the frequency
deviation. If the frequency deviation
is 75kHz and the modulating signal
frequency is 15kHz, the bandwidth
required is 180kHz.
Not equidistant
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4. Explain in detail about single tone FM.(MAY/JUNE 2016, NOV/DEC 2016)
For the single tone frequency modulation,i.e the modulating signal x(t) be a
sinusoidal signal of amplitude Em and frequency fm .
Therefore, x(t) = Em cos (2πfmt) The unmodulated carrier is represented by the
expression :ec = Ec sin (ωct + φ).
Instantaneous frequency of an FM wave
In FM, the frequency f of the FM wave varies in accordance with the modulating
voltage .
Thus,
Where Δf = kf Em and it is called as frequency deviation.
Frequency Deviation (Δf)
Frequency deviation Δf represents the maximum departure of the instantaneous
frequency fi(t) of the FM wave from the carrier frequency fc .
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Since Δf = kf Em, the frequency deviation is proportional to the amplitude of modulating
voltage (Em) and it is independent of the modulating frequency fm .
Maximum frequency of FM Wave:
The maximum frequency of FM wave is given by :
fmax = fc ± Δf
Mathematical Expression for FM:
FM wave is a sine wave having a constant amplitude and a variable instantaneous
frequency .
As the instantaneous frequency is changing continuously, the angular velocity ω of an
FM wave is the function of ωc and ωm .
Therefore, the FM wave is represented by,
As shown in fig.10, Ec sin Θ(t) is a rotating vector . If Ec is rotating at a constant
velocity ‘ω’, then we could have written that Θ(t)=ωt .
Fig.10 Phasor of single tone FM
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But, in FM , this velocity is not constant. In fact, it is changing continuously. The
angular velocity of FM wave is given as,
Modulation Index
The modulation index of an FM wave is defined as under :
The modulation index is very important in FM because it decides the bandwidth of the
FM wave which we will discuss later . The modulation index also decides the number
of sidebands having significant amplitudes .
In AM, the maximum value of the modulation index m is 1 . But, for FM, the modulation
index can be greater than 1.
Deviation Ratio
In FM broadcasting, the maximum value of deviation is limited to 75 kHz. The
maximum modulating frequency is also limited to 15 kHz.
The modulation index corresponding to the maximum deviation and maximum
modulating frequency is called as the deviation ratio .
Percentage Modulation of FM Wave
The percent modulation is defined as the ratio of the actual frequency deviation
produced by the modulating signal to the maximum allowable frequency deviation .
Thus,
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UNIT – III RANDOM PROCESS
PART A
1.
Define random variables? (MAY/JUNE 2012,NOV/DEC2010,NOVDEC
2015)
A random variable, usually written X, is a variable whose possible values are
numerical outcomes of a random phenomenon. Random variable consists of two
types they are discrete and continuous type variables.
2.
What is meant by probability distribution?
The probability distribution of a discrete random variable is a list of
probabilities
associated with each of its possible values. It is also sometimes called the probability
function or the probability mass function.
3.



What are the conditions applied in the central limit theorem?
The mean of the population of means is always equal to the mean of the
parent population from which the population samples were drawn.
The standard deviation of the population of means is always equal to the
standard deviation of the parent population divided by the square root of the
sample size (N).
The distribution of means will increasingly approximate a normal distribution
as the size N of samples increases.
4.
Define stationary process.
Stationary process is a stochastic process whose joint probability distribution
does not change when shifted in time. Consequently, parameters such as the
mean and variance, if they are present, also do not change over time and do not
follow any trends.
5. Write the equation for correlation?
The population correlation coefficient ρX,Y between two random variables X and Y
with expected values μX and μY and standard deviations ςX and ςY is defined as:
6.
What is meant by covariance?
Covariance is a measure of how much two variables change together,
and the covariance function, or kernel, describes the spatial covariance of a
random variable process or field.
7.
Define random process.(APR/MAY-2010) (NOV/DEC-2011)
A random process X(t) is a Gaussian process if for all n and all (t1 ,t2 ,…,tn ),
the
random variables have a jointly Gaussian density function.
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8.
Write the equation of Autocorrelation?(MAY/JUNE 2016)
The autocorrelation function of the output random process Y (t). By definition,
we have RY (t, u) = E[Y (t)Y (u)] where t and u denote the time instants at which
the process is observe
9.
Write the applications of random process?
The available noise power is directly proportional to temperature and it is
independent of value of resistance. This power specified in terms of temperature is
called as noise temperature. It is denoted by Te . It is given as, Te =(F−1)T A
Gaussian process can be used as a prior probability distribution over functions in
Bayesian inference.
10. What are the properties of a autocorrelation function?
Autocorrelation function of a stationary random process X(t) is defined as,
Rx(τ)=E[X(t + τ) X(t)]
for all t
(i).The mean square value of the process may be obtained from R x(τ) by simply
putting τ=0 in the above equation
2
Rx(0)=E [X (t)]
(ii)The auto correlation function Rx(τ) is an even function of
Rx(τ)= Rx(-τ)
From this property we can redefine auto correlation function like this.
Rx(τ)= E[X(t) . X(t-τ)
(iii)The autocorrelation function Rx(τ) has its maximum magnitude as τ = 0
11.State Central limit theorem.( NOV/DEC 2016,MAY/JUNE 2016)
The central limit theorem states that the sampling distribution of the mean of
any independent random variable will be normal or nearly normal, if the sample size
is large enough.
PART-B
1.Differentiate The Strict-Sense Stationary With That Of Wide Stationary
Process. (APR/MAY 2015,MAY/JUN 2016)
In mathematics and statistics, a stationary process or strict stationary process
or strong stationary process) is a stochastic process whose joint probability
distribution does not change when shifted in time. Consequently, parameters such as
the mean and variance, if they are present, also do not change over time and do not
follow any trends.
Stationarity is used as a tool in time series analysis, where the raw data is
often transformed to become stationary; for example, economic data are often
seasonal and/or dependent on a non stationary price level. An important type of non-
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stationary process that does not include a trend like behavior is the cyclo-stationary
process.
A "stationary process" is not the same thing as a "process with a distribution”.
Indeed, there are further possibilities for confusion with the use of "stationary" in the
context of stochastic processes; for example a "time-homogeneous" Markov chain is
sometimes said to have "stationary transition probabilities". Besides, all stationary
Markov random processes are time-homogeneous.
Strict-sense Stationary Process
A random process X (t ) is called strict-sense stationary (SSS) if its
probability structure is invariant with time. In terms of the joint distribution function,
X (t ) is called SSS if
(x , x ..., x )  F
F
X ( t ), X ( t )..., X ( t
1
2
)
1
2
X ( t t ), X ( t t )..., X ( t t
n
n
1 0
2
0
n
)0
(x1 , x2 ..., xn )
n  N , t 0  and for all choices of sample points t1 , t 2 ,...tn .
Thus the joint distribution functions of any set of random variables
does not depend on the placement of the origin of the time axis. This
requirement is a very strict. Less strict form of stationarity may be defined.
Particularly,
F
(x , x
(x , x
X ( t ), X ( t )..... X ( t )
1
2 .....xn )  FX ( t t ), X ( t t )..... X ( t t )
1
2 .....xn ) for n 1,2,.., k,
if
then
X ( t1 ), X ( t 2 ), ..., X ( tn )
12
n
1 0
2
0
X (t ) is called kth order stationary.
 If X (t ) is stationary up to order 1
F (x )  F
(x ) t T
X (t1 )
X (t1 t0 )
1
1
n
0
0
Let us assume t 0 t1. Then
FX ( t1 ) (x1 )  FX (0) (x1 ) which is independent of time.
As a consequence
EX (t1 )  EX (0)  X (0)  constant

F
If X (t ) is stationary up to order 2
(x , x .)  F
X (t1 ), X (t2 )
Put t0 t2
F
1
2
(x , x )
X (t1 t0 ), X (t2 t0 )
(x , x )  F
X ( t1 ), X ( t 2 )
1
2
1
2
(x , x )
X ( t1 t 2 ), X (0)
1
2
This implies that the second-order distribution depends only on the time-lag t1  t2 .
As a consequence, for such a process
R X (t1 , t 2 )  E ( X (t1 ) X (t2 ))
   x1 x2 f X (0) X ( t1 t2 ) ( x1 , x2 )dx1 dx2

= R X (t1  t2 )
Similarly,
C X (t1 , t 2 )= CX (t1  t2 )
Therefore, the autocorrelation function of a SSS process depends only on the time lag

We can also define the joint stationary of two random processes. Two processes


t1  t2 .

X (t ) and
Y (t) are called jointly strict-sense stationary if their joint probability distributions of any


Z (t )  X (t )
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order is invariant under the translation of time. A complex process




 jY (t ) is
called SSS if X (t ) and Y (t) are jointly SSS.
Wide-sense stationary process
It is very difficult to test whether a process is SSS or not. A subclass of the
SSS process called the wide sense stationary process is extremely important from
practical point of view.
A random process { X ( t)} is called wide sense stationary process (WSS) if
EX (t)  X  constant
and
EX (t1 ) X (t 2 )  R X (t1  t 2 ) is a function of time lag t1  t2 .
(Equivalently, Cov ( X (t1 ) X (t 2 ))  CX (t1  t 2 ) is a function of time lag t1  t2 )
2. Explain in detail about Ergodicity Principle
If the time averages converge to the corresponding ensemble averages in the
probabilistic sense, then a time-average computed from a large realization can be
used as the value for the corresponding ensemble average. Such a principle is the
ergodicity principle to be discussed below:
Mean ergodic process
Thus for a mean ergodic process X (t),
lim E X T X
T 
and
lim var X
T 
T
0
We have earlier shown that
E 

X
X
T
and
var  X
1



2T

C X ( )  1 
d
2T 2T

2T 
Therefore, the condition for ergodicity in mean is
T

lim 1 2T C ( ) 1  
 X 
T 
2T 2T


d  0

2T 
If CX ( ) decreases to 0 for  0 , then the above condition is satisfied.
Further,
2T



2T
 CX ( ) d
C X ( )  1 
d  

2T 
2T 2 T
2T 2T
Therefore, a sufficient condition for mean ergodicity is
1
2T

2T
1
C X ( ) d 
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Example
Consider the random binary waveform{ X ( t)} discussed in Example .The process
has the auto-covariance function for   Tp given by

1 
CX ( ) 
  Tp


Tp
0

otherwise
Here
2T
2T

C X ( ) d  2  C X ( ) d
2 T
0
 

Tp


1
2


0

 2T 
 p

2Tp
 3


d
Tp 
T3
p
2
3T p

T2
p
T
p



  C X ( ) d 

Hence { X ( t)}is not mean ergodic.
Autocorrelation ergodicity
R ( )  1 T X (t ) X (t  )dt
X
T
2T

T
If we consider Z (t )  X (t ) X (t  ) so that,  Z  RX ( )
Then { X ( t)} will be autocorrelation ergodic if {Z (t)} is mean ergodic.
Thus { X ( t)} will be autocorrelation ergodic if
2T
lim 1  1  1 C ()d  0
T 

Z
1
1
2T 2T  2T 
where
CZ ( 1 )  EZ (t )Z (t   1 )  EZ (t )EZ (t 1 )
2
 EX (t ) X (t   ) X (t   ) X (t     1 )  RX ( )
Involves
fourth order moment.

Hence the condition for autocorrelation ergodicity of a jointly Gaussian process is
found. Thus X (t) will be autocorrelation ergodic if
2T
lim 1  1   C ( )d  0
T 

z
2T 2T 
2T 
Now C ( )  EZ (t )Z (t   )  R2 ()
Z
X
Hence, X (t) will be autocorrelation ergodic
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If lim
T 
1
2T
 1    Ez (t )z (t   )  R2 ( ) d  0



X
2T 2T  2T 
3.Derive The Equation For Finding The Power Spectral Density Of A One To
One Differential Function Of A Given Random Variable. (NOV/DEC 2013)
Consider a random process Z ( t ) which is sum of two real jointly WSS random
processes
X(t) and Y(t).
RZ ( )  R X ( )  RY ( )  R XY ( )  RYX ( )
If we take the Fourier transform of both sides,
S Z ( )  S X ( )  SY ( )  FT ( RXY ( ))  FT ( RYX ( ))
where FT (.) stands for the Fourier transform.
Thus we see that SZ () includes contribution from the Fourier transform of the crosscorrelation functions RXY ( ) and RYX ( ). These Fourier transforms represent cross power
spectral densities.
Definition of Power Spectral Density
Given two real jointly WSS random processes X(t) and Y(t), the cross power
spectral density (PSD) SXY () is defined as
S
FTX  ( ) FTY ()
XY ()  lim E
2T
T 
T
T
whereFTX T ( )
and FTYT () are the Fourier transform of the truncated processes

X (t)  X(t)rect( t ) and Y (t)  Y(t)rect( t ) respectively and denotes the complex
T
T
2T
2T
conjugate operation.
We can similarly define SYX () by
S
YX

()  lim E
FTY ( ) FTX T ()
T
2T
Proceeding in the same way as the derivation of the Wiener-Khinchin-Einstein
theorem for the WSS process, it can be shown that
T 

S XY ( )  R XY ( ) e
 j
d

and

SYX ( )   RYX ( ) e
 j
d
The cross-correlation function and the cross-power spectral density form a
Fourier transform pair and we can write

R XY ( )   S XY ( ) e
and

RYX ( )   SYX ( ) e
j
j
d
d
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Properties of the PSD
The PSD is a complex function of the frequency . Some properties of the CPSD of
two jointly WSS processes X(t) and Y(t) are listed below:
(1) S XY ( )  SYX* ()
Note that R XY ( )  RYX (  )

 S XY ( )   R XY ( ) e
 j
d
  RYX ( ) e
 j
d
j
d




  RYX ( ) e

*
= S ()
YX
(2) Re( SXY ()) is an even function of  and Im( SXY ()) is an odd function of 
We have

S XY ( )  R XY ( )(cos   j sin  ) d



 R XY ( ) cos d  j  R XY ( )sin  ) d


 Re(S XY ( ))  j Im(S XY ())
where

Re(S XY ( ))  R XY ( ) cos d is an even function of  and


Im(S XY ( ))  R XY ( )sin  d is an odd function of  and

(3) X(t) and Y(t) are uncorrelated and have constant means, then
S XY ( )  SYX ( )   X  Y  ()
Observe that
R XY ( )  EX (t  )Y (t)
 EX (t  )EY (t)




 XY
 YX
 RXY ( )
 S XY ( )  SYX ( )   X  Y  ()

(4)
If X(t) and Y(t) are orthogonal, then
S XY ( )  SYX ()  0
If X(t) and Y(t) are orthogonal,
R XY ( )  EX (t  )Y (t)
 0

 RXY ( )

 S XY ( )  SYX ()  0

(5) The cross power PXY between X(t) and Y(t) is defined by
P
XY
 lim
T 
1
2T
T
E  X (t )Y (t )dt
T
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Applying Parseval’s theorem, we get
P
XY
T
1
E  X (t )Y (t )dt
T  2T
T

1
 lim
E  X T (t )YT (t )dt
T  2T

1
1
*
 lim
E
 FTX T ( ) FTYT ( ) d
T  2T
2 
 lim


P
XY
1
 lim
2  T
1 
EFTX * ( ) FTY ()

T
T
2T
d
 S XY ( ) d
2 
1


 S XY ( ) d
2 
Similarly,
P
YX




1

 SYX ( ) d
2 
1

 S * ( ) d
2 
 PXY*
XY

4. Explain Central limit theorem and its Convergence to the limit.
In probability theory, the central limit theorem states that, given certain
conditions, the arithmetic mean of a sufficiently large number of iterates of
independent random variables, each with a well-defined expected value and welldefined variance, will be approximately normally distributed, regardless of the
underlying distribution.
A simple example of this is that if one flips coin many times, the probability of
getting a given number of heads should follow a normal curve, with mean equal to
half the total number of flips.
It is used to define a sum of many independent and identically distributed
random variables, or alternatively, random variables with specific types of
dependence, will tend to be distributed according to one of a small set of attractor
distributions.
In contrast, the sum of a number of random variables with power law tail
−α−1
distributions decreasing as |x|
where 0 < α < 2 (and therefore having infinite
variance) will tend to an alpha-stable distribution with stability parameter (or index of
stability) of α as the number of variables grows.
Classical Central limit theorem
Let {X1, ..., Xn} be a random sample of size n —∞ that is, a sequence of
independent and identically distributed random variables drawn from distributions of
2
expected values given by µ and finite variances given by σ .
Sn=X1+…….+Xn/n
Suppose we are interested in the sample average of these random variables.
By the law of large numbers, the sample averages converge in probability and
almost surely to the expected value µ as n → ∞.
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Convergence to the limit
The central limit theorem gives only an asymptotic distribution. As an
approximation for a finite number of observations, it provides a reasonable
approximation only when close to the peak of the normal distribution; it requires a
very large number of observations to stretch into the tails.
3
If the third central moment E((X1 − μ) ) exists and is finite, then the above
convergence is uniform and the speed of convergence is at least on the order of
1/2
1/n
(see Berry-Esseen theorem). Stein's method can be used not only to prove
the central limit theorem, but also to provide bounds on the rates of convergence for
selected metrics.
The convergence to the normal distribution is monotonic, in the sense that the
entropy of Zn increases monotonically to that of the normal distribution.
The central limit theorem applies in particular to sums of independent and
identically distributed discrete random variables. A sum of discrete random variables
is still a discrete random variable, so that we are confronted with a sequence of
discrete random variables whose cumulative probability distribution function
converges towards a cumulative probability distribution function corresponding to a
continuous variable (namely that of the normal distribution). This means that if we
build a histogram of the realizations of the sum of n independent identical discrete
variables, the curve that joins the centers of the upper faces of the rectangles
forming the histogram converges toward a Gaussian curve as n approaches infinity,
this relation is known as de Moivre–Laplace theorem. The binomial distribution article
details such an application of the central limit theorem in the simple case of a
discrete variable taking only two possible values.
5.(i). Write Short Notes On Covariance Function.
COVARIANCE FUNCTIONS:
In probability theory and statistics, covariance is a measure of how much two
variables change together, and the covariance function, or kernel, describes the
spatial covariance of a random variable process or field. For a random field or
stochastic process Z(x) on a domain D, a covariance function C(x, y) gives the
covariance of the values of the random field at the two locations x and y:
The same C(x, y) is called the auto covariance function in two instances: in
time series (to denote exactly the same concept except that x and y refer to locations
in time rather than in space), and in multivariate random fields (to refer to the
covariance of a variable with itself, as opposed to the cross covariance between two
different variables at different locations, Cov(Z(x1), Y(x2))).
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A function is a valid covariance function if and only if this variance is nonnegative for all possible choices of N and weights w1, …, wN. A function with this
property is called positive definite.
5. (ii).Write Short Notes On Auto Correlation Function.
In statistics, dependence is any statistical relationship between two random
variables or two sets of data. Correlation refers to any of a broad class of statistical
relationships involving dependence. Familiar examples of dependent phenomena
include the correlation between the physical statures of parents and their offspring,
and the correlation between the demand for a product and its price. Correlations are
useful because they can indicate a predictive relationship that can be exploited in
practice.
For example, an electrical utility may produce less power on a mild day based
on the correlation between electricity demand and weather. In this example there is a
causal relationship, because extreme weather causes people to use more electricity
for heating or cooling; however, statistical dependence is not sufficient to
demonstrate the presence of such
a causal relationship. Formally, dependence refers to any situation in which random
variables do not satisfy a mathematical condition of probabilistic independence. In
loose usage, correlation can refer to any departure of two or more random variables
from independence, but technically it refers to any of several more specialized types
of relationship between mean values. There are several correlation coefficients,
often denoted ρ or r, measuring the degree of correlation.
The most common of these is the Pearson correlation coefficient, which is
sensitive only to a linear relationship between two variables. Other correlation
coefficients have been developed to be more robust than the Pearson correlation
that is, more sensitive to nonlinear relationships. Mutual information can also be
applied to measure dependence between two variables.
Pearson's correlation coefficient: The most familiar measure of
dependence between two quantities is the Pearson product-moment correlation
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coefficient, or "Pearson's correlation coefficient", commonly called simply "the
correlation coefficient". It is obtained by dividing the covariance of the two variables
by the product of their standard deviations. Karl Pearson developed the coefficient
from a similar but slightly different idea by Francis Galton. The population correlation
coefficient ρX,Y between two random variables X and Y with expected values μX
and μY and standard deviations ςX and ςY is defined as:
where E is the expected value operator, cov means covariance, and, corr a
widely used alternative notation for the correlation coefficient. The Pearson
correlation is defined only if both of the standard deviations are finite and nonzero. It
is a corollary of the Cauchy– Schwarz inequality that the correlation cannot exceed 1
in absolute value. The correlation coefficient is symmetric: corr(X,Y) = corr(Y,X). The
Pearson correlation is +1 in the case of a perfect direct (increasing) linear
relationship (correlation), −1 in the case of a perfect decreasing (inverse) linear
relationship (autocorrelation), and some value between −1 and 1 in all other cases,
indicating the degree of linear dependence between the variables.
As it approaches zero there is less of a relationship (closer to uncorrelated).
The closer the coefficient is to either −1 or 1, the stronger the correlation between
the variables. If the variables are independent, Pearson's correlation coefficient is 0,
but the converse is not true because the correlation coefficient detects only linear
dependencies between two variables. For example, suppose the random variable X
is symmetrically distributed about zero, and Y = X2. Then Y is completely
determined by X, so that X and Y are perfectly dependent, but their correlation is
zero; they are uncorrelated. However, in the special case when X and Y are jointly
normal, uncorrelatedness is equivalent to independence. If we have a series of n
measurements of X and Y written as xi and yi where i = 1, 2, ..., n, then the sample
correlation coefficient can be used to estimate the population Pearson correlation r
between X and Y. where x and y are the sample means of X and Y, and sx and sy
are the sample standard deviations of X and Y.
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PART C
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UNIT IV- NOISE CHARACTERIZATION
PART A
1. Define noise.
Noise is defined as any unwanted form of energy, which tends to interfere
with proper reception and reproduction of wanted signal.
2. What are types of internal
noise? Internal noise can be
classified into
1. Thermal noise
2. Shot noise
3. Transit time noise
4. Miscellaneous internal noise
3. Define flicker noise.
Flicker noise is the one appearing in transistors operating at low audio
frequencies. Flicker noise is proportional to the emitter current and junction
temperature and inversely proportional to the frequency.
4. Define thermal noise. Give the expression for the thermal noise voltage
across a resistor.
The electrons in a conductor possess varying amounts of energy. A small
fluctuation in this energy produces small noise voltages in the conductor. These
random fluctuations produced by thermal agitation of the electrons are called thermal
noise.
5. Define equivalent noise temperature. (MAY/JUNE-2010,NOV/DEC2014,MAY/JUN 2016,NOV/DEC 2016)
The available noise power is directly proportional to temperature and it is
independent of value of resistance. This power specified in terms of temperature is
called as equivalent noise temperature. It is denoted by Te. It is given as,
Te = (F −1) T0
Where F-noise figure
T0-Absolute temperature
6. What is shot noise? (MAY/JUNE-2013)
When current flows in electronic device, the fluctuations number of electrons
or holes generates the noise. It is called shot noise. Shot noise also depends upon
operating conditions of the device.
7. What is narrowband noise?
The receiver of a communication system usually includes some provision for
pre-processing the received signal. The pre-processing may take the form of a
narrowband filter whose bandwidth is large enough to pass modulated component of
the received signal essentially undistorted but not so large as to admit excessive
noise through the receiver. The noise process appearing at the output of such filter is
called narrow band noise.
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8. Define noise equivalent bandwidth.
The noise equivalent bandwidth of the filter is defined as the bandwidth of an
ideal filter at which the noise power passed by real filter and ideal filter is same.
9. What is FM threshold effect? (NOV/DEC-2011,APR/MAY2015,NOV/DEC 2015)
As the carrier to noise ratio is reduced, clicks are heard in the receiver output.
As the carrier to noise ratio reduces further, crackling, or sputtering sound appears
at the receiver output. Near the breaking point, the theoretically calculated output
signal to noise ratio becomes large, but its actual value is very small. This
phenomenon is called threshold effect.
10. Define pre-emphasis and de-emphasis. (NOV/DEC-2010,MAY/JUNE2013,APR/MAY 2015)
Pre-emphasis:
It artificially emphasizes the high frequency components before
modulation.This equalizes the low frequency and high frequency portions of the PSD
and complete band is occupied.
De-emphasis:
This circuit attenuates the high frequency components. The attenuation
characteristic is exactly opposite to that of pre-emphasis circuit. De-emphasis
restores the power distribution of the original signal. The signal to noise ratio is
improved because of pre-emphasis and de-emphasis circuits.
11.Define SNR. (APR/MAY-2015)
Signal to noise ratio(SNR) is the ratio of signal power to the noise power at
the same point in a system.
12.Define noise figure. (MAY/JUNE-2013,APR/MAY-2015,NOV/DEC
2015MAY/JUNE 2016)
Noise figure is defined as the ratio of signal to noise power at the input to the
signal to noise power at the output.
13.Define white noise (or) Gaussian noise. (MAY/JUNE-2013)(APR/MAY2011)
(NOV/DEC-2010) (MAY/JUNE-2014)
Many types of noise sources are Gaussian and have flat spectral density over
a wide frequency range. Such spectrum has all frequency components in equal
portion, and is therefore called white noise, the power spectral density of whit noise
is independent of the operating frequency.
PART-B
1. Write Short Notes On Shot Noise, Thermal noise, White Noise .(APRIL/MAY
2015,MAY/JUNE 2013,NOV/DEC 2016)
Noise is random, undesirable electrical energy that enters the
communications system via the communicating medium and interferes with the
transmitted message. However, some noise is also produced in the receiver.
With reference to an electrical system, noise may be defined as any
unwanted form of energy which tends to interfere with proper reception and
reproduction of wanted signal. Noise may be put into following two categories.
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External noises, i.e. noise whose sources are external. External noise may be
classified into the following three types:
Atmospheric noises
Extra-terrestrial noises
Man-made noises or industrial noises.
Internal noise in communication:
Noises which get, generated within the receiver or communication system.
Internal noise may be put into the following four categories.




Thermal noise or white noise or Johnson noise
Shot noise.
Transit time noise
Miscellaneous internal noise.
External noise cannot be reduced except by changing the location of the
receiver or the entire system. Internal noise on the other hand can be easily
evaluated mathematically and can be reduced to a great extent by proper design.
Explanation of External Noise
Atmospheric Noise: 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.
Atmospheric noise accordingly consists of spurious radio signals with components
spread over a wide frequency range. These spurious radio waves constituting the
noise get propagated over the earth in the same fashion as the desired radio waves
of the same frequency. Accordingly at a given receiving point, the receiving antenna
picks up not only the signal but also the static from all the thunderstorms, local or
remote.
Extra-terrestrial noise:
 Solar noise
 Cosmic noise
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.
During other years. The noise is at a minimum level.
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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. Noise is received from the centre of our own galaxy
(The Milky Way) from other distant galaxies and from other virtual point sources
such as quasars and pulsars.
Man-Made Noise (Industrial Noise):
By man-made noise or 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
Explanation of Internal Noise in communication:
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. The analysis of
thermal noise is based on the Kinetic theory. It shows that the temperature of
particles is a way of expressing its internal kinetic energy. Thus "Temperature" of a
body can be said to be equivalent to the statistical rms value of the velocity of motion
of the particles in the body. At -273°C (or zero degree Kelvin) the kinetic energy of
the particles of a body becomes zero .Thus we can relate the noise power generated
by a resistor to be proportional to its absolute temperature. Noise power is also
proportional to the bandwidth over which it is measured. From the above discussion
we can write down.
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Transit Time Noise:
Another kind of noise that occurs in transistors is called transit time noise.
Transit time is the duration of time that it takes for a current carrier such as a hole or
current to move from the input to the output. The devices themselves are very tiny,
so the distances involved are minimal. Yet the time it takes for the current carriers to
move even a short distance is finite. At low frequencies this time is negligible. But
when the frequency of operation is high and the signal being processed is the
magnitude as the transit time, then problem can occur. The transit time shows up as
a kind of random noise within the device, and this is directly proportional to the
frequency of operation.
Miscellaneous Internal Noises Flicker Noise:
Flicker noise or modulation noise is the one appearing in transistors operating
at low audio frequencies. Flicker noise is proportional to the emitter current and
junction temperature. However, this noise is inversely proportional to the frequency.
Hence it may be neglected at frequencies above about 500 Hz and it, Therefore,
possess no serious problem.
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Transistor Thermal Noise:
Within the transistor, thermal noise is caused by the emitter, base and
collector internal resistances. Out of these three regions, the base region contributes
maximum thermal noise.
Partition Noise:
Partition noise occurs whenever current has to divide between two or more
paths, and results from the random fluctuations in the division. It would be expected,
therefore, that a diode would be less noisy than a transistor (all other factors being
equal) If the third electrode draws current (i.e.., the base current). It is for this reason
that the inputs of microwave receivers are often taken directly to diode mixers.
Shot Noise:
The most common type of noise is referred to as shot noise which is
produced by the random arrival of 'electrons or holes at the output element, at the
plate in a tube, or at the collector or drain in a transistor. Shot noise is also produced
by the random movement of electrons or holes across a PN junction. Even through
current flow is established by external bias voltages, there will still be some random
movement of electrons or holes due to discontinuities in the device. An example of
such a discontinuity is the contact between the copper lead and the semiconductor
materials. The interface between the two creates a discontinuity that causes random
movement of the current carriers.
2. Explain the Capture effect, threshold effect Pre-emphasis and de-emphasis
(APR/MAY-2013,NOV/DEC2015,MAY/JUNE 2016)
3.
Capture effect:
In the frequency modulation, the signal can be affected by another frequency
modulated signal whose frequency content is close to the carrier frequency of the
desired FM wave. The receiver may lock such an interference signal and suppress
the desired FM wave when interference signal is stronger than the desired signal.
When the strength of the desired signal and interference signal are nearly equal, the
receiver fluctuates back and forth between them, i.e., receiver locks interference
signal for some times and desired signal for some time and this goes on randomly.
This phenomenon is known as the capture effect.
FM Threshold Effect:
The output signal to noise ratio of FM receiver is valid only if the carrier to
noise ratio is measured at the discriminator input is high compared to unity. It is
observed that as the input noise is increased so that the carrier to noise ratio
decreased, the FM receiver breaks. At first individual clicks are heard in the receiver
output and as the carrier to noise ratio decreases still further, the clicks rapidly
merge in to a crackling or sputtering sound.
FM threshold reduction:
This can be achieved by using an FM demodulator with negative feedback
(FMFB) or by using a phase locked loop demodulator.
Fig.1 FM Threshold reduction
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The conventional local oscillator is replaced by VCO. To understand the
operation of this receiver, suppose that VCO is removed from the circuit and the
feedback path is left open.
Assume that the wide band FM is applied to the receiver input, and a second
FM from the same source but with a modulation index a fraction smaller is applied to
the VCO terminal of the product modulator. The output of the product modulator
consists of sum and difference frequency components. The IF filter is designed to
pass only difference frequency component. The frequency deviation of the IF filter
output would be small, although the frequency deviation of both input FM wave is
large, since the difference between their instantaneous deviations is small.
Hence, the modulation indices would subtract, and the resulting FM wave at the IF
filter output have a smaller modulation index than the input FM waves. This means
that the IF filters bandwidth in fig above need only be a fraction of that required for
either wideband FM wave. It is now apparent that Second wide band FM waves
replaced by VCO feed by o/p of low pass filter.
Pre-Emphasis and De-Emphasis in an FM system
Fig. 2 Pre-emphasis and De-emphasis in FM
In this method, we artificially emphasize the high frequency components of
the message signal prior modulation in the transmitter before the noise is introduced
in the receiver. The low frequency and high frequency portions of the PSD of the
message are equalized in such a way that the message fully occupies the frequency
band allotted to it. Then, at the discriminator output in the receiver perform the
inverse operation by de-emphasizing the high frequency components to restore the
message. In this process, the high frequency noise is reduced thereby effectively
increasing the output SNR of the system.
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