NOORUL ISLAM COLLEGE OF ENGG,
Kumaracoil
DEPARTMENT OF ECE
2 MARKS & QUESTION- ANSWERS
EC 1301 – Communication Theory
Class : S5 ECE
Prepared by :E.P.Kannan ECE
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
SUBJECT CODE: EC 1301
SUBJECT: COMMUNICATION THEORY
(FOR FIFTH SEMESTER ECE)
TWO MARKS QUESTIONS
1. Define 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.
2.What are the types of analog modulation?
Amplitude modulation.
Angle Modulation
1. Frequency modulation
2. Phase modulation.
3.Define depth of modulation.
It is defined as the ratio between message amplitude to that of carrier amplitude.
m=Em/Ec
4. What are the degrees of modulation?
Under modulation. m<1
Critical modulation m=1
Over modulation m>1
5.What is the need for modulation?
Needs for modulation:
Ease of transmission
Multiplexing
Reduced noise
Narrow bandwidth
Frequency assignment
Reduce the equipments limitations.
6.What are the types of AM modulators?
There are two types of AM modulators. They are
Linear modulators
Non-linear modulators
Linear modulators are classified as follows
Transistor modulator
There are three types of transistor modulator.
Collector modulator
Emitter modulator
Base modulator
Switching modulators
Non-linear modulators are classified as follows
Square law modulator
Product modulator
Balanced modulator
7.Give the classification of modulation.
There are two types of modulation. They are
Analog modulation
Digital modulation
Analog modulation is classified as follows
Continuous wave modulation
Pulse modulation
Continuous wave modulation is classified as follows
Amplitude modulation
Double side band suppressed carrier
Single side band suppressed carrier
Vestigial side band suppressed carrier
Angle modulation
Frequency modulation
Phase modulation
Pulse modulation is classified as follows
Pulse amplitude modulation
Pulse position modulation
Pulse duration modulation
Pulse code modulation
Digital modulation is classified as follows
Amplitude shift keying
Phase shift keying
Frequency shift keying
8.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.
9 .The antenna current of an AM transmitter is 8A when only carrier is sent. It increases to 8.93A when
the carrier is modulated by a single sine wave. Find the percentage modulation.
Solution:
Given: Ic =8A It=8.93A m=0.8
Formula: It=Ic (1+m2/2)
½
8.93=8(1+m2/2) ½
m=0.701
It=8 (1+0.82/2)
½
It=9.1A
10.Compare AM with DSB-SC and SSB-SC.
AM signal DSB-SC SSB-SC
Bandwidth=2fm
Bandwidth=2fm Bandwidth=fm
Contains USB, LSB, carrier Contains USB,LSB Contains LSB or USB
More power is required for
transmission
Power required is less than
that of AM.
Power required is less than
AM &DSB-SC
11 What are the advantages of VSB-AM?
1.It has bandwidth greater than SSB but less than DSB system.
2.Power transmission greater than DSB but less than SSB system.
3.No low frequency component lost. Hence it avoids phase distortion.
12 Compare linear and non-linear modulators.
Linear modulators Non-linear modulators
1.Heavy filtering is not 1.Heavy filtering is required
required.
2.These modulators are used in 2.These modulators are used in low level
high level modulation. Modulation.
3.The carrier voltage is very much 3.The modulating signal voltage is very much
greater than modulating signal greater than the carrier signal voltage.
voltage.
13.How will you generating DSBSC-AM ?
There are two ways of generating DSBSC-AM such as
1.balanced modulator 2.ring modulators
14. What are advantages of ring modulator?
1.Its output is stable.
2. It requires no external power source to activate the diodes.
3.Virtually no maintenance.
4. Long life.
15. 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.
16. What are the types of AM detectors?
1. Nonlinear detectors
2. Linear detectors
17.What are the types of linear detectors?
1.Synchronous or coherent detector.
2 .Envelope or non coherent detector.
18.draw the block diagram of coherent detector.
modulated
signal
OUTPUT
Product
modulator
LPF
Carrier
Signal
19.Define multiplexing.
Multiplexing is defined as the process of transmitting several message signals
simultaneously over a single channel.
20.Define sensitivity.
It is defined as a measure of its ability to receive weak signals.
21.Define selectivity.
Selectivity of a receiver is defined as its ability to select the desired signals among
the various signals.
22. Define stability.
It is the ability of the receiver to deliver a constant amount of output for a given a
given period of time.
23.Define super heterodyne principle.
It can be defined as the process of operation of modulated waves to obtain similarly
modulated waves of different frequency. This process uses a locally generated carrier
wave, which determines the change of frequency.
24.A transmitter supplies 8 Kw to the antenna when modulated. Determine the total
power radiated when modulated to 30%.
m=0.3;Pc=8 kw
Pt=Pc(1+m2/2)
=8.36 kw
25.What are the drawbacks of emitter modulator?
1.The amplifier is operated in class A mode, thus the efficiency is low.
2.The output power is very small. Thus it is not suitable for generating high
level modulation.
26. Define 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.
27. Define modulation index of frequency modulation.
It is defined as the ratio of maximum frequency deviation to the
modulating frequency. b = df/fm
28. What do you meant by multitone modulation?
Modulation done for the message signal with more than one frequency component
is called multitone modulation.
29. Define 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.
30. How FM wave can be converted to PM wave?
Message signal PM Signal
31. How PM wave can be converted to FM wave?
Message Signal FM Signal
Integrator
Phase
Modulator
Carrier
Differentiator FM
32. 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
33. 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.
34. 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
35 . Compare WBFM and NBFM.
WBFM NBFM
Modulation index is greater than 1 Modulation index less than 1
Frequency deviation 75 KHz Frequency deviation 5 KHz
Bandwidth 15 times NBFM Bandwidth 2fm
Noise is more suppressed Less suppressing of noise
Carrier
36. List the properties of the Bessel function.
The properties of the Bessel function is given by,
i) Jn (b)=(-1)nJ-n(b) for all n, both positive and negative.
ii) For small values of the modulation index b ,we have
J0 (b)=1
J1 (b)=b/2
Jn(b)=0,n>2.
¥
iii) S J2
n (b)=1
n = -¥
37. Give the average power of an FM signal.
The amplitude of the frequency modulated signal is constant .The power of the
FM signal is same as that of the carrier power. P=1/2 Ec
2 .
38. Define phase deviation.
The maximum phase deviation of the total angle from the carrier angle is called
phase deviation.
39. Define frequency Deviation.
The maximum departure of the instantaneous frequency from the carrier frequency
is called frequency deviation.
40. State the Carson’s rule.
An approximate rule for the transmission bandwidth of an FM Signal generated by
a single tone-modulating signal of frequency fm is defined as
B =2 Df(1+1/ b)
41.Define the deviation ratio D for non-sinusoidal modulation.
The deviation ratio D is defined as the ratio of the frequency deviation Df, which
corresponds to the maximum possible amplitude of the modulation signal m(t),to the
highest modulation frequency .
D = Df / fm
42.What is the use of crystal controlled oscillator?
The crystal-controlled oscillator always produces a constant carrier frequency
there by enhancing frequency stability.
43. What are the disadvantages of FM system?
1. A much wider channel is required by FM.
2. FM transmitting and receiving equipments tend to be more complex and
hence it is expensive
44. 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.
45. What are the types of FM detectors?
Slope detector and phase discriminator.
46. What are the types of phase discriminator?
Foster seely discriminator and ratio detector.
47. What are the disadvantages of balanced slope detector?
1. Amplitude limiting cannot be provided
2. Linearity is not sufficient
3. It is difficult to align because of three different frequency to which various
tuned circuits to be tuned.
4. The tuned circuit is not purely band limited.
48. Define probability.
The probability of occurrence of an event A is defined as,
P(A)= number of possible favorable outcomes
Total number of equal likely outcomes
49.What are mutually exclusive events?
Two possible outcomes of an experiment are defined as being mutually exclusive
if the occurrence of one outcome precludes the occurrence of the other.
50. Define probability density function.
Probability density function is defined as fx(x) is defined in terms of
cumulative distribution function Fx (x) as
fx(x) = d Fx (x)
dx
51. Define noise.
Noise is defined as any unwanted form of energy, which tends to interfere with
proper reception and reproduction of wanted signal.
52. Give the classification of noise.
Noise is broadly classified into two types. They are External noise and internal
noise.
53. What are the types of External noise?
External noise can be classified into
1. Atmospheric noise
2. Extraterrestrial noises
3. Man –made noises or industrial noises
54. 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
55. What are the types of extraterrestrial noise and write their origin?
The two type of extraterrestrial noise are solar noise and cosmic noise
Solar noise is the electrical noise emanating from the sun.
Cosmic noise is the noise received from the center part of our galaxy, other
distant galaxies and other virtual point sources.
56. Define transit time of a transistor.
Transit time is defined as the time taken by the electron to travel from emitter to
the collector.
57. 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.
58. State the reasons for higher noise in mixers.
1. Conversion transconductance of mixers is much lower than the
transconductance of amplifiers.
2. If image frequency rejection is inadequate, the noise associated with the image
frequency also gets accepted.
59. Define signal to noise ratio.
Signal to noise ratio is the ratio of signal power to the noise power at the same
point in a system.
60. Define noise figure.
S/ N at the input
Nose figure F =
S/ N at the output
S/N = Signal power / Noise Power
61. Explain thermal noise.
Thermal noise is the name given to the electrical noise arising from the random
motion of electrons in a conductor.
62. Give the expression for noise voltage in a resistor.
The mean –square value of thermal noise voltage is given by
Vn
2 = 4 K T B R
K – Boltz man constant
R – resistance
T – obsolute temperature
B - Bandwidth
63. Explain White Noise.
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 white noise is independent
of the operating frequency.
64. What is narrowband noise?
The receiver of a communication system usually includes some provision for
preprocessing the received signal. The preprocessing 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.
65. Give the representation of narrowband noise in terms of envelope and phase
components.
Narrowband noise in terms of envelope and phase components as
n(t) = r(t) cos (2 fct + (t) )
r(t) = (nI 2(t) + nQ 2(t))½
(t) = tan -1(nQ(t) / nI (t ))
The function r (t) and (t) are called envelope and phase of n(t).
66. Give the expression for equivalent noise temperature in terms of hypothetical
temperature.
The expression for equivalent noise temperature in terms of hypothetical
temperature
is Te = ( F- 1) T0
Where, F is the noise figure and T0 absolute temperature.
67. Give the Friss formula in terms of noise temperature.
The Friss formula in terms of noise temperature is
Te = T1 + T2 / G1 + T3 / G1 G2 + ………
G1 , G2 ,… Gain of amplifiers
68. What is called image frequency?
Image frequency is defined as the signal frequency plus twice the intermediate
frequency. This has the effect of two stations being received simultaneously and hence it
is undesirable.
fsi = fs + 2 fi
fsi - image frequency
It can be eliminated by providing adequate image signal selectivity between antenna and
mixer input.
69. What is intermediate frequency?
Intermediate frequency (IF) is defined as the difference between the signal
frequency and the oscillator frequency.
IF = fs – fo when fs > fo (or)
IF = fo –fs when fo > fs
70. Define Partition noise.
In an electron tube having one or more positive grids, this noise is caused by
irratic partition of the cathode current among the positive electrodes. In a transistor, the
partition noise is created from the random fluctuation in the division of current between
the collector and base.
71. Give the expression for noise voltage when several sources are cascaded.
Enr = Sqrt (4 KTB (R1 + R2 + …..) )
Where R1 , R2 --- are the resistances of the noise resistors.
K – Boltz man constant
T – absolute temperature
B – Bandwidth
72. Define random variable
Random variable is defined as a rule or mapping from the original sample space
to a numerical sample space subjected to certain constraints. Random variable is also
defined as a function where domain is the set of outcomes es and whose range is R, is
the real line.
73. Define Random process.
A Random process X (s,t) is a function that maps each element of a samples space
into a time function called sample function. Random process is a collection of time
functions.
74. Give the Laws of probability.
Additive law of probability
Case i
When events are mutually exclusive , P (AÇB) =
P(AÈB) = P(A) + P(B)
Case ii
When events are not mutually exclusive
P(AÈB) = P(A) + P(B) - P (AÇB)
Multiplication law of probability:
Case i When events are independent
P(AÇB) = P(A) P(B)
Case ii When events are dependent
P(AÇB) = P(A) P(B/A)
= P(B) P(A/B)
75. What is frequency translation?
Suppose that a signal is band limited to the frequency range extending from a
frequency f1 to a frequency f2. The process of frequency translation is one in which the
original signal is replaced with a new signal whose spectral range extends from f1’ to f2’
and which new signal bears, in recoverable form the same information as was borne by
the original signal.
76. What are two situations identified in frequency translations?
The two situations identified in frequency translation are
i Up conversion
In this case the translated carrier frequency is greater than the incoming carrier
frequency
ii Down conversion
In this case the translated carrier frequency is smaller than the incoming carrier
frequency.
Thus, a narrowband FM signal requires essentially the same transmission bandwidth as
the AM signal.
77. Define Tracking.
Tracking is the process of correctly tuning a number of tunable circuits in a
receiver.
78. What is TRF receiver?
Tuned Radio Frequency is also called straight receiver.Here the receiver operates
in straight forward manner without frequency conversion.
79.What are the advantages of superheterodyne receiver over TRF?
The advantages of superheterodyne receiver over TRF are high selectivity
,improved sensitivity throughout the carrier frequency band..It eliminates image
frequency.
80.What is the figure of merit of DSBSC system ?
The figure of merit of DSBSC signal is unity
81.Compare the noise performance of an AM and FM system?
The figure of merit of AM system is 1/3 when the modulation is 100 percent and
that of FM is(3/2)mf
2.The use of FM offers improved noise performance
over AM when (3/2)mf
2 > 1/3.mf –modulation index in FM.
82.What is Capture effect?
When the interference signal and FM input are of equal strength, the receiver
fluctuates back and froth between them .This phenomenon is known as the capture effect.
83.What is threshold effect?
As the input noise power is increased the carrier to noise ratio is decreased the
receiver breaks and as the carrier to noise ratio is reduced further crackling sound is heard
and the output SNR cannot be predicted by the equation. This phenomenon is known as
threshold effect.
84.How is threshold reduction achieved in FM system?
Threshold reduction is achieved in FM system by using an FM demodulator with
negative feedback or by using a phase locked loop demodulator.
85. What is Pre-emphasis?
The premodulation filtering in the transistor, to raise the power spectral density of
the base band signal in its upper-frequency range is called pre emphasis (or pre
distortion)
Pre emphasis is particularly effective in FM systems which are used for
transmission of audio signals.
86. Define de-emphasis.
The filtering at the receiver to undo the signal pre-emphasis and to suppress noise
is called de-emphasis.
87.Define Sampling theorem.
A band limited signal of finite energy, which has no frequency components higher
than fm Hertz may be completely recovered from a knowledge of its samples taken at the
rate of 2fm samples per second.
88.What do you infer from the receiver output of a coherent detector?
The output equation y(t)=1/2Cacm(t) +1/2nI(t) indicates that the message signal
and in-phase noise component of the filtered noise appear additively at the receiver
output. The quadrature component of the narrow band noise is completely rejected by the
coherent detector.
89.When is the figure of merit of SSBSC system 1?
For the same average transmitted signal power and the same average noise power
in the message bandwidth ,an SSB receiver will have exactly the same output signal to
noise ratio as a DSB-SC receiver when both receivers use coherent detection for the
recovery of the message signal.
90.Compare the noise performance of AM receiver with that of DSB-SC receiver.
The figure of merit of DSB-SC or SSB-SC receiver using coherent detection is
always unity,the figure of merit of AM receiver using envelope detection is always less
than unity.Therefore noise performance of AM receiver is always inferior to that of DSBSC
due to the wastage of power for transmitting the carrier.
91.What is the figure of merit of a AM system with 100 percent modulation?
The figure of merit of a AM system with 100 percent modulation is 1/3.This
means that other factors being equal an AM system must transmit three times as
much average power as a suppressed system in order to achieve the same quality
of noise performance .
92.What are the characteristics of a receiver?
The characteristics of a receiver are sensitivity, selectivity, fidelity, signal to noise
ratio.
96.Why is equivalent noise temperature used for noise measurement?
For low noise devices the noise figure is close to unity, which makes the
comparison difficult and hence it is preferable to use equivalent noise temperature.
97.What is the function of amplitude limiter in FM system?
The function of amplitude limiter in FM system is used to remove the amplitude
variations by clipping the modulated wave at the filter output almost to the zero axis .The
resultant wave is rounded off by another BPF that is an integral part of the limiter thereby
suppressing the harmonics of the carrier frequency.
98.What are components in a frequency discriminator?
Frequency discriminator has got two components .Slope detector or differentiator
with a purely imaginary frequency response that varies linearly with frequency. It
produces output where the amplitude and frequency vary with the message signal. An
envelope detector that recover the amplitude variations and produces message signal.
99.What is a post detection filter?
The post detection filter named as”base-band low pass filter” has a bandwidth that
is just large enough to accommodate the highest frequency component of the messge
signal.
100. Define lossless channel.
The channel described by a channel matrix with only one nonzero element in each
column is called a lossless channel. In the lossless channel no sources information is lost
in transmission.
101. Define Deterministic channel
A channel described by a channel matrix with only one nonzero element in each
row is called a deterministic channel and this element must be unity.
102. Define noiseless channel.
A channel is called noiseless if it is both lossless and deterministic. The channel
matrix has only one element in each row and in each column and this element is unity.
The input and output alphabets are of the same size.
103. Prove that I (xi xj) = I(xi) + I(xj) if xi and xj are independent.
If xi and xj are independent.
P (xi xj) = P(xi) P(xj)
I (xi xj) = log1/P(xi xj)
= log 1/ P(xi) P(xj)
= I(xi) + I(xj)
104. Explain Shannon-Fano coding.
An efficient code can be obtained by the following simple procedure, known as
Shannon- Fano algorthim.
1. List the source symbols in order of decreasing probability.
2. Partition the set into two sets that are as close to equiprobable as possible, and sign 0 to
the upper set and 1 to the lower set.
3. Continue this process, each time partitioning the sets with as nearly equal probabilities
as possible until further partitioning is not possible.
105. What are the types of Correlation?
The types of Correlation are Cross Correlation and Auto Correlation
106. What is the difference between Correlation and Convolution?
1. In Correlation physical time ‘t’ is dummy variable and it disappears after
solution of an integral. But in convolution ‘i’ is a dummy variable.
2. Convolution is a function of delay parameter ‘t‘ but convolution is a function of
‘ t’.
3. Convolution is commutative but correlation is noncom mutative.
107. Define Signal.
A signal is defined as any physical quantity carrying information that varies with
time. The value of signal may be real or complex. The types of signal are continuous
signal and discrete time signal.
108.Define entropy.
Entropy is the measure of the average information content per second. It is given
by the expression
H(X)= I P(xi)log2P(xi) bits/sample.
109.Define mutual information.
Mutual information I(X,Y) of a channel is defined by
I(X,Y)=H(X)-H(X/Y) bits/symbol
H(X)- entropy of the source
H(X/Y)- conditional entropy of Y.
110.State the properties of mutual information.
1. I(X,Y)=I(Y,X)
2. I(X,Y)>=0
3. I(X,Y)=H(Y)-H(Y/X)
4. I(X,Y)=H(X)+H(Y)-H(X,Y).
111.Give the relation between the different entropies.
H(X,Y)=H(X)+H(Y/X)
=H(Y)+H(X/Y)
H(X)- entropy of the source,H(Y/X),H(X/Y)-conditional entropy
H(Y)-entropy of destination
H(X,Y)- Joint entropy of the source and destination
112.Define information rate.
If the time rate at which source X emits symbols is r symbols per second. The
information rate R of the source is given by
R=r H(X) bits/second
H(X)- entropy of the source
113.What is data compaction?
For efficient signal transmission the redundant information must be removed from
the signal prior to transmission .This information with no loss of information is ordinarily
performed on a signal in digital form and is referred to as data compaction or lossless
data compression.
114.State the property of entropy.
1.0< H(X) < log2K , is the radix of the alphabet X of the source.
115.What is differential entropy?
The average amount of information per sample value of x(t) is measured by
H(X)= - fx(x)log fx(x)dx bit/sample
H(X) –differential entropy of X.
116.What is the channel capacity of a discrete signal?
The channel capacity of a discrete signal C= max I(X,Y)
P(xi)
I(X,Y)-mutual information.
117. What is source coding and entropy coding?
A conversion of the output of a DMS into a sequence of binary symbols is called
source coding. he design of a variable length code such that its average cod word length
approaches the entropy of the DMS is often referred to as entropy coding.
118.State Shannon Hartley theorem.
The capacity ‘C’ of a additive Gaussian noise channel is C=B log2 (1+S/N)
B= channel bandwidth ,S/N=signal to noise ratio.
119.What is the entropy of a binary memory-less source?
The entropy of a binary memory-less source H(X)=-p0 log2p0-(1-p0)log2(1-p0)
p0-probability of symbol ‘0’,p1=(1- p0 ) =probability of transmitting
symbol ‘1’
120.How is the efficiency of the coding technique measured?
Efficiency of the code =H(X) /L
L= p(xi)li average code word length .li=length of the code word.
121.What happens when the number of coding alphabet increases?
When the number of coding alphabet increases the efficiency of the coding
technique decreases.
122.What is channel diagram and channel matrix?
The transition probability diagram of the channel is called the channel diagram
and its matrix representation is called the channel matrix.
123.What is information theory?
Information theory deals with the mathematical modeling and analysis of a
communication system rather than with physical sources and physical channels
124.What is the channel capacity of a BSC and BEC?
For BSC the channel capacity C=1+plog2 p +(1-p)log2(1-p).
For BEC the channel capacity C=(1-p)
PART – B
1. Derive the expression for AM & its Power and Efficiency calculation:
AM – Definition
Let m(t) = Em Cos mt
c(t) = Ec Cos ct
EAM = Ec + Em Cos mt
= Ec [ 1+ (Em/Ec) Cos mt ]
m= Em/Ec
s(t)AM = EAM Cos ct
= Ec (1 + m Cos mt) Cos ct
= Ec Cos ct + mEc Cos mt Cos ct
= Ec Cos ct + mEc [Cos( c + m)t + Cos( c – m)t]
2
= Carrier + USB + LSB
Power relation in AM:
Total Power, Pt = PC + PUSB + PLSB
PC - Carrier power
PUSB - Upper Side Band power
PLSB - Lower Side Band power
PC = E2 rms
R
= Ec2
2R
PUSB = PLSB
= m2Ec2
8R
Pt = PC ( 1 + m2/2 )
Current relation in AM:
Pt = I t
2 R
PC = I c
2 R
I t = I c Sqrt (1 + m2/2)
Efficiency:
% = Power in side band x 100
Total Power
= m2 x 100
2+m2
m = 1
= 33.33 %
2. Describe the generation of AM wave by Non-Linear modulators :
Square law modulator:
AM wave
Summer – to add carrier & modulating signal.
Non-Linear element – active element (Diode)
BPF - extracting desired modulating products
To operate diode under Non-Linear region, magnitude of carrier component is higher
during positive cycle of the modulating voltage and lesser during negative half cycle of
the modulating voltage.
The resulting current is,
Io = a1 V1 + a2 V1
2 + ……
V1 = Em Cos mt + Ec Cos ct
Neglecting second and higher order terms,
Io = a1 Em Cos mt + a1 Ec Cos ct + 2a2 EmEc Cos mt Cos ct
After passing through BPF,
Io = a1 Ec Cos ct +a2 EmEc Cos ct Cos mt
Balanced Modulator:
Diagram – Refer Book
Input to the transistor T1,
Vbe1 = m(t) + c(t)
Summer Non-Linear
Element
BPF
Input to the transistor T2,
Vbe2 = m(t) – c(t)
m(t) = Em Cos mt
c(t) = Ec Cos ct
ic1 = a1 Vbe1 + a2 Vbe1
2 + …….
ic2 = a1 Vbe2 + a2 Vbe2
2 +…….
The output is given by,
Vo = K[ ic1 – ic2 ]
Vo = K 2 [ a1 Ec Cos ct + 2a2 Em Ec Cos ct Cos mt ]
m = ( 2a2 Em/a1 ) = modulation index
3.Write short notes on De Modulation of AM wave:
De Modulation – definition
Types:
1. Envelope detector
2. Square law detector
Envelope detector:
Requirements to use envelope detector:
1. AM wave has to be narrow band
2. Percentage of modulation should be less than 100%
Diagram - Refer book
During positive half cycle of the input signal, diode is forward biased and
capacitor C charges to peak value, when the input signal fall below the peak
value, the diode is reverse biased and the capacitor C discharges. The
discharging process continues until the next positive half cycle.
When the input signal is greater than the voltage across the capacitor, the
diode conducts again and the process is repeated.
The charging time constant ( rf + RS ) << 1/fc
rf – diode resistance
RS – source resistance
C – capacitor value
fc – carrier frequency
Discharging time constant,
1/fc << R1 << 1/
– message bandwidth
Square law detector:
s1(t)AM s1
2(t) Y1(t)
s(t)AM = [ A + m(t) ] Cos ct
s2(t)AM = [ A + m(t) ]2 Cos2 ct
Square law
device
LPF
For larger carrier,
[ m(t)/A ]2 is neglected
Blocking capacitor will suppress the dc term A2/2
Then the output is A m(t)
4. Compare the Synchronous Detector and the Costas PLL Detector.
Synchronous or Coherent Detector.
The block diagram of synchronous detector
Operation
All types of linear modulation can be detected by using Synchronous detector.The
incoming signal is first multiplied with locally generated carrier signal and then entered
via a LPF.The LPF bandwidth is usually same as the message BW or sometimes larger.
It is assumed that the local oscillator is exactly synchronized with the carrier in both
phase and velocity,hence the name.
Write the expression for message signal from the modulated signals using
coherent detector.
Thus the synchronous detector is capable of demodulating
DSB-SC and SSB-SC AM
Costas PLL Detector (For DSB-SC-AM)
The Block diagram of costas PLL detector
Operation
It consists of two synchronous detector. 1)In phase coherent detector or I
channel:- This detector is supplied with DSB-SC-AM and a locally generated
carrier which is in phase with the transmitted carrier. 2)Quadrature phase coherent
detector or Q channel:- This detector is fed with DSB-SC-AM and a locally
generated carrier which is in phase with the transmitted carrier. Assume the local
oscillator carrier signal is properly synchronized with transmitting carrier.So IChannel
output contains the desired demodulated signal whereas Q-channel
output is zero. If there is a phase shift of ; between local oscillator carrier and
transmitting carrier then I-channel output will remain in the same value but qchannel
output contains some signal . Thus combining the I and Q channel
outputs in phase discrimination a dc signal is obtained that automatically
corrects the phase errors in VCO.
Comparison
In Synchronous detector the detection is effective only when locally generated
carrier is properly synchronized with the modulated signal Any shift in phase or
frequency of the locally generated carrier results in phase or delay distortion.
To avoid this distortions a pilot carrier is inserted. Costas PLL detector
consists of two coherent detectors. These two detectors are coupled together to
form a negative feedback system designed in such a way to maintain the local
oscillator synchronise with the carrier.
5. Compare Phase shift method and modified Phase shift method
Phase Shift Method:(SSB-SC-AM)
Block diagram for phase shift method
Analysis
The undesired side band is removed by generating two side band components
out of phase.If the undesired sideband is LSB then the two LSB are generated
such that they are 180º out of phase with each other.So that the USB’s get added
and the LSB’s cancel each other.
Show the analysis using Expressions
Thus one of the sideband is cancelled whereas the other is reinforced.
Modified Phase Shift Method or Weaver’s method.
Block diagram
Operation
Here a phase shift is applied to AF carrier frequency only and after the
resulting vge has been applied to BM1 and BM2.
Show the analysis using Expressions
Comparison
Phase shift Method:
• It can switch from one Side Band to other
• Low audio modulating frequency is used
• Generates SSB at any frequency
Weavers Method:
• It does not require a SB filter or any wide band audio phase shift n/w
• Low frequency signals r used.
• Side bands may be easily switched & System is complex
6.Explain the Narrow Band Frequency Modulation
Frequency Modulation.
Frequency modulation is defined as the process of changing the
frequency of the carrier wave in accordance with respect to the message signal
keeping the amplitude and phase as a constant one.
Narrow Band Frequency Modulation: Definition
If the modulation index is less than one, then the FM signal is
narrow and frequency modulated signal.
BLOCK DIAGRAM
coswmt
S(t)NBFM
Carrier(coswct)
S(t)FM=Ec cos[wct+(Kf Em/wm)sinwmt];
Here m(t)=Em coswmt.
Modulation index(b)=Kf Em/wm.
S(t)FM=Ec cos[wct+bsinwmt]
Derivation
Since B<1,
Integrato
r
Product
Modulator Summe
r
-90 degree
phase shift
network
S(t)NBFM=Ec[coswct-b sinwct sinwmt]
7. Explain the Wide Band Frequency Modulation
Definition:
If the modulation index is greater than one, then the FM signal is wide band
frequency modulated signal.
Fourier Series Representation(aperiodic).
S(t)=Ec cos(wct+bsinwmt)
=Re{Ec.e^jwct.e^jbsinwmt}
Let S^(t)=(Ec.e^jbsinwmt)
S^(t)=SCn.e^j2Pfmnt (Complex Fourier Series representation of periodic function)
Cn= S^(t).e^-j2Pfmnt. dt
Solving,
Cn=Ec Jn(b)
S^(t)=SEc J(b).e^j2Pfmnt
8.Explain the method of Generation of FM signal .
(1) Direct FM generation
(2) Indirect FM generation
(1) Direct FM generation
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
(a)Varactor diode implementation of angle modulation.
(b)Reactance tube implementation of angle modulation.
Diagram - explanation
S(t)WBFM=SEc Jn(b).cos(wct+nwmt)
Analysis
(2) Indirect FM generation
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
Diagram - explanation
Analysis
9. Write short notes on Foster seeley Discriminator.
It is used for FM Detection
Circuit Diagram – Operation
Advantages
1. It is much easier to design
2. Only two tuned circuits are necessary and they are tuned to same frequency
3. Linearity is better
Disadvantages:
It requires Amplitude limiting circuit
10. What do you meant by Noise. Give the different types of noise – explain.
Noise – Definition
Noise Classification
1. Internal Noise
2. External Noise
Internal noise - Explanation
Internal Noise – types
a. Thermal nose – Explanation
b. Shot noise - Explanation
c. Transist time noise – Explanation
d. Miscellaneous noise – Explanation
External Noise – Explanation
1. Natural noise – Explanation
2. Man made noise – Explanation
Natural noise – types
a. Terrestial noise – Explanation
b. Extra tyerrestian noise – Explanation
11. Explain in detail about Noise temperature:
Noise performance of any system is indicated by noise figure. Noise figure is not
applicable when we are dealing with VHF & microwave amprs. Because noise power
and signal power obtained in these devices are close to unity. Hence comparison is rather
difficult. So Noise temperature is used.
- Diagram
- Explanation
- Calculation.
- Equivalent noise temperature Te = T(F-1)
obtain an expression for Noise figure when networks are in cascade
- Diagram
- Calculation
2 1 3 1 4 1
1 ...
1 1 2 1 2 3
F F F
F F
G G G G G G
− − −
= + + + +
12. Explain the effect of Noise when amplifiers are connected in cascade
Fig. shows a number of amplifier stages in cascade each having a resistance at its
input and output. We proceed to find the equivalent input noise voltage and its
equivalent noise resistance for the complete receiver.
Diagram
Consider the first two stages of the multi-stage amplifier having gains A1 and A2 and
input resistances R1 and R2 respectively R3forms the output resistance. The rms noise
voltage at the output due to R3 is given by,
Vn3 4kTBR3
The same noise voltage is present in the output if instead of R3 we have resistance
R’3 at the input of stage 2, where R’3 is given by,
' 3
3
2
n
n
V
V
A
= Substituting vn3 and simplify
Henchen this tuned circuit is non-ideal i.e. the
inductor L of the tuned circuit possesses a small resistive element Rs an shown in Fig.
This resistive element Rs generates noise.
In preceding sections, we have considered physical input resistor as the source of
noise. It may, however, be clearly understood that the noise producing resistance need
not necessarily be a physical resistor. Thus the series resistance Rs of the coil forms the
noise source generating a noise voltage Vn as shown in Fig. We are required to calculate
the noise voltage across the capacitor O.
Calculation
_
4 s V = kTBR
.
14. Define Noise figure and obtain an expression for Noise figure of an amplifier
The noise figure F is defined aqs the ratio of signal-to-noise power supplied to the
input terminals of the system (amplifier or receiver) to the signal-to-noise power supplied
by the system to the output load impedance.
Thus Noise Figure
/
/
S N
F
S N
= at the input/ at the output.
Calculation of Noise Figure
Diagram
i. Determine input signal power Si
ii. Determine the input noise power Ni
iii. Calculate the input signal-to-noise power ratio Si/Ni
iv. Determine the output signal power So
v. Determine the output noise power No
vi. Calculate the output signal-to-noise power ratio So/No
vii. From steps (iii) calculate the noise figure F.
Calculation.
_
2
( )
4
L o a t
a t
R N R R
F
k TBA R T
+
=
15. Obtain an expression for Noise Figure in Terms of Equivalent
Noise Resistance
In order to correlate the noise figure and the equivalent noise resistance we define
the term Req
’ as the noise resistance not including Rt.
'
Req = Req−Rt
The total equivalent noise resistance of this receiver is then given by,
' a t
eq
a t
R R
R R
R R
= +
+
The equivalent noise voltage effective at the input of the receiver is given by,
_
4 ni V = k TBR
Calculate the output noise power and calculate Noise Figure.
' 1
.
a t
eq
a t
R R
F R
R R
+
= +
extreme condition Rt > Ras the ratio (Ra + Ri) Rt approaches unity and
1 eq
a
R
F
R
= +
16. Explain in detail how noise figure is measured ?
At high frequencies where transit time becomes dominant, such a calculation is
not possible. In such a case, it becomes necessary to make measurements which enable
us to determine the noise figure. One such method makes use of the diode noise
generator.
Diagram
Calculation
19
3
(1.6 10 )
19.3
2 1.38 10 300
a a
a p
R I x
F R I
x x x
−
− = =
16. Super heterodyne receiver - Explanation
- Definition of receiver
- Functions of receiver
- Features of receiver
- Receiver Block Diagram
- Explanation of Block Diagram
17. Prove that the figure of merit of DSB – SC system is unity.
Block Diagram - refer Simon Haykins
S(t) DSB – SC = c Ac co wc t m(t)
Analysis
Input signal Power = c2 Ac2 P / 2
Input noise Power = wN0
Calculate (Input signal Power / Input noise Power) -------------- (1)
Output signal Power = c2 Ac2 P / 2
Output noise Power = wN0
Calculate (Output signal Power / Output noise Power)--------(2)
(1)
---- = Figure of merit
(2)
18. Noise in AM receivers - AM system using envelope detection
Block Diagram - refer Simon Haykins
AM wave equation
Input signal Power = Ac2 (1 + ka2 P) / 2
Average power of noise in the message bandwidth = wN0 = Input noise Power
Filtered signal = AM signal + noise signal
Analysis
Output signal Power = Ac2 ka2 P/ 2
Output noise Power = wN0
Calculate (Input signal Power / Input noise Power) -------------- (1)
Calculate (Output signal Power / Output noise Power)--------(2)
(1)
---- = Figure of merit
(2)
19. Noise in angle modulation System
Block Diagram
Representation of FM wave
Analysis
Output signal Power = a2 kf2 P
Analysis
a2 N0 2 w3
Output noise Power = --------------
3A2
Output signal Power 3kf2 P
----------------------- = --------
Output noise Power w
OR
Figure of merit = (3/2) b 2
20. Explain FM threshold reduction.
Threshold effect – As the input noise power is increased the carrier to noise ratio
is decreased the receiver breaks and as the carrier to noise ratio is reduced further
crackling sound is heard and the output SNR cannot be predicted by the equation. This
phenomenon is known as threshold effect.
Reduction method:
Block diagram
Explanation .
21. Explain the procedure of Shannon Fano Coding Algorithm and Huffman
Coding algorithm
Shannon Fano Coding Algorithm
1. Arrange the symbol probability in the descending order .
2. Partition the set into two sets that are as close to equiprobable as possible , and
assign 0 to the upper set and 1 to the lower set
3. Continue this process, each time partitioning the sets with as nearly equal
probabilities as possible until further partitioning is not possible
Huffman Coding algorithm
1. Arrange the symbol probability in the descending order .
2. Combine the probabilities of the two symbols having the lowest probabilities and
reorder the resultant probabilities; this step is reduction 1 . This procedure is
repeated until there are two ordered probabilities remaining.
3. Start encoding with the last reduction, which consists of exactly two ordered
probabilities .Assign 0 as the first digit in the code words for all the source
symbols associated with the first probability; assign 1 to the second probability
4. Now go back and assign 0 and 1 to the second digit for the two probabilities that
were combined in the previous reduction step ,retaining all assignments made in
step 3.
5. Keep regressing this way until the first column is reached.
22. .State and prove the properties of mutual information.
1. Mutual information I (xi yj) is symmetric. i.e. I (xi yj) = I (yj xi)
Proof
2. Mutual information I (xi yj) is maximum when p (xi / yj) = 1
Proof
3. I (X,Y) ³ 0
Proof .
4. Mutual information is related to the joint entropy of the channel input and
channel output by I(X,Y) = H (X) + H (Y) – H(X,Y)
Proof
23. Explain the different types of channel.
Loss less Channel
H (X/ Y) = 0 , I(X,Y) = H (X)
Channel capacity = Max (I(X,Y)) = H (X)
Channel diagram - Explanation
Deterministic channel
H (Y/ X) = 0
I(X,Y) = H (Y)
Channel capacity = Max (I(X,Y)) = H (Y) , Channel diagram - Explanation
Noise less Channel
H (X/ Y) = 0
H (Y/ X) = 0
Channel capacity = Max (I(X,Y)) = H (Y) = H (X)
Channel diagram - Explanation
Binary Symmetric Channel
Channel capacity = Max (I(X,Y)) = H (Y) = Plog2 P + (1- P) log2 (1-P)
Channel diagram - Explanation
24.Calculate the capacity of a gaussian channel.
State the Theorem ,Capacity = w log2 (1 + S/N) bits/ symbol
Analysis - refer notes
25.. Find the channel capacity of binary erasure channel P (x1 ) = a
Draw the channel diagram of the binary Erasure channel and get the channel
matrix.
P (y1/ x1) = 1-P
P (y2/ x1) = P
P (y2/ x2) = P
P (y3/ x2) = 1-P
Channel capacity = Max (I(X,Y)) = H (Y) - H (Y/ X)
i. Find H (Y/ X) using formula
H (Y/ X) = - (Plog2 P + (1- P) log2 (1-P))
ii. Find H (Y) using formula
H (Y) = - (1-P) [ a log 2a + log2 (1-P) + log 2(1- a) - alog 2(1- a) ] - Plog2 P
iii . I(X,Y) = (1-P) H (Y)
iv. Channel capacity = Max (I(X,Y)) = 1-P
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Kumaracoil
DEPARTMENT OF ECE
2 MARKS & QUESTION- ANSWERS
EC 1301 – Communication Theory
Class : S5 ECE
Prepared by :E.P.Kannan ECE
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
SUBJECT CODE: EC 1301
SUBJECT: COMMUNICATION THEORY
(FOR FIFTH SEMESTER ECE)
TWO MARKS QUESTIONS
1. Define 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.
2.What are the types of analog modulation?
Amplitude modulation.
Angle Modulation
1. Frequency modulation
2. Phase modulation.
3.Define depth of modulation.
It is defined as the ratio between message amplitude to that of carrier amplitude.
m=Em/Ec
4. What are the degrees of modulation?
Under modulation. m<1
Critical modulation m=1
Over modulation m>1
5.What is the need for modulation?
Needs for modulation:
Ease of transmission
Multiplexing
Reduced noise
Narrow bandwidth
Frequency assignment
Reduce the equipments limitations.
6.What are the types of AM modulators?
There are two types of AM modulators. They are
Linear modulators
Non-linear modulators
Linear modulators are classified as follows
Transistor modulator
There are three types of transistor modulator.
Collector modulator
Emitter modulator
Base modulator
Switching modulators
Non-linear modulators are classified as follows
Square law modulator
Product modulator
Balanced modulator
7.Give the classification of modulation.
There are two types of modulation. They are
Analog modulation
Digital modulation
Analog modulation is classified as follows
Continuous wave modulation
Pulse modulation
Continuous wave modulation is classified as follows
Amplitude modulation
Double side band suppressed carrier
Single side band suppressed carrier
Vestigial side band suppressed carrier
Angle modulation
Frequency modulation
Phase modulation
Pulse modulation is classified as follows
Pulse amplitude modulation
Pulse position modulation
Pulse duration modulation
Pulse code modulation
Digital modulation is classified as follows
Amplitude shift keying
Phase shift keying
Frequency shift keying
8.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.
9 .The antenna current of an AM transmitter is 8A when only carrier is sent. It increases to 8.93A when
the carrier is modulated by a single sine wave. Find the percentage modulation.
Solution:
Given: Ic =8A It=8.93A m=0.8
Formula: It=Ic (1+m2/2)
½
8.93=8(1+m2/2) ½
m=0.701
It=8 (1+0.82/2)
½
It=9.1A
10.Compare AM with DSB-SC and SSB-SC.
AM signal DSB-SC SSB-SC
Bandwidth=2fm
Bandwidth=2fm Bandwidth=fm
Contains USB, LSB, carrier Contains USB,LSB Contains LSB or USB
More power is required for
transmission
Power required is less than
that of AM.
Power required is less than
AM &DSB-SC
11 What are the advantages of VSB-AM?
1.It has bandwidth greater than SSB but less than DSB system.
2.Power transmission greater than DSB but less than SSB system.
3.No low frequency component lost. Hence it avoids phase distortion.
12 Compare linear and non-linear modulators.
Linear modulators Non-linear modulators
1.Heavy filtering is not 1.Heavy filtering is required
required.
2.These modulators are used in 2.These modulators are used in low level
high level modulation. Modulation.
3.The carrier voltage is very much 3.The modulating signal voltage is very much
greater than modulating signal greater than the carrier signal voltage.
voltage.
13.How will you generating DSBSC-AM ?
There are two ways of generating DSBSC-AM such as
1.balanced modulator 2.ring modulators
14. What are advantages of ring modulator?
1.Its output is stable.
2. It requires no external power source to activate the diodes.
3.Virtually no maintenance.
4. Long life.
15. 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.
16. What are the types of AM detectors?
1. Nonlinear detectors
2. Linear detectors
17.What are the types of linear detectors?
1.Synchronous or coherent detector.
2 .Envelope or non coherent detector.
18.draw the block diagram of coherent detector.
modulated
signal
OUTPUT
Product
modulator
LPF
Carrier
Signal
19.Define multiplexing.
Multiplexing is defined as the process of transmitting several message signals
simultaneously over a single channel.
20.Define sensitivity.
It is defined as a measure of its ability to receive weak signals.
21.Define selectivity.
Selectivity of a receiver is defined as its ability to select the desired signals among
the various signals.
22. Define stability.
It is the ability of the receiver to deliver a constant amount of output for a given a
given period of time.
23.Define super heterodyne principle.
It can be defined as the process of operation of modulated waves to obtain similarly
modulated waves of different frequency. This process uses a locally generated carrier
wave, which determines the change of frequency.
24.A transmitter supplies 8 Kw to the antenna when modulated. Determine the total
power radiated when modulated to 30%.
m=0.3;Pc=8 kw
Pt=Pc(1+m2/2)
=8.36 kw
25.What are the drawbacks of emitter modulator?
1.The amplifier is operated in class A mode, thus the efficiency is low.
2.The output power is very small. Thus it is not suitable for generating high
level modulation.
26. Define 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.
27. Define modulation index of frequency modulation.
It is defined as the ratio of maximum frequency deviation to the
modulating frequency. b = df/fm
28. What do you meant by multitone modulation?
Modulation done for the message signal with more than one frequency component
is called multitone modulation.
29. Define 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.
30. How FM wave can be converted to PM wave?
Message signal PM Signal
31. How PM wave can be converted to FM wave?
Message Signal FM Signal
Integrator
Phase
Modulator
Carrier
Differentiator FM
32. 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
33. 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.
34. 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
35 . Compare WBFM and NBFM.
WBFM NBFM
Modulation index is greater than 1 Modulation index less than 1
Frequency deviation 75 KHz Frequency deviation 5 KHz
Bandwidth 15 times NBFM Bandwidth 2fm
Noise is more suppressed Less suppressing of noise
Carrier
36. List the properties of the Bessel function.
The properties of the Bessel function is given by,
i) Jn (b)=(-1)nJ-n(b) for all n, both positive and negative.
ii) For small values of the modulation index b ,we have
J0 (b)=1
J1 (b)=b/2
Jn(b)=0,n>2.
¥
iii) S J2
n (b)=1
n = -¥
37. Give the average power of an FM signal.
The amplitude of the frequency modulated signal is constant .The power of the
FM signal is same as that of the carrier power. P=1/2 Ec
2 .
38. Define phase deviation.
The maximum phase deviation of the total angle from the carrier angle is called
phase deviation.
39. Define frequency Deviation.
The maximum departure of the instantaneous frequency from the carrier frequency
is called frequency deviation.
40. State the Carson’s rule.
An approximate rule for the transmission bandwidth of an FM Signal generated by
a single tone-modulating signal of frequency fm is defined as
B =2 Df(1+1/ b)
41.Define the deviation ratio D for non-sinusoidal modulation.
The deviation ratio D is defined as the ratio of the frequency deviation Df, which
corresponds to the maximum possible amplitude of the modulation signal m(t),to the
highest modulation frequency .
D = Df / fm
42.What is the use of crystal controlled oscillator?
The crystal-controlled oscillator always produces a constant carrier frequency
there by enhancing frequency stability.
43. What are the disadvantages of FM system?
1. A much wider channel is required by FM.
2. FM transmitting and receiving equipments tend to be more complex and
hence it is expensive
44. 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.
45. What are the types of FM detectors?
Slope detector and phase discriminator.
46. What are the types of phase discriminator?
Foster seely discriminator and ratio detector.
47. What are the disadvantages of balanced slope detector?
1. Amplitude limiting cannot be provided
2. Linearity is not sufficient
3. It is difficult to align because of three different frequency to which various
tuned circuits to be tuned.
4. The tuned circuit is not purely band limited.
48. Define probability.
The probability of occurrence of an event A is defined as,
P(A)= number of possible favorable outcomes
Total number of equal likely outcomes
49.What are mutually exclusive events?
Two possible outcomes of an experiment are defined as being mutually exclusive
if the occurrence of one outcome precludes the occurrence of the other.
50. Define probability density function.
Probability density function is defined as fx(x) is defined in terms of
cumulative distribution function Fx (x) as
fx(x) = d Fx (x)
dx
51. Define noise.
Noise is defined as any unwanted form of energy, which tends to interfere with
proper reception and reproduction of wanted signal.
52. Give the classification of noise.
Noise is broadly classified into two types. They are External noise and internal
noise.
53. What are the types of External noise?
External noise can be classified into
1. Atmospheric noise
2. Extraterrestrial noises
3. Man –made noises or industrial noises
54. 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
55. What are the types of extraterrestrial noise and write their origin?
The two type of extraterrestrial noise are solar noise and cosmic noise
Solar noise is the electrical noise emanating from the sun.
Cosmic noise is the noise received from the center part of our galaxy, other
distant galaxies and other virtual point sources.
56. Define transit time of a transistor.
Transit time is defined as the time taken by the electron to travel from emitter to
the collector.
57. 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.
58. State the reasons for higher noise in mixers.
1. Conversion transconductance of mixers is much lower than the
transconductance of amplifiers.
2. If image frequency rejection is inadequate, the noise associated with the image
frequency also gets accepted.
59. Define signal to noise ratio.
Signal to noise ratio is the ratio of signal power to the noise power at the same
point in a system.
60. Define noise figure.
S/ N at the input
Nose figure F =
S/ N at the output
S/N = Signal power / Noise Power
61. Explain thermal noise.
Thermal noise is the name given to the electrical noise arising from the random
motion of electrons in a conductor.
62. Give the expression for noise voltage in a resistor.
The mean –square value of thermal noise voltage is given by
Vn
2 = 4 K T B R
K – Boltz man constant
R – resistance
T – obsolute temperature
B - Bandwidth
63. Explain White Noise.
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 white noise is independent
of the operating frequency.
64. What is narrowband noise?
The receiver of a communication system usually includes some provision for
preprocessing the received signal. The preprocessing 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.
65. Give the representation of narrowband noise in terms of envelope and phase
components.
Narrowband noise in terms of envelope and phase components as
n(t) = r(t) cos (2 fct + (t) )
r(t) = (nI 2(t) + nQ 2(t))½
(t) = tan -1(nQ(t) / nI (t ))
The function r (t) and (t) are called envelope and phase of n(t).
66. Give the expression for equivalent noise temperature in terms of hypothetical
temperature.
The expression for equivalent noise temperature in terms of hypothetical
temperature
is Te = ( F- 1) T0
Where, F is the noise figure and T0 absolute temperature.
67. Give the Friss formula in terms of noise temperature.
The Friss formula in terms of noise temperature is
Te = T1 + T2 / G1 + T3 / G1 G2 + ………
G1 , G2 ,… Gain of amplifiers
68. What is called image frequency?
Image frequency is defined as the signal frequency plus twice the intermediate
frequency. This has the effect of two stations being received simultaneously and hence it
is undesirable.
fsi = fs + 2 fi
fsi - image frequency
It can be eliminated by providing adequate image signal selectivity between antenna and
mixer input.
69. What is intermediate frequency?
Intermediate frequency (IF) is defined as the difference between the signal
frequency and the oscillator frequency.
IF = fs – fo when fs > fo (or)
IF = fo –fs when fo > fs
70. Define Partition noise.
In an electron tube having one or more positive grids, this noise is caused by
irratic partition of the cathode current among the positive electrodes. In a transistor, the
partition noise is created from the random fluctuation in the division of current between
the collector and base.
71. Give the expression for noise voltage when several sources are cascaded.
Enr = Sqrt (4 KTB (R1 + R2 + …..) )
Where R1 , R2 --- are the resistances of the noise resistors.
K – Boltz man constant
T – absolute temperature
B – Bandwidth
72. Define random variable
Random variable is defined as a rule or mapping from the original sample space
to a numerical sample space subjected to certain constraints. Random variable is also
defined as a function where domain is the set of outcomes es and whose range is R, is
the real line.
73. Define Random process.
A Random process X (s,t) is a function that maps each element of a samples space
into a time function called sample function. Random process is a collection of time
functions.
74. Give the Laws of probability.
Additive law of probability
Case i
When events are mutually exclusive , P (AÇB) =
P(AÈB) = P(A) + P(B)
Case ii
When events are not mutually exclusive
P(AÈB) = P(A) + P(B) - P (AÇB)
Multiplication law of probability:
Case i When events are independent
P(AÇB) = P(A) P(B)
Case ii When events are dependent
P(AÇB) = P(A) P(B/A)
= P(B) P(A/B)
75. What is frequency translation?
Suppose that a signal is band limited to the frequency range extending from a
frequency f1 to a frequency f2. The process of frequency translation is one in which the
original signal is replaced with a new signal whose spectral range extends from f1’ to f2’
and which new signal bears, in recoverable form the same information as was borne by
the original signal.
76. What are two situations identified in frequency translations?
The two situations identified in frequency translation are
i Up conversion
In this case the translated carrier frequency is greater than the incoming carrier
frequency
ii Down conversion
In this case the translated carrier frequency is smaller than the incoming carrier
frequency.
Thus, a narrowband FM signal requires essentially the same transmission bandwidth as
the AM signal.
77. Define Tracking.
Tracking is the process of correctly tuning a number of tunable circuits in a
receiver.
78. What is TRF receiver?
Tuned Radio Frequency is also called straight receiver.Here the receiver operates
in straight forward manner without frequency conversion.
79.What are the advantages of superheterodyne receiver over TRF?
The advantages of superheterodyne receiver over TRF are high selectivity
,improved sensitivity throughout the carrier frequency band..It eliminates image
frequency.
80.What is the figure of merit of DSBSC system ?
The figure of merit of DSBSC signal is unity
81.Compare the noise performance of an AM and FM system?
The figure of merit of AM system is 1/3 when the modulation is 100 percent and
that of FM is(3/2)mf
2.The use of FM offers improved noise performance
over AM when (3/2)mf
2 > 1/3.mf –modulation index in FM.
82.What is Capture effect?
When the interference signal and FM input are of equal strength, the receiver
fluctuates back and froth between them .This phenomenon is known as the capture effect.
83.What is threshold effect?
As the input noise power is increased the carrier to noise ratio is decreased the
receiver breaks and as the carrier to noise ratio is reduced further crackling sound is heard
and the output SNR cannot be predicted by the equation. This phenomenon is known as
threshold effect.
84.How is threshold reduction achieved in FM system?
Threshold reduction is achieved in FM system by using an FM demodulator with
negative feedback or by using a phase locked loop demodulator.
85. What is Pre-emphasis?
The premodulation filtering in the transistor, to raise the power spectral density of
the base band signal in its upper-frequency range is called pre emphasis (or pre
distortion)
Pre emphasis is particularly effective in FM systems which are used for
transmission of audio signals.
86. Define de-emphasis.
The filtering at the receiver to undo the signal pre-emphasis and to suppress noise
is called de-emphasis.
87.Define Sampling theorem.
A band limited signal of finite energy, which has no frequency components higher
than fm Hertz may be completely recovered from a knowledge of its samples taken at the
rate of 2fm samples per second.
88.What do you infer from the receiver output of a coherent detector?
The output equation y(t)=1/2Cacm(t) +1/2nI(t) indicates that the message signal
and in-phase noise component of the filtered noise appear additively at the receiver
output. The quadrature component of the narrow band noise is completely rejected by the
coherent detector.
89.When is the figure of merit of SSBSC system 1?
For the same average transmitted signal power and the same average noise power
in the message bandwidth ,an SSB receiver will have exactly the same output signal to
noise ratio as a DSB-SC receiver when both receivers use coherent detection for the
recovery of the message signal.
90.Compare the noise performance of AM receiver with that of DSB-SC receiver.
The figure of merit of DSB-SC or SSB-SC receiver using coherent detection is
always unity,the figure of merit of AM receiver using envelope detection is always less
than unity.Therefore noise performance of AM receiver is always inferior to that of DSBSC
due to the wastage of power for transmitting the carrier.
91.What is the figure of merit of a AM system with 100 percent modulation?
The figure of merit of a AM system with 100 percent modulation is 1/3.This
means that other factors being equal an AM system must transmit three times as
much average power as a suppressed system in order to achieve the same quality
of noise performance .
92.What are the characteristics of a receiver?
The characteristics of a receiver are sensitivity, selectivity, fidelity, signal to noise
ratio.
96.Why is equivalent noise temperature used for noise measurement?
For low noise devices the noise figure is close to unity, which makes the
comparison difficult and hence it is preferable to use equivalent noise temperature.
97.What is the function of amplitude limiter in FM system?
The function of amplitude limiter in FM system is used to remove the amplitude
variations by clipping the modulated wave at the filter output almost to the zero axis .The
resultant wave is rounded off by another BPF that is an integral part of the limiter thereby
suppressing the harmonics of the carrier frequency.
98.What are components in a frequency discriminator?
Frequency discriminator has got two components .Slope detector or differentiator
with a purely imaginary frequency response that varies linearly with frequency. It
produces output where the amplitude and frequency vary with the message signal. An
envelope detector that recover the amplitude variations and produces message signal.
99.What is a post detection filter?
The post detection filter named as”base-band low pass filter” has a bandwidth that
is just large enough to accommodate the highest frequency component of the messge
signal.
100. Define lossless channel.
The channel described by a channel matrix with only one nonzero element in each
column is called a lossless channel. In the lossless channel no sources information is lost
in transmission.
101. Define Deterministic channel
A channel described by a channel matrix with only one nonzero element in each
row is called a deterministic channel and this element must be unity.
102. Define noiseless channel.
A channel is called noiseless if it is both lossless and deterministic. The channel
matrix has only one element in each row and in each column and this element is unity.
The input and output alphabets are of the same size.
103. Prove that I (xi xj) = I(xi) + I(xj) if xi and xj are independent.
If xi and xj are independent.
P (xi xj) = P(xi) P(xj)
I (xi xj) = log1/P(xi xj)
= log 1/ P(xi) P(xj)
= I(xi) + I(xj)
104. Explain Shannon-Fano coding.
An efficient code can be obtained by the following simple procedure, known as
Shannon- Fano algorthim.
1. List the source symbols in order of decreasing probability.
2. Partition the set into two sets that are as close to equiprobable as possible, and sign 0 to
the upper set and 1 to the lower set.
3. Continue this process, each time partitioning the sets with as nearly equal probabilities
as possible until further partitioning is not possible.
105. What are the types of Correlation?
The types of Correlation are Cross Correlation and Auto Correlation
106. What is the difference between Correlation and Convolution?
1. In Correlation physical time ‘t’ is dummy variable and it disappears after
solution of an integral. But in convolution ‘i’ is a dummy variable.
2. Convolution is a function of delay parameter ‘t‘ but convolution is a function of
‘ t’.
3. Convolution is commutative but correlation is noncom mutative.
107. Define Signal.
A signal is defined as any physical quantity carrying information that varies with
time. The value of signal may be real or complex. The types of signal are continuous
signal and discrete time signal.
108.Define entropy.
Entropy is the measure of the average information content per second. It is given
by the expression
H(X)= I P(xi)log2P(xi) bits/sample.
109.Define mutual information.
Mutual information I(X,Y) of a channel is defined by
I(X,Y)=H(X)-H(X/Y) bits/symbol
H(X)- entropy of the source
H(X/Y)- conditional entropy of Y.
110.State the properties of mutual information.
1. I(X,Y)=I(Y,X)
2. I(X,Y)>=0
3. I(X,Y)=H(Y)-H(Y/X)
4. I(X,Y)=H(X)+H(Y)-H(X,Y).
111.Give the relation between the different entropies.
H(X,Y)=H(X)+H(Y/X)
=H(Y)+H(X/Y)
H(X)- entropy of the source,H(Y/X),H(X/Y)-conditional entropy
H(Y)-entropy of destination
H(X,Y)- Joint entropy of the source and destination
112.Define information rate.
If the time rate at which source X emits symbols is r symbols per second. The
information rate R of the source is given by
R=r H(X) bits/second
H(X)- entropy of the source
113.What is data compaction?
For efficient signal transmission the redundant information must be removed from
the signal prior to transmission .This information with no loss of information is ordinarily
performed on a signal in digital form and is referred to as data compaction or lossless
data compression.
114.State the property of entropy.
1.0< H(X) < log2K , is the radix of the alphabet X of the source.
115.What is differential entropy?
The average amount of information per sample value of x(t) is measured by
H(X)= - fx(x)log fx(x)dx bit/sample
H(X) –differential entropy of X.
116.What is the channel capacity of a discrete signal?
The channel capacity of a discrete signal C= max I(X,Y)
P(xi)
I(X,Y)-mutual information.
117. What is source coding and entropy coding?
A conversion of the output of a DMS into a sequence of binary symbols is called
source coding. he design of a variable length code such that its average cod word length
approaches the entropy of the DMS is often referred to as entropy coding.
118.State Shannon Hartley theorem.
The capacity ‘C’ of a additive Gaussian noise channel is C=B log2 (1+S/N)
B= channel bandwidth ,S/N=signal to noise ratio.
119.What is the entropy of a binary memory-less source?
The entropy of a binary memory-less source H(X)=-p0 log2p0-(1-p0)log2(1-p0)
p0-probability of symbol ‘0’,p1=(1- p0 ) =probability of transmitting
symbol ‘1’
120.How is the efficiency of the coding technique measured?
Efficiency of the code =H(X) /L
L= p(xi)li average code word length .li=length of the code word.
121.What happens when the number of coding alphabet increases?
When the number of coding alphabet increases the efficiency of the coding
technique decreases.
122.What is channel diagram and channel matrix?
The transition probability diagram of the channel is called the channel diagram
and its matrix representation is called the channel matrix.
123.What is information theory?
Information theory deals with the mathematical modeling and analysis of a
communication system rather than with physical sources and physical channels
124.What is the channel capacity of a BSC and BEC?
For BSC the channel capacity C=1+plog2 p +(1-p)log2(1-p).
For BEC the channel capacity C=(1-p)
PART – B
1. Derive the expression for AM & its Power and Efficiency calculation:
AM – Definition
Let m(t) = Em Cos mt
c(t) = Ec Cos ct
EAM = Ec + Em Cos mt
= Ec [ 1+ (Em/Ec) Cos mt ]
m= Em/Ec
s(t)AM = EAM Cos ct
= Ec (1 + m Cos mt) Cos ct
= Ec Cos ct + mEc Cos mt Cos ct
= Ec Cos ct + mEc [Cos( c + m)t + Cos( c – m)t]
2
= Carrier + USB + LSB
Power relation in AM:
Total Power, Pt = PC + PUSB + PLSB
PC - Carrier power
PUSB - Upper Side Band power
PLSB - Lower Side Band power
PC = E2 rms
R
= Ec2
2R
PUSB = PLSB
= m2Ec2
8R
Pt = PC ( 1 + m2/2 )
Current relation in AM:
Pt = I t
2 R
PC = I c
2 R
I t = I c Sqrt (1 + m2/2)
Efficiency:
% = Power in side band x 100
Total Power
= m2 x 100
2+m2
m = 1
= 33.33 %
2. Describe the generation of AM wave by Non-Linear modulators :
Square law modulator:
AM wave
Summer – to add carrier & modulating signal.
Non-Linear element – active element (Diode)
BPF - extracting desired modulating products
To operate diode under Non-Linear region, magnitude of carrier component is higher
during positive cycle of the modulating voltage and lesser during negative half cycle of
the modulating voltage.
The resulting current is,
Io = a1 V1 + a2 V1
2 + ……
V1 = Em Cos mt + Ec Cos ct
Neglecting second and higher order terms,
Io = a1 Em Cos mt + a1 Ec Cos ct + 2a2 EmEc Cos mt Cos ct
After passing through BPF,
Io = a1 Ec Cos ct +a2 EmEc Cos ct Cos mt
Balanced Modulator:
Diagram – Refer Book
Input to the transistor T1,
Vbe1 = m(t) + c(t)
Summer Non-Linear
Element
BPF
Input to the transistor T2,
Vbe2 = m(t) – c(t)
m(t) = Em Cos mt
c(t) = Ec Cos ct
ic1 = a1 Vbe1 + a2 Vbe1
2 + …….
ic2 = a1 Vbe2 + a2 Vbe2
2 +…….
The output is given by,
Vo = K[ ic1 – ic2 ]
Vo = K 2 [ a1 Ec Cos ct + 2a2 Em Ec Cos ct Cos mt ]
m = ( 2a2 Em/a1 ) = modulation index
3.Write short notes on De Modulation of AM wave:
De Modulation – definition
Types:
1. Envelope detector
2. Square law detector
Envelope detector:
Requirements to use envelope detector:
1. AM wave has to be narrow band
2. Percentage of modulation should be less than 100%
Diagram - Refer book
During positive half cycle of the input signal, diode is forward biased and
capacitor C charges to peak value, when the input signal fall below the peak
value, the diode is reverse biased and the capacitor C discharges. The
discharging process continues until the next positive half cycle.
When the input signal is greater than the voltage across the capacitor, the
diode conducts again and the process is repeated.
The charging time constant ( rf + RS ) << 1/fc
rf – diode resistance
RS – source resistance
C – capacitor value
fc – carrier frequency
Discharging time constant,
1/fc << R1 << 1/
– message bandwidth
Square law detector:
s1(t)AM s1
2(t) Y1(t)
s(t)AM = [ A + m(t) ] Cos ct
s2(t)AM = [ A + m(t) ]2 Cos2 ct
Square law
device
LPF
For larger carrier,
[ m(t)/A ]2 is neglected
Blocking capacitor will suppress the dc term A2/2
Then the output is A m(t)
4. Compare the Synchronous Detector and the Costas PLL Detector.
Synchronous or Coherent Detector.
The block diagram of synchronous detector
Operation
All types of linear modulation can be detected by using Synchronous detector.The
incoming signal is first multiplied with locally generated carrier signal and then entered
via a LPF.The LPF bandwidth is usually same as the message BW or sometimes larger.
It is assumed that the local oscillator is exactly synchronized with the carrier in both
phase and velocity,hence the name.
Write the expression for message signal from the modulated signals using
coherent detector.
Thus the synchronous detector is capable of demodulating
DSB-SC and SSB-SC AM
Costas PLL Detector (For DSB-SC-AM)
The Block diagram of costas PLL detector
Operation
It consists of two synchronous detector. 1)In phase coherent detector or I
channel:- This detector is supplied with DSB-SC-AM and a locally generated
carrier which is in phase with the transmitted carrier. 2)Quadrature phase coherent
detector or Q channel:- This detector is fed with DSB-SC-AM and a locally
generated carrier which is in phase with the transmitted carrier. Assume the local
oscillator carrier signal is properly synchronized with transmitting carrier.So IChannel
output contains the desired demodulated signal whereas Q-channel
output is zero. If there is a phase shift of ; between local oscillator carrier and
transmitting carrier then I-channel output will remain in the same value but qchannel
output contains some signal . Thus combining the I and Q channel
outputs in phase discrimination a dc signal is obtained that automatically
corrects the phase errors in VCO.
Comparison
In Synchronous detector the detection is effective only when locally generated
carrier is properly synchronized with the modulated signal Any shift in phase or
frequency of the locally generated carrier results in phase or delay distortion.
To avoid this distortions a pilot carrier is inserted. Costas PLL detector
consists of two coherent detectors. These two detectors are coupled together to
form a negative feedback system designed in such a way to maintain the local
oscillator synchronise with the carrier.
5. Compare Phase shift method and modified Phase shift method
Phase Shift Method:(SSB-SC-AM)
Block diagram for phase shift method
Analysis
The undesired side band is removed by generating two side band components
out of phase.If the undesired sideband is LSB then the two LSB are generated
such that they are 180º out of phase with each other.So that the USB’s get added
and the LSB’s cancel each other.
Show the analysis using Expressions
Thus one of the sideband is cancelled whereas the other is reinforced.
Modified Phase Shift Method or Weaver’s method.
Block diagram
Operation
Here a phase shift is applied to AF carrier frequency only and after the
resulting vge has been applied to BM1 and BM2.
Show the analysis using Expressions
Comparison
Phase shift Method:
• It can switch from one Side Band to other
• Low audio modulating frequency is used
• Generates SSB at any frequency
Weavers Method:
• It does not require a SB filter or any wide band audio phase shift n/w
• Low frequency signals r used.
• Side bands may be easily switched & System is complex
6.Explain the Narrow Band Frequency Modulation
Frequency Modulation.
Frequency modulation is defined as the process of changing the
frequency of the carrier wave in accordance with respect to the message signal
keeping the amplitude and phase as a constant one.
Narrow Band Frequency Modulation: Definition
If the modulation index is less than one, then the FM signal is
narrow and frequency modulated signal.
BLOCK DIAGRAM
coswmt
S(t)NBFM
Carrier(coswct)
S(t)FM=Ec cos[wct+(Kf Em/wm)sinwmt];
Here m(t)=Em coswmt.
Modulation index(b)=Kf Em/wm.
S(t)FM=Ec cos[wct+bsinwmt]
Derivation
Since B<1,
Integrato
r
Product
Modulator Summe
r
-90 degree
phase shift
network
S(t)NBFM=Ec[coswct-b sinwct sinwmt]
7. Explain the Wide Band Frequency Modulation
Definition:
If the modulation index is greater than one, then the FM signal is wide band
frequency modulated signal.
Fourier Series Representation(aperiodic).
S(t)=Ec cos(wct+bsinwmt)
=Re{Ec.e^jwct.e^jbsinwmt}
Let S^(t)=(Ec.e^jbsinwmt)
S^(t)=SCn.e^j2Pfmnt (Complex Fourier Series representation of periodic function)
Cn= S^(t).e^-j2Pfmnt. dt
Solving,
Cn=Ec Jn(b)
S^(t)=SEc J(b).e^j2Pfmnt
8.Explain the method of Generation of FM signal .
(1) Direct FM generation
(2) Indirect FM generation
(1) Direct FM generation
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
(a)Varactor diode implementation of angle modulation.
(b)Reactance tube implementation of angle modulation.
Diagram - explanation
S(t)WBFM=SEc Jn(b).cos(wct+nwmt)
Analysis
(2) Indirect FM generation
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
Diagram - explanation
Analysis
9. Write short notes on Foster seeley Discriminator.
It is used for FM Detection
Circuit Diagram – Operation
Advantages
1. It is much easier to design
2. Only two tuned circuits are necessary and they are tuned to same frequency
3. Linearity is better
Disadvantages:
It requires Amplitude limiting circuit
10. What do you meant by Noise. Give the different types of noise – explain.
Noise – Definition
Noise Classification
1. Internal Noise
2. External Noise
Internal noise - Explanation
Internal Noise – types
a. Thermal nose – Explanation
b. Shot noise - Explanation
c. Transist time noise – Explanation
d. Miscellaneous noise – Explanation
External Noise – Explanation
1. Natural noise – Explanation
2. Man made noise – Explanation
Natural noise – types
a. Terrestial noise – Explanation
b. Extra tyerrestian noise – Explanation
11. Explain in detail about Noise temperature:
Noise performance of any system is indicated by noise figure. Noise figure is not
applicable when we are dealing with VHF & microwave amprs. Because noise power
and signal power obtained in these devices are close to unity. Hence comparison is rather
difficult. So Noise temperature is used.
- Diagram
- Explanation
- Calculation.
- Equivalent noise temperature Te = T(F-1)
obtain an expression for Noise figure when networks are in cascade
- Diagram
- Calculation
2 1 3 1 4 1
1 ...
1 1 2 1 2 3
F F F
F F
G G G G G G
− − −
= + + + +
12. Explain the effect of Noise when amplifiers are connected in cascade
Fig. shows a number of amplifier stages in cascade each having a resistance at its
input and output. We proceed to find the equivalent input noise voltage and its
equivalent noise resistance for the complete receiver.
Diagram
Consider the first two stages of the multi-stage amplifier having gains A1 and A2 and
input resistances R1 and R2 respectively R3forms the output resistance. The rms noise
voltage at the output due to R3 is given by,
Vn3 4kTBR3
The same noise voltage is present in the output if instead of R3 we have resistance
R’3 at the input of stage 2, where R’3 is given by,
' 3
3
2
n
n
V
V
A
= Substituting vn3 and simplify
Henchen this tuned circuit is non-ideal i.e. the
inductor L of the tuned circuit possesses a small resistive element Rs an shown in Fig.
This resistive element Rs generates noise.
In preceding sections, we have considered physical input resistor as the source of
noise. It may, however, be clearly understood that the noise producing resistance need
not necessarily be a physical resistor. Thus the series resistance Rs of the coil forms the
noise source generating a noise voltage Vn as shown in Fig. We are required to calculate
the noise voltage across the capacitor O.
Calculation
_
4 s V = kTBR
.
14. Define Noise figure and obtain an expression for Noise figure of an amplifier
The noise figure F is defined aqs the ratio of signal-to-noise power supplied to the
input terminals of the system (amplifier or receiver) to the signal-to-noise power supplied
by the system to the output load impedance.
Thus Noise Figure
/
/
S N
F
S N
= at the input/ at the output.
Calculation of Noise Figure
Diagram
i. Determine input signal power Si
ii. Determine the input noise power Ni
iii. Calculate the input signal-to-noise power ratio Si/Ni
iv. Determine the output signal power So
v. Determine the output noise power No
vi. Calculate the output signal-to-noise power ratio So/No
vii. From steps (iii) calculate the noise figure F.
Calculation.
_
2
( )
4
L o a t
a t
R N R R
F
k TBA R T
+
=
15. Obtain an expression for Noise Figure in Terms of Equivalent
Noise Resistance
In order to correlate the noise figure and the equivalent noise resistance we define
the term Req
’ as the noise resistance not including Rt.
'
Req = Req−Rt
The total equivalent noise resistance of this receiver is then given by,
' a t
eq
a t
R R
R R
R R
= +
+
The equivalent noise voltage effective at the input of the receiver is given by,
_
4 ni V = k TBR
Calculate the output noise power and calculate Noise Figure.
' 1
.
a t
eq
a t
R R
F R
R R
+
= +
extreme condition Rt > Ras the ratio (Ra + Ri) Rt approaches unity and
1 eq
a
R
F
R
= +
16. Explain in detail how noise figure is measured ?
At high frequencies where transit time becomes dominant, such a calculation is
not possible. In such a case, it becomes necessary to make measurements which enable
us to determine the noise figure. One such method makes use of the diode noise
generator.
Diagram
Calculation
19
3
(1.6 10 )
19.3
2 1.38 10 300
a a
a p
R I x
F R I
x x x
−
− = =
16. Super heterodyne receiver - Explanation
- Definition of receiver
- Functions of receiver
- Features of receiver
- Receiver Block Diagram
- Explanation of Block Diagram
17. Prove that the figure of merit of DSB – SC system is unity.
Block Diagram - refer Simon Haykins
S(t) DSB – SC = c Ac co wc t m(t)
Analysis
Input signal Power = c2 Ac2 P / 2
Input noise Power = wN0
Calculate (Input signal Power / Input noise Power) -------------- (1)
Output signal Power = c2 Ac2 P / 2
Output noise Power = wN0
Calculate (Output signal Power / Output noise Power)--------(2)
(1)
---- = Figure of merit
(2)
18. Noise in AM receivers - AM system using envelope detection
Block Diagram - refer Simon Haykins
AM wave equation
Input signal Power = Ac2 (1 + ka2 P) / 2
Average power of noise in the message bandwidth = wN0 = Input noise Power
Filtered signal = AM signal + noise signal
Analysis
Output signal Power = Ac2 ka2 P/ 2
Output noise Power = wN0
Calculate (Input signal Power / Input noise Power) -------------- (1)
Calculate (Output signal Power / Output noise Power)--------(2)
(1)
---- = Figure of merit
(2)
19. Noise in angle modulation System
Block Diagram
Representation of FM wave
Analysis
Output signal Power = a2 kf2 P
Analysis
a2 N0 2 w3
Output noise Power = --------------
3A2
Output signal Power 3kf2 P
----------------------- = --------
Output noise Power w
OR
Figure of merit = (3/2) b 2
20. Explain FM threshold reduction.
Threshold effect – As the input noise power is increased the carrier to noise ratio
is decreased the receiver breaks and as the carrier to noise ratio is reduced further
crackling sound is heard and the output SNR cannot be predicted by the equation. This
phenomenon is known as threshold effect.
Reduction method:
Block diagram
Explanation .
21. Explain the procedure of Shannon Fano Coding Algorithm and Huffman
Coding algorithm
Shannon Fano Coding Algorithm
1. Arrange the symbol probability in the descending order .
2. Partition the set into two sets that are as close to equiprobable as possible , and
assign 0 to the upper set and 1 to the lower set
3. Continue this process, each time partitioning the sets with as nearly equal
probabilities as possible until further partitioning is not possible
Huffman Coding algorithm
1. Arrange the symbol probability in the descending order .
2. Combine the probabilities of the two symbols having the lowest probabilities and
reorder the resultant probabilities; this step is reduction 1 . This procedure is
repeated until there are two ordered probabilities remaining.
3. Start encoding with the last reduction, which consists of exactly two ordered
probabilities .Assign 0 as the first digit in the code words for all the source
symbols associated with the first probability; assign 1 to the second probability
4. Now go back and assign 0 and 1 to the second digit for the two probabilities that
were combined in the previous reduction step ,retaining all assignments made in
step 3.
5. Keep regressing this way until the first column is reached.
22. .State and prove the properties of mutual information.
1. Mutual information I (xi yj) is symmetric. i.e. I (xi yj) = I (yj xi)
Proof
2. Mutual information I (xi yj) is maximum when p (xi / yj) = 1
Proof
3. I (X,Y) ³ 0
Proof .
4. Mutual information is related to the joint entropy of the channel input and
channel output by I(X,Y) = H (X) + H (Y) – H(X,Y)
Proof
23. Explain the different types of channel.
Loss less Channel
H (X/ Y) = 0 , I(X,Y) = H (X)
Channel capacity = Max (I(X,Y)) = H (X)
Channel diagram - Explanation
Deterministic channel
H (Y/ X) = 0
I(X,Y) = H (Y)
Channel capacity = Max (I(X,Y)) = H (Y) , Channel diagram - Explanation
Noise less Channel
H (X/ Y) = 0
H (Y/ X) = 0
Channel capacity = Max (I(X,Y)) = H (Y) = H (X)
Channel diagram - Explanation
Binary Symmetric Channel
Channel capacity = Max (I(X,Y)) = H (Y) = Plog2 P + (1- P) log2 (1-P)
Channel diagram - Explanation
24.Calculate the capacity of a gaussian channel.
State the Theorem ,Capacity = w log2 (1 + S/N) bits/ symbol
Analysis - refer notes
25.. Find the channel capacity of binary erasure channel P (x1 ) = a
Draw the channel diagram of the binary Erasure channel and get the channel
matrix.
P (y1/ x1) = 1-P
P (y2/ x1) = P
P (y2/ x2) = P
P (y3/ x2) = 1-P
Channel capacity = Max (I(X,Y)) = H (Y) - H (Y/ X)
i. Find H (Y/ X) using formula
H (Y/ X) = - (Plog2 P + (1- P) log2 (1-P))
ii. Find H (Y) using formula
H (Y) = - (1-P) [ a log 2a + log2 (1-P) + log 2(1- a) - alog 2(1- a) ] - Plog2 P
iii . I(X,Y) = (1-P) H (Y)
iv. Channel capacity = Max (I(X,Y)) = 1-P
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