1. Analog and Digital Communication(NEC-702)

2. Lecture-1

3. Unit-1

4. Text Books Book Title Author Edition Publication Communication System
Simon Haykin & Michael Moher
5th Edition
Wiley India Publication
Principles of Communication System
Hebert Taub and Donald L. Schilling
3rd Edition
Tata McGraw Hill

5. REFERENCES BOOK TITLE AUTHOR PUBLICATION Communication System
Simon Haykin
Wiley India Publication
Principles of communicatrion Systems
Herbert Taub and Donald L. Schilling
Tata McGraw Hill
Modern Digital and Analog Communication System
B P Lathi & ZhiDing
Oxford University Press
R P Singh and Sapre
Analog and Digital Communication
H P HSU & D Mitra

6. Abstract
To have the knowledge about basics of communication with different modulation techniques (AM, DSB-SC, SSB-SC, VSB)
To study angle modulation, pulse modulation, different types of transmitters and receivers.
To understand why and how digital communication came into the picture.
To study the different digital modulation techniques (ASK, FSK, PSK)for digital communication.
Effect of noise in analog and digital communication.

7. Advantages and Limitations
Advantages of Digital Communication:
The Digital Communication's main advantage is that it provides us added security to our information signal.
The digital Communication system has more immunity to noise and external interference.
Digital information can be saved and retrieved when necessary while it is not possible in analog.
In Digital Communication System, the error correction and detection techniques can be implemented easily.
Digital information can be stored easily as compared to analog information.

8. Limitations:
There is quantization error in digital communication during analog to digital conversion.
less accurate due to finite set of data as compared to analog.

9. Limitations of analog communication:
In analog communication, the quality of data often degraded due to noise.
Requires high quality processing which in turn demand costly hardware.
Requires costly storage due to more data.
Requires high power for transmission.

10. Applications
There are various applications of analog and digital communication:
Satellite Communication
Telecommunication
Fibre Optics
Aerospace and Defense
Security and Surveillance

11. Lecture-2

12. Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Introduction
Analog Signals
Digital Signals
Continuous
Infinite range of values
More exact values, but more difficult to work with
Discrete
Finite range of values (2)
Not as exact as analog, but easier to work with
This slide defines analog and digital signals and gives several examples of each.
Project Lead The Way, Inc.
Copyright 2009

13. Concept of Modulation(General)
Suppose we want to send some information to a long distant destination.
So we need some medium through which our message could reach as soon as possible.

14. Basic Communication System
Definition: Communication is the process of transferring information from one place to another or from transmitter to receiver.
Block Diagram of Basic Communication System (Wired):
Basic Communication System

15. Input Information: It is the source of information.
Input Transducer: It converts the non – electrical information to electrical for transmission.
Transmitter: It is the device which makes input electrical information suitable for efficient transmission over a given channel.
Channel: Channel is the media by which information is sent. It could be a wire or wireless.

16. Wireless Communication System
For long distance communication, wireless communication system is used.
Block diagram of wireless communication system is similar to that of wired communication system with modulator block before an transmitting antenna and demodulator after a receiving antenna.
Antenna is used to convert Electrical signal into electromagnetic (EM) signal.

17. Need of Modulation
Multiplexing: Multiplexing is used to send multiple signals through a single channel. Multiplexing is not possible without modulation.
Practicability of Antenna: Modulation helps to reduce the antenna height. The antenna height ‘h’ can be given as:
h = λ/4 = c/4f
This indicates signal with high frequency required minimum height antenna.

18. Example
If the signal of 5 KHz is to be transmitted without modulation, the size of the antenna needed for the effective radiation would be
If this signal is modulated with a 10 MHz carrier signal, the antenna height required will be
This antenna height can be practically achieved.

19. Narrowbanding: Suppose we have to send a signal having frequency range from 50 Hz to 10KHz.
the ratio of highest to lowest wavelength is 200. If an antenna is designed for 50 Hz, it will be too long for 10 KHz and vice-versa.
Suppose the audio signal is modulated with 1 MHz, then the ratio of lowest to highest frequency will be approximately 1 and the same antenna will be suitable for the entire band.
Thus modulation converts wideband signal into narrow band.

20. Fourier Transform
Fourier transform is basically used to find the frequency components contained by the given time domain signal.
Suppose we want to find the frequency components contained by the following signal.

21. Bandwidth of the signal is ∞, so to send this signal, we have a channel whose BW is ∞, but practically no channel exists with infinite BW.
So we use bandlimiting process to send this signal. In bandlimiting process, all the significant frequencies has to be retained and insignificant frequencies has to be eliminated.
Significant frequencies contained almost 95% to 99% of total strength of the signal.

22. For bandlimiting, the given signal should be pass through a proper low pass filter, i.e. cut – off frequency of the LPF should be such that it has to allow all the significant frequencies.

23. Lecture-3

24. Modulation
Modulation is the process of changing the characteristics (Amplitude, Frequency and Phase) of the carrier signal according to the message signal.
Carrier signal having high
frequency is modulated in
the adjacent figure.
Demodulation is the
process of recovering the
original massage signal
from the modulated signal.

25. Types of Modulation
Single Tone Modulation: If the message signal contains single frequency then corresponding modulation is called as single tone modulation.
Multi – Tone Modulation: If the message signal contains more than one frequency then the corresponding modulation is called as multi – tone modulation.
𝑚 𝑡 = 𝐴 𝑚 𝑐𝑜𝑠2𝜋 𝑓 𝑚 𝑡 Single tone
𝑚 𝑡 = 𝐴 𝑚1 𝑐𝑜𝑠2𝜋 𝑓 𝑚1 𝑡+ 𝐴 𝑚2 𝑐𝑜𝑠2𝜋 𝑓 𝑚2 Multi-tone

26. Amplitude Modulation
Definition: Modulation is the process of changing the amplitude of the carrier signal according to the message signal.
The carrier signal is represented by
c(t) = Accos(wct)
The modulating signal is represented by
m(t)
Then the final modulated signal is
= [1 + 𝑘 𝑎 m(t)] c(t)
𝑘 𝑎 = amplitude sensitivity of AM mod
= Ac [1 + 𝑘 𝑎 m(t)] cos(wct)
= Ac cos(wct) + 𝑘 𝑎 m(t)cos(wct)

27. 𝐴𝑀 𝐵𝑊=2×𝑚𝑒𝑠𝑠𝑎𝑔𝑒 𝑠𝑖𝑔𝑛𝑎𝑙 𝐵𝑊
Spectrum
𝐴𝑀 𝐵𝑊= 𝑓 𝑐 +𝜔 − 𝑓 𝑐 −𝜔 =2𝜔
𝐴𝑀 𝐵𝑊=2×𝑚𝑒𝑠𝑠𝑎𝑔𝑒 𝑠𝑖𝑔𝑛𝑎𝑙 𝐵𝑊
AM spectrum consists of
Carrier frequency component exist at 𝑓 𝑐
USB exists above 𝑓 𝑐
LSB exists below 𝑓 𝑐
Single Tone A. M.
Assume 𝑚 𝑡 = 𝐴 𝑚 𝑐𝑜𝑠2𝜋 𝑓 𝑚 𝑡
𝑆 𝐴𝑀 𝑡 = 𝐴 𝑐 𝑐𝑜𝑠2𝜋 𝑓 𝑐 𝑡+ 𝐴 𝑐 𝜇 2 𝑐𝑜𝑠2𝜋 𝑓 𝑐 + 𝑓 𝑚 𝑡+ 𝐴 𝑐 𝜇 2 𝑐𝑜𝑠2𝜋 𝑓 𝑐 − 𝑓 𝑚 𝑡

28. 𝜇<1→𝑈𝑛𝑑𝑒𝑟 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝜇=1→𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝜇>1→𝑂𝑣𝑒𝑟 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛
Where 𝑘 𝑎 𝐴 𝑚 =𝜇=𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐼𝑛𝑑𝑒𝑥
𝜇<1→𝑈𝑛𝑑𝑒𝑟 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝜇=1→𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝜇>1→𝑂𝑣𝑒𝑟 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝐴𝑀 𝐵𝑊=2 𝑓 𝑚

29. Power of AM Signal 𝑃 𝑡 = 𝑃 𝑐 + 𝑃 𝑈𝑆𝐵 + 𝑃 𝐿𝑆𝐵 𝑃 𝑐 = 𝐴 𝑐 2 2
𝑃 𝑐 = 𝐴 𝑐 2 2
𝑃 𝐿𝑆𝐵 = 𝑃 𝑈𝑆𝐵 = 𝐴 𝐶 𝜇 2 2𝑅 = 𝐴 𝑐 2 𝜇 2 8𝑅
𝑃 𝑡 = 𝑃 𝑐 1+ 𝜇 2 2

30. Modulation Efficiency
It specifies the share of sideband power in total power.
η = 𝑆𝑖𝑑𝑒 𝑏𝑎𝑛𝑑 𝑝𝑜𝑤𝑒𝑟 𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑤𝑒𝑟
η = 𝑃 𝑆𝐵 𝑃 𝑡 = 𝜇 𝜇 2
Maximum peak of AM signal 𝐴 𝑚𝑎𝑥 = 𝐴 𝑐 1+𝜇
Maximum peak of AM signal 𝐴 𝑚𝑖𝑛 = 𝐴 𝑐 1−𝜇
𝐴 𝑐 = 𝐴 𝑚𝑎𝑥 + 𝐴 𝑚𝑖𝑛 2
𝜇= 𝐴 𝑚𝑎𝑥 − 𝐴 𝑚𝑖𝑛 𝐴 𝑚𝑎𝑥 + 𝐴 𝑚𝑖𝑛

31. Lecture-4

32. Voltage and Current Relation in AM
𝐼 𝑡 = 𝐼 𝑐 𝜇 where 𝐼 𝑡 = AM transmitter current
𝐼 𝑐 = Carrier current
𝑉 𝑡 = 𝑉 𝑐 𝜇 2 2
Ques. An unmodulated AM transmitted current is given by 5A.
Find AM transmitted current with 50% of modulation.

33. Multi – tone AM 𝑚 𝑡 = 𝐴 𝑚1 𝑐𝑜𝑠2𝜋 𝑓 𝑚1 𝑡+ 𝐴 𝑚2 𝑐𝑜𝑠2𝜋 𝑓 𝑚2
𝑐 𝑡 = 𝐴 𝑐 𝑐𝑜𝑠2𝜋 𝑓 𝑐 𝑡
So, 𝑆 𝐴𝑀 𝑡 = 𝐴 𝑐 𝑐𝑜𝑠2𝜋 𝑓 𝑐 𝑡+ 𝐴 𝑐 𝜇 1 2 𝑐𝑜𝑠2𝜋 𝑓 𝑐 + 𝑓 𝑚 1 𝑡+ 𝐴 𝑐 𝜇 1 2 𝑐𝑜𝑠2𝜋 𝑓 𝑐 − 𝑓 𝑚 1 𝑡+ 𝐴 𝑐 𝜇 2 2 𝑐𝑜𝑠2𝜋 𝑓 𝑐 + 𝑓 𝑚 2 𝑡+ 𝐴 𝑐 𝜇 2 2 𝑐𝑜𝑠2𝜋 𝑓 𝑐 − 𝑓 𝑚 2 𝑡
AM BW = 2× 𝑓 𝑚 2
AM BW = 2×Highest frequency of the message signal

34. Power of Multi - Tone AM Signal

35. Current, Voltage Relation and Efficiency of Multi – tone AM Signal
Current Relation:
Voltage Relation:
Efficiency:

36. Under, Critical and Over Modulation
Under Modulation
𝜇= 𝐴 𝑚 𝐴 𝑐 <1
Critical Modulation
𝜇= 𝐴 𝑚 𝐴 𝑐 =1
𝜇= 𝐴 𝑚 𝐴 𝑐 >1

37. Generation of AM
Square Law Modulator: Block diagram of square law modulator is shown in the following figure.
Square Law Modulator
(Active Device)o/p = a1u(t) + a2u2(t) + a3u3(t)…

38. Comparing with

39. Lecture-5

40. Demodulation of AM Square Law Demodulator Envelope Detector
Synchronous Detector → Any value of µ
1. Square Law Demodulator: The block diagram of square law demodulator is shown in the following figure.

41. noise signal So ; if

42. for = 1,
To get S/N = 100, µ = 0.02, which gives 𝜂 = 1%
For proper reconstruction of the message signal S/N should be very high. To get high value of S/N, correspondingly, µ should be very small. If µ is very small then 𝜂 will also be very small.
But for efficient power distribution, 𝜂 should be high, so square law demodulator is not preferred for AM demodulation.

43. Envelope Detector:
ED extract positive envelope of the applied signal and produces at the output.
For µ ≤ 1, positive envelope of AM signal corresponds to message signal and can be reconstructed by using ED.
For µ ˃ 1, message signal is not stored in the form of positive envelope so demodulation is not possible by using ED.

44. The circuit diagram of the envelope detector is shown in the following figure.
If RSC is high, capacitor slowly charges and voltage across capacitor does not reach to peak voltage of input.

45. If RSC is very small then voltage across capacitor reaches to peak voltage of input and envelope of the applied signal will be followed.
Proper Choice of RLC: For proper reconstruction of message signal the value of RLC should be as follows

46. Synchronous Detector: The block diagram of synchronous detector is shown in the following figure.
For proper reconstruction of message signal, LO output should be perfectly synchronized in both frequency and phase w.r.t. transmitter carrier.

47. Frequency synchronization can be easily achieved but to achieve phase synchronization, additional circuitry has to be used, which makes synchronous detector very complex.
Case I: Assume

48. Case II:
If ϕ = 900
Quadrature Null Effect[QNE]

49. Advantages of AM: Drawbacks of AM: Demodulation is simple
AM is used for long distance communication.
Drawbacks of AM:
Transmitter power wastage
Need high channel bandwidth
AM transmitter is highly noise
QNE

50. Lecture-6

51. Double Side Band – Suppressed Carrier (DSB - SC)
Assume message signal = m(t) Carrier signal General expression of DSB signal = m(t)c(t)

52. DSB BW = 2× BW of message signal
Channel BW requirement for AM and DSB is same.
Carrier frequency is there but no additional carrier component is present.
Single Tone DSB:

53. USB LSB Spectrum:

54. Power of DSB: Modulation Efficiency:
Multi – tone DSB:
Try yourself

55. Generation of DSB - SC
Balanced Modulator
Ring Modulator
1. Balanced Modulator: The block diagram of balanced modulator is shown in the following fig.

56. Balanced modulator consists of two AM modulators in balanced to generate DSB signal.

57. Ring Modulator: Ring modulator is constructed with 4 diodes and center tapped transformer with 1:1 type. The circuit diagram of ring modulator is shown in the following figure.

58. Demodulation of DSB - SC
Synchronous Detector: The block diagram of the synchronous detector is shown in the following fig.
Case I: Assume
(𝑀𝑢𝑙) 𝑜 𝑝 = 𝐴 𝑐 2 𝑚(𝑡) 𝑐𝑜𝑠 2 2𝜋 𝑓 𝑐 𝑡
(𝐿𝑃𝐹) 𝑜 𝑝 = 𝐴 𝐶 2 𝑚(𝑡) 2

59. Case II: (𝑀𝑢𝑙) 𝑜 𝑝 = 𝐴 𝐶 2 𝑚 𝑡 2 𝑐𝑜𝑠 4𝜋 𝑓 𝑐 𝑡+⏀ + 𝐴 𝐶 2 𝑚 𝑡 2 cos⏀
If ⏀=900 then
(𝐿𝑃𝐹) 𝑜 𝑝 = 0 [QNE]

60. Advantages: Drawbacks: Application: Transmitter Power is saved.
DSB is used for long distance communication.
Drawbacks:
Demodulation is very complex.
It needs high channel BW.
Quadrature null effect.
Application:
It is used in quadrature carrier multiplexing.

61. Lecture-7

62. Single Side Band Suppressed Carrier
From DSB-SC spectrum:
Information m is carried twice
Bandwidth is high
c - m c c + m
Carrier
USB
LSB
Single frequency
Question: Can one suppress one of the side bandcarrier?
Ans.: Yes, just transmit one side band (i.e SSB-SC)
But what is the penalty?
System complexity at the receiver

63. SSB-SC - Implementation
Frequency discrimination
Band pass
filter
c+ c
Upper sideband
DSB-SC
Message
m(t)
Multiplier
Local oscillator
c(t) = cos ct
Band pass
filter
c- c
Lower sideband

64. SSB-SC - Waveforms
B = 2m
USB
B = m
Bandwidth B = m

65. SSB-SC - Implementation cont.
Phase discrimination (Hartley modulator)
v(t) =Em cos mt cos ct + Em sin mt sin ct
= Em cos (m - c)t LSB
Em cos mt
Message
m(t) X
Em cos mt cos ct
Carrier
cos ct  + -
SSB-SC
signal
90o
phase shift
90o
phase shift
sin ct
Em sin mt sin ct X
Em sin mt
v(t) =Em cos mt cos ct - Em sin mt sin ct
= Em cos (m + c)t USB

66. SSB-SC - Hartley Modulator
Advantages
No need for bulky and expensive band pass filters
Easy to switch from a LSB to an USB SSB output
Disadvantage:
Requires Hilbert transform of the message signal. Hilbert transform changes the phase of each +ve frequency component by exactly - 90o.

67. SSB-SC - Detection Synchronous detection Low pass filter
Multiplier
Message signal
Local oscillator
c(t) = cos ct
Condition:
Local oscillator has the same
frequency and phase as that of the
carrier signal at the transmitter.
information
high frequency m
2c+m
Low pass filter

68. SSB-SC - Synch. Detection cont.
Case 1 - Phase error
Low pass
filter
SSB-SC
Multiplier
Message signal
Local oscillator
c(t) = cos (ct+)
Condition:
Local oscillator has the same
frequency but different phase as
that of the carrier signal at the
transmitter.
information
high frequency m
2c+m
Low pass filter

69. SSB-SC - Synch. Detection cont.
Case 2- Frequency error
Low pass
filter
SSB-SC
Multiplier
Message signal
Local oscillator
c(t) = cos (c+)t
Condition:
Local oscillator has the same
phase but different frequency as
that of the carrier signal at the
transmitter.
information
high frequency
m +
2c+m +
Low pass filter

70. SSB-SC - Power The total power (or average power):
The maximum and peak envelop power

71. SSB-SC - Summary Advantages: - Demodulation is very complex
Transmitter power is saved
It needs less channel BW requirement
No quadrature null effect
Disadvantage:
- Demodulation is very complex
- It is limited to voice signal transmission.
Applications:
- Two way radio communications
- Frequency division multiplexing
- Up conversion in numerous telecommunication systems

72. Lecture-8

73. Vestigial Sideband (VSB)
VSB is a compromise between DSB and SSB.
VSB is used for video signal transmission.
VSB provides almost of same BW of SSB.
SSB (Upper sideband)
VSB Spectrum
DSB

74. Filtering scheme for the generation of VSB modulated wave.

75. Demodulation of VSB BW Comparison: AM & DSB > VSB > SSB Power:
For demodulation of VSB, synchronous detector is used.
BW Comparison:
AM & DSB > VSB > SSB
Power:
AM > DSB > VSB and SSB

76. AM transmitter and Receiver
Transmitters that transmit AM signals are known as AM transmitters.
These transmitters are used in medium wave (MW) and short wave (SW) frequency bands for AM broadcast.
The MW band has frequencies between 550 KHz and 1650 KHz, and the SW band has frequencies ranging from 3 MHz to 30 MHz .

77. The two types of AM transmitters that are used based on their transmitting powers are:
High Level
Low Level
High level transmitters use high level modulation, and low level transmitters use low level modulation.
The choice between the two modulation schemes depends on the transmitting power of the AM transmitter.
In broadcast transmitters, where the transmitting power may be of the order of kilowatts, high level modulation is employed. In low power transmitters, where only a few watts of transmitting power are required , low level modulation is used.

78. High-Level and Low-Level Transmitters
Below figure's show the block diagram of high-level and low-level transmitters. The basic difference between the two transmitters is the power amplification of the carrier and modulating signals.
Figure shows the block diagram of high-level AM transmitter.

79. In high-level transmission, the powers of the carrier and modulating signals are amplified before applying them to the modulator stage, as shown in figure (a). In low-level modulation, the powers of the two input signals of the modulator stage are not amplified. The required transmitting power is obtained from the last stage of the transmitter, the class C power amplifier.
The various sections of the figure (a) are:
Carrier oscillator
Buffer amplifier
Frequency multiplier
Power amplifier
Audio chain
Modulated class C power amplifier

80. Following figure shows the block diagram of a low-level AM transmitter.
The low-level AM transmitter shown in the figure (b) is similar to a high-level transmitter, except that the powers of the carrier and audio signals are not amplified. These two signals are directly applied to the modulated class C power amplifier.
Modulation takes place at the stage, and the power of the modulated signal is amplified to the required transmitting power level. The transmitting antenna then transmits the signal.

81. Receivers There are two types of receivers: Tuned Radio Frequency
Super Heterodyne
For AM:
Standard given by Federation Committee of Communication (FCC)
Carrier – 550 KHz to 1650 KHz
AM BW – 10 KHz
For FM:
Carrier – 88MHz to 108 MHz
FM BW – 200 KHz

82. Lecture-9

83. AM Receiver (TRF Type)
The block diagram of TRF receiver is shown in the following figure.
The basic function of a receiver will be proper selection and rejection.
For TRF receiver, proper selection and rejection is carried out by tuned amplifier.

84. ~ Mixer as a Converter Mixer may be used a frequency converter
Changes the selected RF frequency to the IF frequency using a tuneable LO signal.
LO can be above or below the RF
IF can be above or below the RF
Mixer
145MHz–123.6MHz=21.4MHz
IF frequency
RF (fs =145MHz) ~
LO (fl = 123.6MHz)

85. AM Receiver (SHD Type)
The block diagram of TRF receiver is shown in the following figure.
IF Amplifier: Standard tuned amplifier.
fr = IF = 455KHz
BW = 10KHz

86. In SHD receiver, tuning is achieved by changing fl of the mixer, whereas in TRF receiver, tuning is achieved by changing fr of the tuned amplifier.
In SHD receiver, BW of IF amplifier is fixed and equal to 10 KHz so that the selectivity of the SHD receiver will be very good.
Image Frequency:- Suppose there are three stations at the input of the mixer called 600KHz, 1000 KHz, and 1600 KHz.
Second station will appear on 𝑓 𝑙 − 𝑓 𝑠 = 1100− − =100 KHz.

87. Image station is given by 𝑓 𝑠 𝑖 = 𝑓 𝑠 +2 𝐼 𝐹
1st station will appear on 𝑓 𝑙 − 𝑓 𝑠 = 1100−600 =500KHz and 3rdstation will also appear on 𝑓 𝑙 − 𝑓 𝑠 = 1100−1600 =500 KHz. Hence 3rd station causing interference.
Image station is given by
𝑓 𝑠 𝑖 = 𝑓 𝑠 +2 𝐼 𝐹
For proper reconstruction of the desired station, image station should be suppressed.
To suppress image station, tuned amplifier will be used before mixer.

88. Image Rejection Ratio: It specifies the effectiveness of the tuned amplifier in suppressing the image station.
𝐼𝑅𝑅= 𝐺𝑎𝑖𝑛 𝑜𝑓𝑓𝑒𝑟𝑒𝑑 𝑏𝑦 𝑇𝐴 𝑡𝑜 𝑓 𝑠 𝐺𝑎𝑖𝑛 𝑜𝑓𝑓𝑒𝑟𝑒𝑑 𝑏𝑦 𝑇𝐴 𝑡𝑜 𝑓 𝑠 𝑖 =𝛼
𝛼= 𝐺 𝑓 𝑠 𝐺 𝑓 𝑠 𝑖

89. 𝑤ℎ𝑒𝑟𝑒 𝑄=𝑄𝑢𝑎𝑙𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟
𝛼= 1+ 𝑃 2 𝑄 2
𝑤ℎ𝑒𝑟𝑒 𝑄=𝑄𝑢𝑎𝑙𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟
𝑃= 𝑓 𝑠 𝑖 𝑓 𝑠 − 𝑓 𝑠 𝑓 𝑠 𝑖
If tuned amplifiers are connected in cascade then
𝛼= 𝛼 1 . 𝛼 2 . 𝛼 3 …
If two tuned amplifiers having different characteristics are connected in cascade, then

90. 𝛼= 1+ 𝑃 2 𝑄 𝑃 2 𝑄 2 2
FM Receiver:
𝑓 𝑐 =88𝑀𝐻𝑧−108 𝑀𝐻𝑧
𝐹𝑀 𝐵.𝑊.=200 𝐾𝐻𝑧
𝐼𝐹=10.7 𝑀𝐻𝑧
The block diagram of the FM receiver is shown in the following figure.

91. In FM, message signal is stored in the form of frequency variations and these frequency variations are little affected by channel noise. So FM transmission is very much of noise free.
In AM, message signal is stored in the form of peak amplitude variations and these amplitude variations are highly affected by the channel noise. so AM transmission is noisy.

92. Frequency Division Multiplexing (FDM)
FDM is used for multiplexing continuous signals.
FDM Process:

93. FDM De-multiplexing Process: