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1. Analog
Communications
1
21EEB0A12 Deepak chaurasiya

2. Modulation
2
 Modulation is a process of mixing a signal with a sinusoid to produce a new
signal.
 This new signal, will have certain benefits over an un-modulated signal.
 Mixing of low frequency signal with high frequency carrier signal is called
modulation.
 Low frequency signals cannot be transmitted for longer distances.
 So we modify the carrier signal with respect to modulating (message) signal.
 Modulating Signal: Message signal
 Carrier Signal: Signal which carries message signal.
 Modulated Signal: The resultant signal after modulation.

3. Need for Modulation
1. Reducing the height of antenna
 Usually the size of antenna is around 𝜆/4.
ƒ 3×103
 For voice signal ranging from 300 Hz to 3.4 KHz, 𝜆 = 𝑐
= 3×108
= 105 𝑚 =
100 km. So the height of antenna becomes 25 km which is not practically
possible.
 If we modulate the signal to higher frequency (1MHz), 𝜆 = 3×108
= 300 𝑚.
3
1×106
So antenna size becomes 300/4 = 75 m, which can be installed easily.

4. Need for Modulation
4
2. Multiplexing
 If 3 users are transmitting voice signals simultaneously, all the signals get
mixed together and a receiver can not separate them from each other.
 If we modulate the 3 voice signals on to 3 different carrier signals, they will
not interfere with each other.
 This process is called Frequency Division Multiplexing (FDM).
 Multiplexing is a process in which two or more signals can be transmitted
over the same communication channel simultaneously.

5. Need for Modulation
5
3. Increase the Range of Communication
 Low frequency signals can not travel long distance when they are transmitted
as they get heavily attenuated .
 The attenuation reduces with increase in frequency of the transmitted signal,
and they travel longer distance .
 The modulation process increases the frequency of the signal to be
transmitted. Therefore, it increases the range of communication..

6. Types of Modulation
 Consider a carrier signal 𝑐 𝑡 = 𝐴𝑐cos(2𝜋ƒ𝑐𝑡 + ɸ𝑐).
 𝐴𝑐 is the amplitude of the carrier.
 ƒ𝑐 is the frequency of the carrier.
 ɸ𝑐 is the phase of the carrier.
 Modulation is the process of varying the characteristic of a carrier signal in
accordance with the modulating (message) signal.
 Amplitude Modulation
 Frequency Modulation
 Phase Modulation
6

7. Amplitude Modulation (AM)
 Consider a carrier signal 𝑐 𝑡 = 𝐴𝑐cos(2𝜋ƒ𝑐𝑡).
 Amplitude Modulation is defined as a process in which the amplitude of
carrier wave 𝑐 𝑡 is varied linearly with message signal 𝑚 𝑡 .
Time-Domain Description ofAM
 The standard form ofAM wave is defined by
𝑠 𝑡 = 𝐴𝑐 1 + 𝑘𝑎𝑚(𝑡) cos(2𝜋ƒ𝑐𝑡)
 where 𝑘𝑎 is a constant called amplitude sensitivity of the modulator.
 The amplitude of time function multiplying cos(2𝜋ƒ𝑐𝑡) is called the envelope
of theAM wave.
7

8. Time-Domain Description of AM
 The amplitude of time function multiplying cos(2𝜋ƒ𝑐𝑡) is called the envelope
ofAM wave, denoted by
𝑎 𝑡 = 𝐴𝑐 1 + 𝑘𝑎𝑚(𝑡)
 The maximum absolute value of 𝑘𝑎𝑚(𝑡) multiplied by 100 is referred to as the
percentage modulation.
8
 If 𝑘𝑎𝑚(𝑡) < 1, Under modulated
 If 𝑘𝑎𝑚(𝑡) = 1, Critically modulated
 If 𝑘𝑎𝑚(𝑡) > 1, Over modulated

9. 9

10. Time-Domain Description of AM
 𝐴𝑐 = 1, 𝑘𝑎 = 1
, 𝑚 𝑡 = cos 2𝜋ƒ𝑚 𝑡 , ƒ𝑚 = 1
2 2
1
𝑎 𝑡 = 𝐴𝑐 1 + 𝑘𝑎 𝑚(𝑡) = 1 +
2
cos 𝜋𝑡
1
𝑠 𝑡 = 1 +
2
cos 𝜋𝑡 cos(2𝜋ƒ𝑐𝑡)
10

11. Time-Domain Description of AM
 𝐴𝑐 = 1, 𝑘𝑎 = 3
, 𝑚 𝑡 = cos 2𝜋ƒ𝑚 𝑡 , ƒ𝑚 = 1
2 2
3
𝑎 𝑡 = 𝐴𝑐 1 + 𝑘𝑎 𝑚(𝑡) = 1 +
2
cos 𝜋𝑡
3
𝑠 𝑡 = 1 +
2
cos 𝜋𝑡 cos(2𝜋ƒ𝑐𝑡)
11

12. 12

13. 13

14. Time-Domain Description of AM
 If 𝑘𝑎𝑚(𝑡) > 1, modulated wave will suffer from envelope distortion as it is
over modulated.
 So percentage modulation should be less than 100%, to avoid envelope
distortion.
14

15. Fourier Transform
 FT{1} = ð ƒ
 FT{cos 2𝜋ƒ𝑐𝑡 }=FT 1
2
e−j2𝜋ƒ𝑐𝑡 + ej2𝜋ƒ𝑐𝑡 = 1
2
ð ƒ − ƒ𝑐 + ð ƒ + ƒ𝑐
 FT{𝑚(𝑡)} = 𝑀(ƒ)
 FT{𝑚(𝑡) cos 2𝜋ƒ𝑐𝑡 }= 1
2
𝑀 ƒ − ƒ𝑐 + 𝑀 ƒ + ƒ𝑐
15

16. Frequency-Domain Description of AM
 The standard form ofAM wave is defined by
𝑠 𝑡 = 𝐴𝑐 1 + 𝑘𝑎𝑚(𝑡) cos 2𝜋ƒ𝑐𝑡
𝑠 𝑡 = 𝐴𝑐 cos 2𝜋ƒ𝑐 𝑡 + 𝐴𝑐 𝑘𝑎 𝑚(𝑡) cos 2𝜋ƒ𝑐 𝑡
 To determine frequency description of this AM wave, take Fourier transform on
both sides.
=
𝐴𝑐
+
𝑘𝑎𝐴𝑐
2 2
𝑆 ƒ ð ƒ − ƒ + ð ƒ + ƒ 𝑀 ƒ − ƒ + 𝑀 ƒ + ƒ
16
𝑐 𝑐 𝑐
𝑐
 𝑀(ƒ) is the FT of 𝑚(𝑡) and 𝑚(𝑡) is band-limited to the interval −W ≤ ƒ ≤ W
 ƒ𝑐 > W

17. 𝑆 ƒ
=
𝐴𝑐
2
ð ƒ − ƒ𝑐 + ð ƒ + ƒ𝑐
+
𝑘𝑎𝐴𝑐
2
𝑀 ƒ − ƒ𝑐 + 𝑀 ƒ + ƒ𝑐
17

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

19. Frequency-Domain Description of AM
19
 The difference between these two frequencies defines transmission bandwidth
B ofAM wave, which is exactly twice the message bandwidth W.
 B=2W
 This spectrum of the AM wave is full i.e., the carrier, the upper sideband, and
the lower sideband are all completely represented.
 Hence this form of amplitude modulation is treated as standard.

20. Single-Tone modulation of AM
 Consider a modulating wave m 𝑡 = 𝐴𝑚cos(2𝜋ƒ𝑚𝑡).
 TheAM wave is described by
𝑠 𝑡 = 𝐴𝑐 1 + 𝑘𝑎𝐴𝑚cos(2𝜋ƒ𝑚𝑡) cos 2𝜋ƒ𝑐𝑡
𝑠 𝑡 = 𝐴𝑐 1 + 𝜇 cos(2𝜋ƒ𝑚𝑡) cos 2𝜋ƒ𝑐𝑡
 where 𝜇 = 𝑘𝑎𝐴𝑚 is called modulation factor or modulation index.
 To avoid envelope distortion due to over modulation, the modulation factor 𝜇
must be kept below unity.
 Let 𝐴𝑚𝑎𝑥 and 𝐴𝑚i𝑛 be the maximum and minimum values of the envelope of
the modulated wave.
20

21. Single-Tone modulation of AM
𝐴𝑚𝑎𝑥
=
𝐴𝑐(1 + 𝜇)
𝐴𝑚i𝑛 𝐴𝑐(1 − 𝜇)
 That is
𝜇 =
𝐴𝑚𝑎𝑥 − 𝐴𝑚i𝑛
𝑠 𝑡
𝐴𝑚𝑎𝑥 + 𝐴𝑚i𝑛
= 𝐴𝑐 1 + 𝜇 cos(2𝜋ƒ𝑚𝑡) cos 2𝜋ƒ𝑐𝑡
𝑠 𝑡 = 𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 + 𝐴𝑐 𝜇 cos(2𝜋ƒ𝑚𝑡)cos 2𝜋ƒ𝑐𝑡
1
 Using the relation cos(A)cos(B) = 2
[cos(A+B)+cos(A-B)]
𝑠 𝑡 = 𝐴
1 1
𝑐 cos 2𝜋ƒ𝑐 𝑡 +
2
𝐴𝑐 𝜇 cos 2𝜋 ƒ𝑐 + ƒ𝑚 𝑡 +
2
𝐴𝑐 𝜇 cos 2𝜋 ƒ𝑐 − ƒ𝑚 𝑡
21

22. Single-Tone modulation of AM
𝑠 𝑡 = 𝐴
1 1
𝑐 cos 2𝜋ƒ𝑐 𝑡 +
2
𝐴𝑐 𝜇 cos 2𝜋 ƒ𝑐 + ƒ𝑚 𝑡 +
2
𝐴𝑐 𝜇 cos 2𝜋 ƒ𝑐 − ƒ𝑚 𝑡
 FT of s(t) is
𝑆 ƒ =
𝐴𝑐
2
ð ƒ − ƒ𝑐 𝑐
+ ð ƒ + ƒ +
𝐴 𝜇
𝑐
4
ð ƒ − ƒ𝑐 − ƒ𝑚 + ð ƒ + ƒ𝑐 + ƒ𝑚
+
𝐴 𝜇
𝑐
4
ð ƒ − ƒ𝑐 + ƒ𝑚 + ð ƒ + ƒ𝑐 − ƒ𝑚
22
 Thus the spectrum of an AM wave, for special case of sinusoidal modulation,
consists of delta functions at ±ƒ𝑐, ƒ𝑐 ± ƒ𝑚 and −ƒ𝑐 ± ƒ𝑚.

23. Single-Tone modulation of AM
23

24. Power Calculation in AM
𝑠 𝑡 = 𝐴
1 1
𝑐 cos 2𝜋ƒ𝑐 𝑡 +
2
𝐴𝑐 𝜇 cos 2𝜋 ƒ𝑐 + ƒ𝑚 𝑡 +
2
𝐴𝑐 𝜇 cos 2𝜋 ƒ𝑐 − ƒ𝑚 𝑡
 Power = 𝑉𝑟𝑚𝑠𝐼𝑟𝑚𝑠 =
𝑉r𝑚𝑠
2
=
𝑉𝑝
2 1 𝑉𝑝
2 𝑉𝑝
2
2 𝑅
= 2𝑅
= 2
when R=1.
𝑐
 Carrier Power, 𝑃 =
Æ𝑐
𝑅
2
2
𝑈𝑆
𝐵
 Upper Sideband Power, 𝑃 =
𝐿𝑆
𝐵
 Lower Sideband Power, 𝑃 =
Æ𝑐𝜇/2 2
= Æ𝑐
2𝜇2
= 𝑃𝑐𝜇2
2 8 4
Æ𝑐𝜇/2 2
= Æ𝑐
2𝜇2
= 𝑃𝑐𝜇2
2 8 4
 Total power, 𝑃𝑡 = 𝑃𝑐 + 𝑃𝑈𝑆𝐵 𝐿𝑆
𝐵
𝑐
+ 𝑃 = 𝑃 + 𝑐
𝑃 𝜇
4
+ 𝑐
𝑃 𝜇
2 2
4 𝑐
= 𝑃 + 𝑐
𝑃 𝜇 2
2
24

25. Power Calculation in AM
𝑡
𝑐
= Æ𝑐
2
 Total power, 𝑃 = 𝑃 1 + 𝜇2
1 + 𝜇2
2 2 2
 Transmission Efficiency, 5 =
𝑇o𝑡𝑎𝑙 𝑠i𝑑e𝑏𝑎𝑛𝑑 𝑝owe𝑟
𝑇o𝑡𝑎𝑙 𝑡𝑟𝑎𝑛𝑠𝑚i𝑡𝑡e𝑑 𝑝owe𝑟
=
𝑃 𝜇2
𝑐 2
𝑐
𝑃 1+
𝜇2
2
=
𝜇2
2+𝜇2
2 2
 Let 𝑃𝑡 = 300W, 𝜇 = 1 then 300 = 𝑃𝑐 1 + 1
= 3
𝑃𝑐
25
 i.e., 𝑃𝑐 = 200W, 𝑃𝑆𝐵 = 𝑃𝑡 − 𝑃𝑐 = 100W
 So 200W of the power is wasted to transmit carrier. 2/3rd of power is lost in
transmitting carrier and only 1/3rd of power is used to transmit sidebands.

26. Generation of AM Waves
Square Law Modulator
 It requires 3 features:
 a means of summing the carrier and modulating waves,
 a nonlinear element, and
 a band pass filter for extracting the desired modulation products.
26

27. Square Law Modulator
 Semiconductor diodes and transistors are the most common nonlinear devices
used for implementing square law modulators.
 The filtering requirement is usually satisfied by using a single or double tuned
filter.
1
 The nonlinear device can be modeled as, 𝑣2 𝑡 = 𝑎1𝑣1 𝑡 + 𝑎2𝑣2(𝑡)
 where 𝑎1 and 𝑎2 are constants.
 The input voltage 𝑣1 𝑡 consists of the
carrier wave plus the modulated wave
i.e., 𝑣1 𝑡 = 𝑚 𝑡 + 𝐴𝑐 cos 2𝜋ƒ𝑐𝑡
27

28. Square Law Modulator
 𝑣2 𝑡 = 𝑎1[𝑚 𝑡 + 𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 ] + 𝑎2[𝑚 𝑡 + 𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 ]2
2 𝑐
 𝑣2 𝑡 = 𝑎1𝑚 𝑡 + 𝑎1𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 + 𝑎2𝑚2 𝑡 + 𝑎 𝐴2𝑐o𝑠2 2𝜋ƒ𝑐𝑡 + 2𝑎2𝑚(𝑡)𝐴𝑐 cos 2𝜋ƒ𝑐𝑡
 𝑣2 𝑡 = 𝑎 𝐴
1 𝑐
2𝑎2
𝑎1
2 2 2
𝑐 1 2 2 𝑐 𝑐
1 + 𝑚(𝑡) cos 2𝜋ƒ 𝑡 + 𝑎 𝑚 𝑡 + 𝑎 𝑚 𝑡 + 𝑎 𝐴 𝑐o𝑠 2𝜋ƒ 𝑡
 The first term is the desiredAM wave with amplitude sensitivity 𝑘𝑎 = 2𝑎2/𝑎1.
 The remaining 3 terms are unwanted and are removed by appropriate filtering.
28

29. Switching Modulator
 It is assumed that carrier wave applied to diode is larger in amplitude.
 We assume that diode acts as an ideal switch, it is short circuited (zero
impedance) when it is forward biased and is open circuited (infinite impedance)
when it is reverse biased.
29

30. Switching Modulator
30

31. Switching Modulator
31

32. Switching Modulator
32

33. Switching Modulator
33

34. Switching Modulator
34

35. Switching Modulator
35

36. Switching Modulator
36

37. Switching Modulator
37

38. Detection of AM Waves
 The process of detection or demodulation means recovering the message signal
from an incoming modulated wave.
 Detection is the inverse of modulation.
Square Law Detector
 A square law detector is obtained by using a square law modulator for the
purpose of detection.
1
 The nonlinear device can be modeled as, 𝑣2 𝑡 = 𝑎1𝑣1 𝑡 + 𝑎2𝑣2(𝑡)
 The input to the detector isAM wave given by
𝑣1 𝑡 = 𝐴𝑐 1 + 𝑘𝑎𝑚(𝑡) cos 2𝜋ƒ𝑐𝑡
38

39. Square Law Detector
 Substituting 𝑣1 𝑡 in 𝑣2 𝑡 , we get
2
𝑣2 𝑡 = 𝑎1𝐴𝑐 1 + 𝑘𝑎𝑚(𝑡) cos 2𝜋ƒ𝑐𝑡 + 𝑎2 𝐴𝑐 1 + 𝑘𝑎𝑚(𝑡) cos 2𝜋ƒ𝑐𝑡
𝑣2 𝑡 = 𝑎1𝐴𝑐 1 + 𝑘𝑎𝑚(𝑡) cos 2𝜋ƒ𝑐𝑡
+𝑎2𝐴2 1 + 2𝑘 𝑚 𝑡 + 𝑘2𝑚2(𝑡)
𝑐 𝑎 𝑎
1 + cos 4𝜋ƒ𝑐𝑡
2
 The desired signal, 𝑎 𝐴2𝑘 𝑚 𝑡 is due to the 𝑎 𝑣2(𝑡)
39
2 𝑐 𝑎 2 1
description square law detector.
term, hence the
 This component can be extracted by means of a low pass filter.
 This is not the only contribution within the baseband spectrum, because
2 𝑐 𝑎
𝑎 𝐴2𝑘2𝑚2(𝑡)/2 will give rise to a plurality of similar frequency components.

40. Square Law Detector
 The ratio of wanted signal to distortion is equal to 𝑐
𝑐
𝑎
𝑎2Æ2k2𝑚2(𝑡)/2
𝑎2Æ2k𝑎𝑚 𝑡 2
k𝑎 𝑚 𝑡
= .
 To make this ratio large, we choose 𝑘𝑎𝑚 𝑡 small compared to unity.
40

41. Envelope Detector
 An envelope detector is a simple yet highly effective device that is well suited
for demodulation of a narrowband AM wave (carrier frequency is large
compared with message bandwidth), for which percentage modulation is less
than 100%.
 Ideally an envelope detector produces an output signal that follows the envelope
of the input signal exactly.
 Envelope detector consists of a diode and
a resistor capacitor filter.
41

42. Envelope Detector
 On the +ve half cycle of input signal, the diode is forward biased and capacitor
charges up rapidly to the peak value of input signal.
 When input signal falls below this value, the diode becomes reverse biased and
the capacitor discharges slowly through the load resistor Rl.
 The discharging process continues until the next +ve half cycle.
 When the input signal becomes greater than the voltage across the capacitor, the
diode conducts again and the process is repeated.
 We assume that the diode is ideal and the envelope detector is supplied by a
voltage source of internal impedance Rs.
42

43. Envelope Detector
 The charging time constant 𝑅𝑠𝐶 must be short compared with the carrier period,
1/ƒ𝑐 , that is
𝑠
𝑅 𝐶 ≪
1
ƒ𝑐
 Hence, capacitor charges rapidly and thereby follows the applied voltage up to
the positive peak when the diode is conducting.
 On the other hand, the discharging time constant 𝑅𝑙𝐶 must be long enough to
ensure that the capacitor discharges slowly through the load resistor 𝑅𝑙 between
positive peaks of carrier wave, but not so long that capacitor voltage will not
discharge at maximum rate of change of the modulating wave, that is
𝑙
1
≪ 𝑅 𝐶 ≪
1
ƒ𝑐 W
43

44. Envelope Detector
 where W is the message bandwidth.
 The result is that the capacitor voltage or the detector output is very nearly same
as the envelope ofAM wave.
 The detector output usually has a small ripple at carrier frequency, which is
removed by low pass filtering.
44

45. Envelope Detector
45

46. Envelope Detector
46

47. Envelope Detector
47

48. Applications of AM
48
 In radio broadcasting, a central transmitter is used to radiate message signals for
reception at a large number of remote points.
 AM broadcasting is radio broadcasting using amplitude modulation (AM)
transmissions.
 One of the most important factors which promoted the use of AM in radio
broadcasting is the simple circuitry required at the receiver’s end.
 A simple diode circuit is enough at the receiver’s end to properly receive the
modulated signal and get the original message.

49. Applications of AM
49
 Since, while broadcasting, there are a large number of receivers which are the
common masses of public, it is essential that circuitry involved be simple and
compact so that everyone can accommodate and use it properly.
 Amplitude modulation serves this purpose perfectly as explained above and
hence is used for broadcasting.

50. Double Sideband Suppressed Carrier
(DSB-SC)
 The spectrum of standard AM wave is full i.e., the carrier, the upper sideband,
and the lower sideband are all completely represented.
 Hence it is called as Double Sideband with Full Carrier.
 But 2/3rd of power is lost in transmitting carrier and only 1/3rd of power is used
to transmit sidebands. i.e., Transmission efficiency is only 33.33% when 𝜇=1.
 Transmission Efficiency, 5 =
𝑇o𝑡𝑎𝑙 𝑠i𝑑e𝑏𝑎𝑛𝑑 𝑝owe𝑟
𝑇o𝑡𝑎𝑙 𝑡𝑟𝑎𝑛𝑠𝑚i𝑡𝑡e𝑑 𝑝owe𝑟
=
𝜇2
2+𝜇
2
 This is the main drawback of standardAM wave.
 To overcome this drawback, we can suppress the carrier component from the
modulated wave resulting in Double Sideband Suppressed Carrier modulation.
50

51. Double Sideband Suppressed Carrier
(DSB-SC)
wave that is
 Thus by suppressing the carrier, we obtain a modulated
proportional to the product of carrier wave and message signal.
Time-Domain Description of DSB-SC
 DSB-SC wave can be expressed as
𝑠 𝑡 = 𝑐 𝑡 𝑚(𝑡)
𝑠 𝑡 = 𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 𝑚(𝑡)
51
 This modulated wave undergoes a phase reversal whenever the message signal
crosses zero.
 Hence the envelope of DSB-SC modulated wave is different from the message
signal.

52. Time-Domain Description of DSB-SC
52

53. Frequency-Domain Description of DSB-SC
 By taking the Fourier transform on both sides of time-domain signal, 𝑠 𝑡
𝑠 𝑡 = 𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 𝑚(𝑡)
=
𝐴𝑐
2
𝑆 ƒ 𝑀 ƒ − ƒ + 𝑀 ƒ + ƒ
𝑐 𝑐
 where 𝑆 ƒ is the FT of modulated wave, and 𝑀(ƒ) is the FT of message signal
 When message signal is limited to the interval −W ≪ ƒ ≪ W, the modulation
process simply translates the spectrum of baseband signal by ±ƒ𝑐.
53

54. Frequency-Domain Description of DSB-SC
 The transmission bandwidth required
by DSB-SC modulation is same as that
for standardAM, i.e., 2W.
 However, the carrier is suppressed in
DSB-SC as there are no delta functions
at ±ƒ𝑐.
54

55. Generation of DSB-SC Waves
55
 A DSB-SC wave consists simply the product of the message signal and the
carrier wave.
 A device for achieving this requirement is called a product modulator.
 We have two forms of product modulator namely balanced modulator and ring
modulator.

56. Balanced Modulator
 A balanced modulator consists of two standard amplitude modulators arranged
in a balanced configuration so as to suppress the carrier wave.
 We assume that the two modulators are identical,
except for the sign reversal of the modulating
wave applied to the input of one of them.
56

57. Balanced Modulator
 Thus the outputs of two modulators may be expressed as
𝑠1 𝑡
𝑠2 𝑡
 Subtracting 𝑠2 𝑡
= 𝐴𝑐 1 + 𝑘𝑎𝑚(𝑡) cos 2𝜋ƒ𝑐𝑡
= 𝐴𝑐 1 − 𝑘𝑎𝑚(𝑡) cos 2𝜋ƒ𝑐𝑡
from 𝑠1 𝑡 , we obtain
𝑠 𝑡 = 𝑠2 𝑡 − 𝑠1 𝑡 = 2𝑘𝑎𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 𝑚(𝑡)
 Hence, except for the scaling factor 2𝑘𝑎, the balanced
modulator output is equal to the product of modulating
wave and carrier, as required.
57

58. Ring Modulator
 One of the most useful product modulators that is well suited for generating a
DSB-SC modulated wave is the ring modulator.
 It is also known as lattice or double-balanced modulator.
 The four diodes form a ring in which they all point in the same way.
 The diodes are controlled by a square wave carrier of frequency fc, which is
applied by means of two center-tapped transformers.
 We assume that the diodes are ideal and the
transformers are perfectly balanced.
58

59. Ring Modulator
 When the carrier supply is positive, the outer diodes are switched ON,
presenting zero impedance, where as the inner diodes are switched OFF,
presenting infinite impedance, so that the modulator multiplies the message
signal m(t) by +1.
 When the carrier supply is negative, the situation becomes reversed
and the modulator multiplies the message signal m(t) by -1.
 Thus a ring modulator is a product modulator for a square wave carrier
and the message signal.
59

60. Ring Modulator
 Thus a ring modulator is a product modulator for a
square wave carrier and the message signal.
 The square wave carrier can be expressed by a Fourier
series as
 The ring modulator output is therefore
 We can see that there is no output from modulator at carrier frequency.
60

61. Coherent Detection of DSB-SC Waves
 The message signal is recovered from a DSB-SC wave s(t) by first multiplying
s(t) with a locally generated sinusoidal wave and then low pass filtering the
product.
 It is assumed that the local oscillator output is exactly coherent or synchronized,
in both frequency and phase with the carrier wave c(t) used in the product
modulator to generate s(t).
 This method of demodulation is known as
coherent detection or synchronous detection.
61

62. Coherent Detection of DSB-SC Waves
 Let the signal generated from local oscillator is having same frequency and
phase, measured with respect to the carrier wave c(t).
assuming 𝐴𝑐=1
 Then the local oscillator signal can be denoted by cos 2𝜋ƒ𝑐𝑡
for convenience.
 The output of product modulator is given by
𝑣 𝑡 = cos 2𝜋ƒ𝑐𝑡 𝑠(𝑡)
𝑣 𝑡 = cos 2𝜋ƒ𝑐𝑡 𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 𝑚(𝑡)
=
cos 2𝜋ƒ𝑐𝑡 + 2𝜋ƒ𝑐𝑡 + cos 2𝜋ƒ𝑐𝑡 − 2𝜋ƒ𝑐𝑡
2 𝑐
𝑣 𝑡 𝐴 𝑚(𝑡)
𝑣 𝑡 =
𝑐
cos 4𝜋ƒ 𝑡 + 1
2 𝑐
62
𝐴 𝑚(𝑡)

63. Coherent Detection of DSB-SC Waves
𝑣 𝑡 =
𝐴 𝐴
𝑐
𝑐
2 2 𝑐
𝑚 𝑡 + cos 4𝜋ƒ 𝑡 𝑚(𝑡)
 The low pass filter removes unwanted term in the product modulator output.
 The final output is therefore given by
0
𝑣 𝑡 =
𝐴𝑐
𝑚 𝑡
 The demodulated signal 𝑣0 𝑡
2
is therefore proportional to 𝑚 𝑡
63
when local
oscillator is perfectly synchronized.

64. Effect of phase drift in Coherent Detector
 Let the signal generated from local oscillator is having same frequency but
arbitrary phase difference ɸ, measured with respect to the carrier wave c(t).
assuming
 Then the local oscillator signal can be denoted by cos 2𝜋ƒ𝑐𝑡 + ɸ
𝐴𝑐=1 for convenience.
 The output of product modulator is given by
𝑣 𝑡 = cos 2𝜋ƒ𝑐𝑡 + ɸ 𝑠(𝑡)
𝑣 𝑡 = cos 2𝜋ƒ𝑐𝑡 + ɸ 𝐴𝑐 cos 2𝜋ƒ𝑐𝑡 𝑚(𝑡)
=
cos 2𝜋ƒ𝑐𝑡 + ɸ + 2𝜋ƒ𝑐𝑡 + cos 2𝜋ƒ𝑐𝑡 + ɸ − 2𝜋ƒ𝑐𝑡
2 𝑐
𝑣 𝑡 𝐴 𝑚(𝑡)
𝑣 𝑡 =
cos 4𝜋ƒ𝑐𝑡 + ɸ + cos ɸ
2 𝑐
64
𝐴 𝑚(𝑡)

65. Effect of phase drift in Coherent Detector
𝑣 𝑡 =
𝐴 𝐴
𝑐
𝑐
2 2 𝑐
cos ɸ 𝑚 𝑡 + cos 4𝜋ƒ 𝑡 + ɸ 𝑚(𝑡)
 The low pass filter removes unwanted term in the product modulator output.
 The final output is therefore given by
𝑣 𝑡 =
𝐴𝑐
cos ɸ 𝑚 𝑡
2
is therefore proportional to 𝑚 𝑡 when the phase
65
0
 The demodulated signal 𝑣0 𝑡
error ɸ is constant.
 The amplitude of this demodulated is maximum when ɸ = 0, and is minimum
(zero) when ɸ = ±𝜋/2.

66. Effect of phase drift in Coherent Detector
66
 The zero demodulated signal which occurs for ɸ = ±𝜋/2, represents the
quadrature null effect of the coherent detector.
 Thus the phase error ɸ in the local oscillator causes the detector output to be
attenuated by a factor equal to cosɸ.
 As long as the phase error ɸ is constant, the detector output provides an
undistorted version of the original message signal 𝑚(𝑡).
 In practice, phase error varies randomly with time because of random variations
in the communication channel, which is undesirable.
 Therefore, circuitry must be provided in the receiver to maintain the local
oscillator in perfect synchronism, in both frequency and phase, with the carrier
wave used to generate DSB-SC wave in the transmitter.

67. Effect of phase drift in Coherent Detector
67
 The resulting increase in receiver complexity is the price that must be paid for
suppressing the carrier wave to save transmitter power.

68. Single Tone Modulation of DSB-SC Wave
 Consider a sinusoidal modulating wave m 𝑡 = 𝐴𝑚cos(2𝜋ƒ𝑚𝑡).
 The corresponding DSB-SC wave is given by
𝑠 𝑡 = 𝑚 𝑡 𝑐 𝑡 = 𝐴𝑚cos(2𝜋ƒ𝑚𝑡)𝐴𝑐 cos 2𝜋ƒ𝑐𝑡
𝑠 𝑡 =
𝐴 𝐴 𝐴 𝐴
𝑐 𝑚 𝑐 𝑚
2 2
𝑐 𝑚 𝑐 𝑚
cos 2𝜋 ƒ + ƒ 𝑡 + cos 2𝜋 ƒ − ƒ 𝑡
 Assuming perfect synchronism between the local oscillator and carrier wave in
coherent detector, the product modulator output is
𝑐
𝑣 𝑡 = cos 2𝜋ƒ 𝑡
𝑐 𝑚
2 𝑐 𝑚
cos 2𝜋 ƒ + ƒ 𝑡 +
𝐴 𝐴 𝐴 𝐴
𝑐 𝑚
2
cos 2𝜋 ƒ𝑐 − ƒ𝑚 𝑡
68

69. Single Tone Modulation of DSB-SC Wave
𝑣 𝑡 =
4
𝐴 𝐴 𝐴 𝐴
𝑐 𝑚 𝑐 𝑚
4
𝑐 𝑚 𝑚
cos 2𝜋 2ƒ + ƒ 𝑡 + cos 2𝜋ƒ 𝑡
+
𝐴 𝐴
𝑐 𝑚
cos 2𝜋 2ƒ𝑐 − ƒ𝑚 𝑡 +
𝐴 𝐴
𝑐 𝑚
2 4 𝑚
69
cos 2𝜋ƒ 𝑡
 The first two terms are produced by upper side frequency, and last two terms
are produced by lower side frequency.
 The first and third terms are removed by low pass filter.
 The coherent detector output hence reproduces the original message signal.
 The detector output has two equal terms, one derived from upper side frequency
and the other from lower side frequency.
 Hence for transmission of information, only one side frequency is necessary.