1) Amplitude modulation involves varying the amplitude of a carrier signal based on the amplitude of a message signal. 2) The mathematical representation of an amplitude modulated wave shows it consists of three components: the carrier wave, a lower sideband at the difference frequency, and an upper sideband at the sum frequency. 3) The modulation index, which ranges from 0 to 1, represents the ratio of the message signal amplitude to the carrier signal amplitude and determines the degree of modulation. Higher modulation indices lead to distortion.

1. 1

2. UNIT-1
AMPLITUDE MODULATION
2

3. CONTENTS
Analog Communication
 Amplitude Modulation
 Definition
 Mathematical Representation
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4. AMPLITUDE MODULATION
 If the amplitude of the carrier signal is modulated with respect to
the variation in the amplitude of the message signal.
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5. Mathematical Representation
where - Constant amplitude of carrier signal
where - Constant amplitude of message signal
Let instantaneous voltage of AM wave is
Amplitude of AM wave is
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Let the carrier signal be
t
w
E
e c
c
c sin

c
E
Let the message signal be
t
w
E
e m
m
m sin

m
E
t
w
A
e c
sin
mod 
)
(t
e
E
A c
c 

c
c e
t
e 
)
(
where

6. The output modulated signal is given by
  t
w
t
w
E
E
e c
m
m
c sin
sin
mod 

t
w
t
w
E
t
w
E c
m
m
c
c sin
sin
sin 


   t
w
w
E
t
w
w
E
t
w
E m
c
m
m
c
m
c
c 



 cos
2
cos
2
sin
Here SinA SinB =1/2[Cos(A-B)-Cos(A+B)]
A= ;B=
t
wm
sin t
wc
sin

7. Let m= Em/Ec (Modulation Index)
AM wave consists of 3 terms:
a) The carrier component -
b) Lower side band (LSB)/ Difference freq. component –
c) Upper side band (USB)/ Sum freq. component -
   t
w
w
mE
t
w
w
mE
t
w
E
e m
c
c
m
c
c
c
c 



 cos
2
cos
2
sin
mod
 
m
c w
w 
 
m
c w
w 
c
w

8. Frequency spectrum of AM wave:
Bandwidth of AM wave:
Phasor representation:
All phasor rotates in
counter clockwise
direction

9. Modulation index (m)/Modulation
factor/Modulation Coefficient/
Degree of modulation:
• It is the measure of mixing of the carrier signal and
message signal
• Its value varies from 0 to 1. ‘1’ means over
modulation. So, proper selection of m is necessary
• Ratio of unmodulated carrier wave to the message
signal.
• Formula:
(i) m= Em/Ec
(ii) m=(Emax-Emin)/(Emax+Emin)
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10. Why modulation index M/Ma number is between 0 &1?
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11. 11

12. Derivation for ‘m’/M/Ma
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14. Time domain representation of
AM wave
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15. 15

16. 16

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18. Note:
 Ma>1 – Distortion
 Ma>>1 – Distortion by over modulation (ex: Ma=1.5)
 Ma=1 – 100% modulation
 Ma<1 – Under modulation
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19. 19

20. Power Relation in AM wave- The total power in
modulated AM wave is the sum of unmodulated carrier
power & 2 side band powers.
Total power
of AM wave:

21. For m=1; Ptotal =1.5Pc
In terms of current,

22. Note:
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23. Power relations
Power Analysis:
• Psb/Ptotal =
• For 100% modulation (m=1), Psb/Ptotal = 1/3.
• Since the information is available only in sidebands, only
one-third of the power is useful and the rest of the power is
wasted.
“Hence, AM is inefficient in terms of power consumption”
• For modulation with many sine waves
 
2
2
2
/ m
m 

24. Efficiency
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Ma =M