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Question : 18
Total: 27
A signal of low frequency f m f c
Solution:
Derive expression for amplitude modulated wave.
Deducing expression for lower and upper side bands.
Obtaining expression for modulation index.
Let a carrier wave be given by
c ( t ) = A c s i n ω c t ω c = 2 π f c
And signal wave be
m ( t ) s i n ω m t ω m = 2 π f m
The modulated signal is
c m ( t ) = ( A c + A m s i n ω m t ) s i n ω c t
c m ( t ) = A c ( 1 +
s i n ω m t ) s i n ω c t
c m ( t ) = A c s i n ω c t + µ
cos ( ω c − ω m ) t − µ
cos ( ω c + ω m ) t
The modulation indexµ =
Lower frequency bandω c − ω m
Upper frequency bandω c + ω m
Deducing expression for lower and upper side bands.
Obtaining expression for modulation index.
Let a carrier wave be given by
And signal wave be
The modulated signal is
The modulation index
Lower frequency band
Upper frequency band
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