(a) If and represent the maximum and minimum amplitudes of an amplitude modulated wave, write the expression for the modulation index in terms of & .
(b) A message signal of frequency and peak voltage is used to modulate a carrier of frequency and peak voltage of . Calculate the modulation index. Why the modulation index is generally kept less than one?
(a) We have given that:-
Maximum amplitude,
Minimum Amplitude,
Let, the amplitude of the carrier wave be and
the amplitude of the message signal be
Now, we know that,
_____(1)
______(2)
On adding(1) and (2), we have
and, On sunstracting (2) from (1), we have
Hence, we know, the modulation index in terms of
and can be given as ;
(b) We know, the modulation index is given by :-
Hence, is given as and
is given as So,
To avoid the Distortion of the signal, the modulation index is generally kept less than one.