question_answer

What is modulation index? Its value is kept always less than one in practice, explain its reason.

A carrier wave of frequency 1.75 MHz, an amplitude 60V is modulated by a sinusoidal wave of frequency 12kHz producing 60% amplitude modulation. Find out the amplitude of the amplitude modulation wave.

Answer:

Amplitude modulation index is the ratio of the modulating signal to the maximum amplitude of carrier wave. Practically, it is kept less than one. If its value is greater than one, the carrier wave will be over modulated and distortion will take place during reception as negative peak of modulating signal will be missing. Therefore, μ is kept less than one. Frequency of sinusoidal wave,                         \[{{v}_{m}}=12\,\,kHz\] Amplitude of carrier wave, \[{{A}_{c}}=60\text{ }V\] Modulation index, \[\mu =60\,%=\frac{600}{100}=\frac{3}{5}\] \[\therefore \] \[\mu =\frac{{{A}_{m}}}{{{A}_{c}}}\] \[\Rightarrow \] \[\frac{2}{3}=\frac{{{A}_{m}}}{60}\] \[\Rightarrow \] \[{{A}_{m}}=60\times \frac{2}{3}=40\,V\] Thus, the amplitude of AM wave, \[{{A}_{m}}=40V\]