Question:
A carrier wave of peak voltage 12 V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 75%?
Solution:
Amplitude of the carrier wave, Ac = 12 V
Modulation index, m = 75% = 0.75
Amplitude of the modulating wave = Am
Using the relation for modulation index:
$m=\frac{A_{\mathrm{m}}}{A_{\mathrm{c}}}$
$\therefore A_{\mathrm{m}}=m A_{\mathrm{c}}$
$=0.75 \times 12=9 \mathrm{~V}$