Question

The carrier wave of a signal is given by C(t) = 3 sin (8πt) volt. The modulating signal is a square wave as shown. Find its modulation index.

Answer 1

Modulation index (\[\mu\]) is the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave.

The generalised equation of a carrier wave is given below:

\[c(t) = A_c \sin \omega_c t\]

The generalised equation of a modulating wave is given below:

\[c_m (t) = A_c \sin \omega_c t + \mu A_c \sin \omega_m t\sin \omega_c t\]

Here, 

\[\mu\]  is defined as \[\frac{A_m}{A_c}\].

On comparing this with the equations of carrier wave and modulating wave, we get:
Amplitude of a modulating signal, \[A_m = 1 . 5\] V
Amplitude of a carrier wave, 

\[A_c = 3\]V

∴  \[\mu = \frac{A_m}{A_c} = \frac{1 . 5}{3} = \frac{1}{2} = 0 . 5\]