Question

The carrier wave is represented by

\[C(t) = 5 \sin(10\pi t)\]

A modulating signal is a square wave as shown. Determine 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 modulating signal,

\[A_m = 2 V\]

Amplitude of carrier wave,

\[A_c = 5 V\]

∴ \[\mu = \frac{A_m}{A_c} = \frac{2}{5} = 0 . 4\]