A modulating signal is a square wave, as shown in Fig. 15.14.
Question:

A modulating signal is a square wave, as shown in Fig. 15.14.

The carrier wave is given by $c(t)=2 \sin (8 \pi t)$ volts.

(i) Sketch the amplitude modulated waveform

(ii) What is the modulation index?

Solution:

It can be observed from the given modulating signal that the amplitude of the modulating signal, Am = 1 V

It is given that the carrier wave c (t) = 2 sin (8πt)

Amplitude of the carrier wave, Ac = 2 V

Time period of the modulating signal Tm = 1 s

The angular frequency of the modulating signal is calculated as:

$\omega_{\mathrm{m}}=\frac{2 \pi}{T_{\mathrm{m}}}$

$=2 \pi \mathrm{rad} \mathrm{s}^{-1}$     …(i)

The angular frequency of the carrier signal is calculated as:

$\omega_{\mathrm{c}}=8 \pi \mathrm{rad} \mathrm{s}^{-1}$     ….(ii)

From equations (i) and (ii), we get:

$\omega_{\mathrm{c}}=4 \omega_{\mathrm{m}}$

The amplitude modulated waveform of the modulating signal is shown in the following figure.

(ii)Modulation index, $m=\frac{A_{\mathrm{m}}}{A_{\mathrm{c}}}=\frac{1}{2}=0.5$