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?
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, $m=\frac{A_{\mathrm{m}}}{A_{\mathrm{c}}}=\frac{1}{2}=0.5$