Question

A modulating signal is a square wave, as shown in Fig. 15.14. The carrier wave is given by c(t) = 2sin(8πt) volts (i) Sketch the amplitude modulated waveform (ii) What is the modulation index?

Answer 1

from fig 15.14, it can be observed that the amplitude of the modulating signal, $A_m$ = 1V

also it is given that the carrier wave, c(t) = 2sin(8πt) volts

so, amplitude of the carrier wave, $A_c$ = 2V

time period of the modulating signals, $T_m$ = 1s [ see fig 15.14, wave completes one cycle in a second.]

the angular frequency of the modulating signal is calculated as $\omega_m$ = 2π/$T_m$ = 2π/1 = 2π rad/s.....(1)

also angular frequency of the carrier signal is $\omega_c=\frac{8\pi}$ [ from equation of carrier wave ].....(2)

from equations (1) and (2),

$\omega_c=4\omega_m$

so, The amplitude modulated waveform of the modulating signal is shown in the 2nd figure.

(ii) modulation index , $m=\frac{A_m}{A_c}$

= 1/2 = 0.5