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?
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) = 2sin(8πt) volts
∴ 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:
(t)m = 2π/Tm
= 2π rad s-1 (as Tm = 1)……………….(i)
The angular frequency of the carrier signal is calculated as:
(t)m = 8π rad s-1 ……….(ii)
From equations (i) and (ii), we get:
(t)m = 4(t)c
The amplitude modulated waveform of the modulating signal is shown in the following figure.
(ii) Modulation index,
m = Am/Ac = 1/2 = 0.5