Question

A modulating signal is a square wave, as shown

The carrier wave is given by  `c(t) = 2 sin (8pit) "volts"`

(i) Sketch the amplitude modulated waveform

(ii) What is the modulation index?

Answer 1

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

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

∴Amplitude of the carrier wave, A_c = 2 V

Time period of the modulating signal T_m = 1 s

The angular frequency of the modulating signal is calculated as:

`omega_m = 2pi/T_m`

`= 2pi "rad" s^(-1)`  ... (1)

The angular frequency of the carrier signal is calculated as:

`omega_c = 8pi "rad" s^(-1)`  ... (ii)

From equations (i) and (ii), we get:

`mega_c = 4omega_m`

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

(ii)Modulation index, `m = A_m/A_c = 1/2 = 0.5`