#### 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?

#### Solution

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 (8π*t*)

∴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`