Question

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

Answer 1

(i)

From the above modulating signal, it can be observed that the amplitude of the modulating signal is,

A m =1 V

The equation of carrier wave is,

c( t )=2sin( 8πt )

Thus,

Amplitude of the carrier wave, A C =2 V

Time period of the modulating signal, T m =1 s

Let, ω m be the angular frequency of the modulating signal

The angular frequency is given as,

ω m = 2π T m

Thus

ω m = 2π 1 =2π  rads -1

From above expression of c( t )=2sin( 8πt ), it can be observed that the angular frequency of the carrier signal is,

ω c =8π  rads -1

Thus,

ω c =4 ω m

Therefore, the amplitude modulated waveform of modulating signal will be,

(ii)

The modulation index is given as,

m= A m A c

Substitute the values in above expression.

m= 1 2 =0.5