The carrier wave is given by c(t)=2sin(8πt)volts.

(1) Sketch the amplitude modulated waveform

(2) What is the modulation index?

Answer –

(1)

The modulating signal’s amplitude, Am = 1V, can be simply determined from the supplied modulating signal.

c(t) = 2 sin c(t) = 2 sin c(t) = 2 sin c(t) = 2 sin c(t) (8nt)

Ac = 2v is the carrier wave’s amplitude.

Tm = 1s is the time period.

The modulating signal’s angular frequency is provided by,

Ѡ_m = 2π/T                                                                      

Ѡ_m = 2π rad s^-1—————–(1)

The angular frequency of carrier signal is given by

Ѡ_c = 8π rad s^-1 ——————–(2)

From equations (1) and (2), we get –

we get,

Ѡ_c = 4Ѡ_m

Following figure shows modulating signal having the amplitude modulated waveform.

(2)

 Modulation index, m is given by the relation –

M = Am/Ac = ½

M = 0.5