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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, Am = 1 V
It is given that the carrier wave c (t) = 2 sin (8πt)
∴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:
`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`
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