A modulating signal is a square wave. Sketch the amplitude modulated waveform - Physics

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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?

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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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Chapter 15: Communication Systems - Exercise [Page 530]

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NCERT Physics Class 12
Chapter 15 Communication Systems
Exercise | Q 6 | Page 530

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