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The Carrier Wave of a Signal is Given by C(T) = 3 Sin (8πT) Volt. the Modulating Signal is a Square Wave as Shown. Find Its Modulation Index. - Physics

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ConceptModulation and Its Necessity

Question

The carrier wave of a signal is given by C(t) = 3 sin (8πt) volt. The modulating signal is a square wave as shown. Find its modulation index.

Solution

Modulation index (\[\mu\]) is the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave.

The generalised equation of a carrier wave is given below:

\[c(t) = A_c \sin \omega_c t\]
The generalised equation of a modulating wave is given below:
\[c_m (t) = A_c \sin \omega_c t + \mu A_c \sin \omega_m t\sin \omega_c t\]
Here, 
\[\mu\]  is defined as \[\frac{A_m}{A_c}\].
On comparing this with the equations of carrier wave and modulating wave, we get:
Amplitude of a modulating signal, \[A_m = 1 . 5\] V
Amplitude of a carrier wave, 
\[A_c = 3\]V
∴  \[\mu = \frac{A_m}{A_c} = \frac{1 . 5}{3} = \frac{1}{2} = 0 . 5\]
  Is there an error in this question or solution?

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Solution The Carrier Wave of a Signal is Given by C(T) = 3 Sin (8πT) Volt. the Modulating Signal is a Square Wave as Shown. Find Its Modulation Index. Concept: Modulation and Its Necessity.
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