A message signal of frequency \(20\ \mathrm{kHz}\) and peak voltage of \(20\) volt is used to modulate a carrier wave of frequency \(1\ \mathrm{MHz}\) and peak voltage of \(20\) volt. The modulation index will be :

Question

The percentage of the total power carried by the sidebands of the AM wave for tone modulation when the modulation index is 0.3 is:

Answer 1

For amplitude modulation, \(\mu = \dfrac{A_m}{A_c}\), the fractional change of carrier amplitude.
The carrier amplitude varies between \(A_c - A_m = 0\) and \(A_c + A_m = 40\ \mathrm{V}\), so \(\mu = \dfrac{40-0}{40+0} = 1\) (100% modulation).
Answer: 1

List-I (Modulation Schemes)	List-II (Wave Expressions)
(A) Amplitude Modulation	(I) \( x(t) = A\cos(\omega_c t + k m(t)) \)
(B) Phase Modulation	(II) \( x(t) = A\cos(\omega_c t + k \int m(t)dt) \)
(C) Frequency Modulation	(III) \( x(t) = A + m(t)\cos(\omega_c t) \)
(D) DSB-SC Modulation	(IV) \( x(t) = m(t)\cos(\omega_c t) \)

A message signal of frequency \(20\ \mathrm{kHz}\) and peak voltage of \(20\) volt is used to modulate a carrier wave of frequency \(1\ \mathrm{MHz}\) and peak voltage of \(20\) volt. The modulation index will be :

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Correct Answer: 1

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