In amplitude modulation, sinusoidal carrier frequency used is denoted by \(\omega_c\) and the signal frequency is denoted by \(\omega_m\). The bandwidth (\(\Delta\omega_m\)) of the signal is such that \(\Delta\omega_m \lt\lt \omega_c\). Which of the following frequencies is not contained in the modulated wave?
Show Hint
- \(\omega_m\)
- \(\omega_c\)
- \(\omega_m + \omega_c\)
- \(\omega_c - \omega_m\)
The Correct Option is A
Solution and Explanation
AM wave: \(c_m(t) = A_c\sin\omega_c t + \mu A_c\sin\omega_m t\,\sin\omega_c t\).
Using \(\sin A \sin B = \frac{1}{2}[\cos(A-B) - \cos(A+B)]\):
\(c_m(t) = A_c\sin\omega_c t + \frac{\mu A_c}{2}\cos(\omega_c - \omega_m)t - \frac{\mu A_c}{2}\cos(\omega_c + \omega_m)t\).
So the modulated wave has only the frequencies \(\omega_c\), \(\omega_c - \omega_m\) and \(\omega_c + \omega_m\). The signal frequency \(\omega_m\) itself is not present.
Answer: (1) \(\omega_m\)
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