Physics

Physics

Problem

In an amplitude modulator circuit, the carrier wave is given by C(t)=4sin⁡(20000πt)C(t) = 4 \sin (20000 \pi t) while the modulating signal is given by m(t)=2sin⁡(2000πt)m(t) = 2 \sin (2000 \pi t). Find the modulation index and the lower side band frequency. a. 0.5 and 10 kHz b. 0.4 and 10 kHz c. 0.3 and 9 kHz d. 0.5 and 9 kHz
Intuitive explanation

Amplitude modulation works by letting a low-frequency signal "ride on" a high-frequency carrier wave. The modulation index tells you how much the carrier's amplitude is being squeezed and stretched by the message signal—it's the ratio of the modulating signal's amplitude to the carrier's amplitude. The sidebands are new frequencies created by this mixing process; the lower sideband is simply the difference between the carrier frequency and the modulating frequency.

Intuitive explanation

Amplitude modulation works by letting a low-frequency signal "ride on" a high-frequency carrier wave. The modulation index tells you how much the carrier's amplitude is being squeezed and stretched by the message signal—it's the ratio of the modulating signal's amplitude to the carrier's amplitude. The sidebands are new frequencies created by this mixing process; the lower sideband is simply the difference between the carrier frequency and the modulating frequency.

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