Question

Suppose the carrier wave is modulated in accordance with the amplitude of a message signal.

The modulation index is m. The Instantaneous carrier voltage is represented by, v_e = v_esin 2πf_et. The instantaneous modulating voltage is presented by, v_m = V_m sin 2πf_mt.

The bandwidth of the amplitude modulated wave is equal to,

(1) 2f_m

(2) 2f_c

(3) f_c - f_m

(4) f_c + f_m

Answer 1

(1) 2f_m

Instantaneous voltage of the amplitude modulated wave is represented by,

This implies that in addition to the original central frequency, there exist side bands in an amplitude modulated wave. The frequency of upper sideband is equal to, f_c + f_m . The frequency of lower sideband is equal to f_c – f_m . The bandwidth is the difference in frequency of the side bands, which is given by,