Amplitude Modulation

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When the amplitude of high frequency carrier wave is changed in accordance with the intensity of the signal, it is called amplitude modulation.

In amplitude modulation, only the amplitude of the carrier wave is changed in accordance with the intensity of the signal. However, the frequency of the modulated wave remains the same as the carrier frequency. The Below figure shows the principle of amplitude modulation (a) shows the audio electrical signal, whereas (b) shows the carrier wave of constant amplitude and (c) shows the amplitude-modulated wave.

Note that the amplitude of both positive and negative half cycles of carrier wave are changed in accordance with the signal. For instance, when the signal is increasing in the positive sense, the amplitude of carrier wave also increases. During negative half cycle of the signal, the amplitude of carrier decreases. Amplitude modulation is done by an electronic circuit called modulator.

The following points are worth noting in amplitude modulation:

(i) The amplitude of the carrier wave changes according to the intensity of the signal.

(ii) The amplitude variation of the carrier wave is at the signal frequency f_s.

(iii) The frequency of the amplitude modulated wave remains the same, i.e., carrier frequency, f_c.

In amplitude modulation, the amplitude of the wave is varied duplicating faithfully the fluctuations of the message. At the receiver these variations are detected or demodulated i.e., the message is removed from the carrier. (Although the more precise terms are demodulation for the process and demodulator for the device, the terms detection and detector are widely used.) After reception and demodulation at the receiver, the carrier is of no further use and is discarded.

Three Sinusoidal Waves in AM Wave

Let the carrier voltage and the modulating voltage be represented by:

where e_c and e_m represent instantaneous voltages of carrier wave and modulating wave respectively, E_c and E_m represent the amplitudes of carrier wave and modulating wave respectively, w_c and w_m represent angular velocities at carrier frequency v_c and modulating frequency v_m respectively.

The amplitude E_c of the carrier wave is varied in accordance with the modulating wave. For the modulated wave, e = E sin w_ct

Here E is the amplitude of the modulated wave.

Now, e = (E_c + e_m) sin w_ct

= (E_c + E_m sin w_mt) sin w_ct

= E_c sin w_ct + E_m sin w_mt sin w_ct

(Because 2sinA sinB = cos (B-A) - cos (B+A))

It is clear from the above equation that the AM wave may be regarded as a combination of three sinusoidal waves, one having amplitude E_c and the other two having amplitudes  each.

Side Band Frequencies

Corresponding to w_c, (w_c + w_m) and (w_c - w_m), there are three frequencies n_c, n_c + n_m, and n_c - n_m. Clearly, the frequency of the unmodulated carrier wave is not changed. However, two new frequencies (n_c + n_m) and (n_c - n_m) are produced. These are known as side-band frequencies. n_c + n_m is called the upper side band frequency (USB). n_c - n_m is called the lower side-band frequency (LSB). The two side-band lie on either side of the carrier frequency at equal frequency interval n_m. So, band width is 2n_m.