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Amplitude modulation

The process of changing the amplitude of a carrier wave in accordance with the amplitude of the audio frequency (AF) signal is known as amplitude modulation (AM). In AM frequency of the carrier wave remains unchanged. The amplitude of modulated wave is varied in accordance with the amplitude of modulating wave (Fig. 10).
 
77900.png
Fig. 10

Modulation index

The ratio of change of amplitude of the carrier wave to the amplitude of original carrier wave is called the modulation factor or degree of modulation or modulation index (ma).
 
 
77926.png
 
where k is a factor which determines the maximum change in the amplitude for a given amplitude Em of the modulating signal. If k = 1, then
 
77937.png
 
If a carrier wave is modulated by several sine waves, the total modulated index mt is given by
 
77943.png

Voltage equation for AM wave

Suppose voltage equations for carrier wave and modulating wave are ec = Ec cos ωct and em = Em sin ωmt = mEc sinωmt, where ec is the instantaneous voltage of carrier wave, Ec amplitude of carrier wave, ωc(=2πfc) angular velocity at carrier frequency fc, em instantaneous voltage of modulating, Em amplitude of modulating wave, and ωm (=2πfm) angular velocity of modulating frequency fm.
 
Voltage equation for AM wave is
77956.png
 
The above AM wave indicated that the AM wave is equivalent to the summation of three sinusoidal waves, one having amplitude Ec and the other two having amplitude maEc /2.

Side band frequencies

An AM wave contains three frequencies: fc (called carrier frequency), (fc + fm), and (fcfm) (latter two called side band frequencies).
 
(fc + fm): Upper side band (USB) frequency
 
(fcfm): Lower side band (LSB) frequency
 
Side band frequencies are generally close to the carrier frequency.

Bandwidth in AM wave

The two side bands lie on either side of the carrier frequency at equal frequency interval fm. So, bandwidth = (fc + fm) – (fcfm) = 2fm.
 
77906.png
Fig. 11

Power in AM waves

Power dissipated in any circuit, P = V2rms/R. Hence,
Carrier power, 77968.png
 
Total power of side bands,
 
77974.png
 
Total power of AM wave,
 
Ptotal = Pc + Psb 77980.png
77986.png and 77992.png
 
Maximum power in AM (without distortion) will occur when ma = 1, i.e., Pt = 1.5P = 3Psb
 
If Ic = unmodulated current and It = total or modulated current, then 78003.png 78013.png

Limitations of amplitude modulation

  1. Noisy reception
  2. Low efficiency
  3. Small operating range
  4. Poor audio quality




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