Determine the average % power in each sideband frequency in case of AM using sinusoidal modulating wave. Given that the percentage modulation = 20%

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Determine the average % power in each sideband frequency in case of AM using sinusoidal modulating wave. Given that the percentage modulation = 20%
1. 10%
2. 5%
3. 1%
4. 18%

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Correct Answer - Option 3 : 1%

Concept:

The power of a transmitted AM wave is given as:

$P_t = {P_c}\left( {1 + \frac{{{μ ^2}}}{2}} \right)$

$P_t = {P_c} + P_c\frac{μ ^2}{2}$

Power in the carrier = Pc

$P_c=\frac{{A_m}^2}{2}$

Power in both the sidebands is given by:

$P_s= \frac{{{P_c}{μ^2}}}{2}$

Since the power is distributed equally to the left and to the right side of the sideband, the power in one of the sidebands is given by:

$P_{s1}= \frac{{{P_c}{u^2}}}{4}$

Calculation:

Given μ = 20% = 0.2

$P_c=\frac{{A_m}^2}{2}$

Total Sideband power is:

$P_{sb}=\frac{{A_m}^2\mu^2}{4}$

Assume Am = 1

$P_{sb}=\frac{0.2^2}{4} \ \times \ 100$

Psb = 1%

Hence option (3) is the correct answer.