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# A transmitter puts out a total power of 40 Watts of 30% AM signal. Calculate how much power is contained in each of the sidebands and the fraction of power in the carrier.

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The total power in an AM signal when the carrier power and the percentage of modulation are known is $P_T = P_c \big ( 1 + \large\frac{m^2}{2}$$\big ) \Rightarrow 40 = P_c \big ( 1 + \large\frac{0.30^2}{2}$$\big )$
$\Rightarrow P_c = \large\frac{40}{1.045}$$= 38.28\;W The total power in both side bands = 40-38.28 = 1.72\;W The power in each side band is half of this = 0.86\;W \Rightarrow The fraction of the power in the carrier is \large\frac{38.28}{40}$$\approx 0.96$
answered Jul 13, 2014

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