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The transmitted power in Frequency Modulation (FM) is primarily a function of the modulation index (β), defined as the ratio of the frequency deviation to the modulating frequency. The power in an FM signal is given by the equation:
[
P = P_0 left(1 + frac{β^2}{2}right)
]
where ( P_0 ) is the carrier power, and ( β ) is the modulation index.
1. When the modulation index (β) is 0, the equation simplifies to ( P = P_0 ). Therefore, the transmitted power is equal to the carrier power.
2. When the modulation index is increased to 1, we substitute β into the formula:
[
P = P_0 left(1 + frac{1^2}{2}right) = P_0 left(1 + 0.5right) = P_0 times 1.5
]
This means that when the modulation index is changed from 0 to 1, the transmitted power increases by 50%.
In summary, the transmitted power increases from ( P_0 ) to ( 1.5P_0 ).
C. gets increased by 50 percent