Discussion
An FM system uses a deviation of \( 75 \ \mathrm{kHz} \) with a highest message frequency of \( 15 \ \mathrm{kHz} \). Its figure of merit is about
Answer: B
The index is five, so applying the wideband result:
\[ \begin{aligned} \text{FoM} &= 3\beta^{2}(\beta+1) \\ &= 3(25)(6) = 450 \end{aligned} \]
giving about 450, some thirty decibels better than single sideband at the same transmitted power. 150 drops the factor of \( \beta+1 \), which is the commonest slip. 75 comes from \( 3\beta^{2} \) with \( \beta \) mistaken. And 1500 overcounts by the index. The cubic growth in the index is what makes the trade so attractive, and it is why the bandwidth limit rather than the arithmetic sets the design.
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