For an FM signal with carrier f_c = 100,text MHz , modulating frequency f_m = 10,text kHz , and peak frequency deviation Delta f = 75,text kHz , the modulation index beta and Carson's rule bandwidth are:

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Electrical Engineering QUESTION #2188

Question 1

For an FM signal with carrier $f_c = 100\,\text{MHz}$, modulating frequency $f_m = 10\,\text{kHz}$, and peak frequency deviation $\Delta f = 75\,\text{kHz}$, the modulation index $\beta$ and Carson's rule bandwidth are:

$\beta = 7.5$, $BW = 170\,\text{kHz}$✔️
$\beta = 7.5$, $BW = 150\,\text{kHz}$
$\beta = 0.133$, $BW = 20\,\text{kHz}$
$\beta = 7.5$, $BW = 75\,\text{kHz}$

Correct Answer Explanation

$\beta = \Delta f/f_m = 75/10 = 7.5$. Carson's rule: $BW = 2(\Delta f + f_m) = 2(75+10) = 2\times85 = 170\,\text{kHz}$.

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