For FM f(t)=[2 f ct+ 1(2 f 1t)+ 2(2 f 2t)], find maximum instantaneous-frequency deviation from f c.

GATE 2014 EC (EC3) – Question 33

Communications · Analog Communications · 1 mark · Multiple choice

For FM $f(t)=\cos[2\pi f_ct+\beta_1\sin(2\pi f_1t)+\beta_2\sin(2\pi f_2t)]$, find maximum instantaneous-frequency deviation from $f_c$.

$\beta_1f_1+\beta_2f_2$
$\beta_1f_2+\beta_2f_1$
$\beta_1+\beta_2$
$f_1+f_2$

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Correct answer: (A) $\beta_1f_1+\beta_2f_2$

Explanation

Instantaneous frequency is the time derivative of phase divided by2π, giving fc+β1f1cos(2πf1t)+β2f2cos(2πf2t). The largest deviation is **β1f1+β2f2,A** for positive modulation indices; both cosine terms reach1at t=0. Modulation indices alone are dimensionless and are not frequencies.