GATE 2019 EC – Question 32
The baseband signal $m(t)$ shown in the figure is phase-modulated to generate the PM signal $\varphi(t)=\cos(2\pi f_ct+k\,m(t))$. The time $t$ on the x-axis in the figure is in milliseconds. If the carrier frequency is $f_c=50$ kHz and $k=10\pi$, then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is ________ (rounded off to 2 decimal places).
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Correct answer: 0.74 to 0.76
Explanation
The instantaneous frequency is $f_i=f_c+\frac{k}{2\pi}\frac{dm}{dt}=50+5\,m'(t)$ kHz, with $m'$ in units per ms. From the figure, $m(t)$ rises by 2 in 1 ms (slope $+2$ per ms) and falls by 2 in 2 ms (slope $-1$ per ms), which gives $f_{max}=60$ kHz and $f_{min}=45$ kHz, so the ratio is $\frac{45}{60}=0.75$.