GATE 2021 EC – Question 59
A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant 2 rad/volt. If the carrier signal is $c(t)=2\cos(2\pi10^6t)$, the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is ________ Hz.
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Correct answer: 1006257.13 to 1016370.27
Explanation
The message amplitude is $A_m=4\sqrt2$ V. For phase modulation the instantaneous frequency is $f_i=f_c+\frac{k_p}{2\pi}\frac{dm}{dt}$, whose maximum deviation is $k_pA_mf_m=2\times4\sqrt2\times1000=11313.7$ Hz. So the maximum instantaneous frequency is $10^6+11313.7=1{,}011{,}313.7$ Hz.