GATE EC|| COMMUNICATION SYSTEM|| ANGLE MODULATION ||PYQs(2000-2025)

Consider the frequency modulated signal 10cos[2 π×10 ⁵ t + 5sin(2π× 1500t) + 7.5sin(2π× 1000t)] with carrier frequency of 10 ⁵ Hz. The modulation index is

(PYQ || 2008 MCQ || 1 MARK)

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 (2π10 ⁶ t), the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is _____ Hz.

(PYQ || 2021 NAT|| 2 MARK)

(PYQ || 2020 NAT|| 2 MARK)

( PYQ || 2019 NAT|| 1 MARK)

A modulating signal given by

x(t)=5sin(4 π10 ³ t–10 πcos2 π 10 ³ t)V

is fed to a phase modulator with phase deviation constant k_p = 5 rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is _______.

The block diagram of a frequency synthesizer consisting of a Phase Locked Loop (PLL) and a divide-by-N counter (comprising ÷ 2, ÷ 4, ÷ 8, ÷ 16 outputs) is sketched below. The synthesizer is excited with a 5 kHz signal (Input 1). The free-running frequency of the PLL is set to 20 kHz. Assume that the commutator switch makes contacts repeatedly in the order 1-2-3-4.

The corresponding frequency synthesized are :

(PYQ || 2016 MCQ || 1 MARK)

A message signal m(t) = A m sin(2πf _m t) is used to modulate the phase of a carrier A c cos(2πf _c t) to get the modulated signal y(t) = A c cos(2 πf _c t + m(t)). The bandwidth of y(t)

(PYQ || 2015 MCQ || 1 MARK)

( PYQ || 2014 MCQ || 1 MARK)

The signal m(t) as shown is applied both to a phase modulator (with k _p as the phase constant) and a frequency modulator with (k _f as the frequency constant) having the same carrier frequency

The ratio k _p /k _f (in rad/Hz) for the same maximum phase deviation is

(PYQ || 2012 MCQ || 2 MARK)

Consider an angle modulation signal

x(t) = 6cos[2 π×10 ⁶ t + 2sin(8000πt) + 4cos(8000 πt)]V.

The average power of x(t) is

(PYQ || 2010 MCQ || 1 MARK)