Sub.
: Communication Theory and Telemetry
Assignment-1
Last date of submission is 13/02/2024 (both soft and hard copy)
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Problem 1:
A sinusoidally modulated ordinary AM waveform is shown below.
(a) Determine the modulation index.
(b) Calculate the transmission efficiency.
(c) Determine the amplitude of the carrier which must be added to attain a modulation index of
0.3.
Problem 2:
The output signal from an AM modulator is:
s(t) = 5cos(1800π t) + 20cos (2000π t) + 5cos (2200π t)
(a) Determine the modulation index.
(b) Determine the ratio of the power in the sidebands to the power in the carrier.
Problem 3:
A normalized sinusoidal signal a(t) has a bandwidth of 5,000 Hz and its average power is 0.5W.
The carrier Acos2πfct has an average power of 50W. Determine the bandwidth and the average
power of the modulated signal if the following analog modulation scheme is employed:
(a) single-side band modulation with suppressed carrier modulation (SSBSC), which is generated
by phase-shift method with the given carrier ;
(b) double-side band with suppressed carrier modulation (DSB-SC);
(c) AM or double-side band with carrier (DSB-FC) with a modulation index of 0.8.
Problem 4:
Consider the following circuit with an input signal, v(t), an amplifier with gain K, a sinusoidal
carrier signal at ωc, and two nonlinear devices:
(a) Express the output signal s(t) in terms of v(t), A, K, cos (ωct), a and b.
(b) Determine the choice of the gain K so that the above circuit performs as a DSB-SC
modulator without output filtering.
Problem 5:
An AM wave is represented by the expression:
v = 5 (1 + 0.6 cos 6280 t) sin 211 × 104 t volts
(i) What are the minimum and maximum amplitudes of the AM wave?
(ii) What frequency components are contained in the modulated wave and what is the amplitude
of each component?
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