S. L. Arora Solutions for Chapter: Communication Systems, Exercise 1: Problems For Practice

A message signal of $12 \mathrm{kHz}$ and peak voltage $20 \mathrm{V}$ is used to modulate a carrier wave of frequency $12 \mathrm{MHz}$ and peak voltage $30 \mathrm{V}.$ Calculate the
(i) modulation index
(ii) side-band frequencies.

A sinusoidal carrier voltage of frequency $1 \mathrm{M}\mathrm{H}\mathrm{z}$ and amplitude $100 \mathrm{V}$ is modulated by a sinusoidal voltage of frequency $5 \mathrm{k}\mathrm{H}\mathrm{z}$ producing $50 \mathrm{\%}$ modulation. Calculate the frequency and amplitude of upper and lower sidebands.

A sinusoidal carrier voltage of amplitude $80 \mathrm{V}$ and frequency $800 \mathrm{k}\mathrm{H}\mathrm{z}$ is amplitude modulated by a sinusoidal voltage of frequency $15 \mathrm{k}\mathrm{H}\mathrm{z}$ resulting in minimum carrier amplitude of $72 \mathrm{V}.$ Find
(i) the sideband frequencies and
(ii) modulation index.

An audio signal given by $15\mathrm{}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{}2\mathrm{\pi }\mathrm{}\left(2000\mathrm{}\mathrm{t}\right)$ amplitude modulates a sinusoidal carrier wave $60\mathrm{}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{}2\mathrm{\pi }\mathrm{}\left(100000\mathrm{}\mathrm{t}\right).$ Determine
(i) percent modulation
(ii) frequencies of modulating signal and carrier and
(iii) frequency spectrum of the modulated wave.

A $100 \mathrm{k}\mathrm{H}\mathrm{z}$ bandwidth is to accommodate $10 \mathrm{A}.\mathrm{M}.$ broadcasts simultaneously. What is the maximum modulating frequency permissible for each station?

A carrier wave of frequency $10 \mathrm{M}\mathrm{H}\mathrm{z}$ and peak value $10 \mathrm{V}$ is amplitude modulated by a $5 \mathrm{k}\mathrm{H}\mathrm{z}$ sine wave of amplitude $6 \mathrm{V}.$ Calculate the frequency and amplitude of the two side-bands.