CO3:

10 M

9. In an AM transmission, the carrier signal is modulated with a message signal

.
(i) Derive the mathematical equation for AM.
(ii) Find and sketch the spectrum of AM signal.
(iii) Identify the frequency components available in AM signal?
(iv) Determine the carrier power, sideband power and total power.
(v) Find the efficiency of the AM system?
(vi) Calculate the bandwidth of modulated wave.
10. Explain the coherent detector used in DSB-SC system. Discuss the effect of frequency
error in the demodulation of DSB-SC wave using synchronous detector.
9. A carrier signal with amplitude of 2.4 Volts and frequency of 1o KHz is amplitude modulated

with a modulating signal .

(a) Find and sketch the spectrum of modulated signal.
(b) Find the transmitted power for each of the following cases and comment on the results:
(i) If the modulating signal voltage is doubled.
(ii) If the carrier signal voltage is doubled.
(iii) If the modulating signal frequency is doubled.
(iv) If the carrier signal is removed from the transmitted signal.

10. A DSB-SC signal is demodulated using a locally generated carrier

using a scheme shown below.

Show that the scheme can demodulate the signal as long as is constant (not time varying)

and is not . What is the output if and .

9. Consider a baseband signal , and carrier signal .

Perform the following:
 (i) Sketch the spectrum of. and

(ii) Derive the time expression for DSB-SC signal

(iii) Find and sketch the spectrum of DSB-SC signal.
(iv) Identify the frequencies in the baseband, and corresponding frequencies in the DSB-
SC, USB, and LSB spectra.
(v) Find the bandwidth of the modulated wave.
10. Discuss how an envelope detector is useful in detecting AM wave. Illustrate with block
diagram and corresponding waveforms.

9. It is desired to develop a DSB-SC modulated signal with the following specifications:

A baseband signal , and carrier signal .

Compute the following:
(i) Derive the time expression for modulated signal

(ii) Find and sketch the spectrum of , and modulated signal.

(iii) Identify the frequencies in the baseband, and corresponding frequencies in the DSB-
SC, USB, and LSB spectra.
(iv) Find the bandwidth of the modulated wave.
10. Design a simple envelope detector in detecting AM wave. Illustrate with block diagram
and corresponding waveforms.

FM 15 M
11(a) Discuss the phase and frequency deviations in PM and FM. Find the frequency deviation

for an angle modulated wave .

(b) An frequency modulated voltage wave is given by the equation:
.
Find
(i) the modulating signal and carrier frequencies
(ii) modulation index
(iii) maximum frequency deviation
(iv) power dissipated by the FM wave in 10-ohm resistor.

12(a) Consider an angle modulated signal . Assume PM and

.
(i) Calculate the modulation index.
 Find the bandwidth when

(ii) is doubled

(iii) is decreased by one half

(iv) is doubled

(v) is decreased by one half

(b) Explain the basic principle of FM demodulation. With this principle how an FM wave is
demodulated using a single slope detector. Illustrate its limitations.

11(a) (i) Derive equation for single tone FM wave.

(ii) A 25 MHz carrier is modulated by a 400 Hz audio sine wave. If the carrier voltage is 4V
and the maximum frequency deviation is 10 KHz, write down the voltage equation of
the
FM wave.
(b) A frequency modulated signal which is modulated by a 3-KHz sine wave reaches a
maximum frequency of 100.02 MHz and minimum frequency of 99.98 MHz.
(i) Determine the carrier swing.
(ii) Find the carrier frequency.
(iii) Calculate the frequency deviation of the signal
(iv) Find the modulation index

12(a) Consider an angle modulated signal . Assume FM and

.
(i) Calculate the modulation index.
Find the bandwidth when

(ii) is doubled

(iii) is decreased by one half

(iv) is doubled

(v) is decreased by one half.

(b) Explain the frequency stabilized FM modulator.

11(a) (i) Justify that FM can be derived using PM and Vice-Versa with the help of differentiator
or integrator networks.
 (ii) Find the modulating signal if and .
(b) A 107.6 MHz carrier frequency modulated by 7 KHz sinewave. The resultant FM signal
has a frequency deviation of 50 KHz.
(i) Find the carrier swing.
(ii) Determine the highest and lowest frequencies attained by the modulated signal.
(iii) Find the modulation index of FM wave.

12(a) Consider an FM modulator with f  10 kHz, a modulating signal frequency 10 kHz,

Vc  10 V and a 500 kHz carrier frequency.
Determine
(i) Actual minimum bandwidth if the number of significant sidebands is 3
(ii) Minimum bandwidth using Carson’s rule.
(iii) Comment the results
(iv) The unmodulated carrier power in the FM modulator (Assume load resistance 50 Ω).
(b) Explain the dual slope detector method for FM demodulation.

11(a) Summary of Phase Modulation and Frequency Modulation.

(b) Consider an angle modulated signal . Find the

(i) maximum phase deviation, and (ii) maximum frequency deviation.

12(a) A frequency modulated signal is given by . Estimate

the bandwidth as per (i) Frequency deviation, (ii) Bessel approximation with 3 number of
significant side bands, and (iii) The Carson’s rule. (iv) Find the transmitted power

dissipated in resistor.
(b) Discuss direct method of FM demodulator that achieves frequency stability.