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Sheet 2-1

The document outlines various tasks related to amplitude modulation, including sketching spectra for baseband message signals, designing a DSB-SC modulator, and analyzing the power efficiency of AM signals. It also covers the multiplexing of signals, modulation indices, and the effects of different modulation parameters on the output. Additionally, it addresses the requirements for demodulation and the characteristics of the modulated signals in different scenarios.

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زياد عبدالله عبدالحميد
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60 views3 pages

Sheet 2-1

The document outlines various tasks related to amplitude modulation, including sketching spectra for baseband message signals, designing a DSB-SC modulator, and analyzing the power efficiency of AM signals. It also covers the multiplexing of signals, modulation indices, and the effects of different modulation parameters on the output. Additionally, it addresses the requirements for demodulation and the characteristics of the modulated signals in different scenarios.

Uploaded by

زياد عبدالله عبدالحميد
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Sheet 2

Amplitude modulation
1. Consider the following baseband message signals
(i) m1(t) = sin 150πt; (ii) cos 200πt + rect(100t);
For each of the two message signals,
(a) Sketch the spectrum of m(t);
(b) Sketch the spectrum of the DSB-SC signal 2m(t) cos 2000πt;
(c) Identify the USB and the LSB spectra.

2. You are asked to design a DSB-SC modulator to generate a modulated signal


Acm(t) cos ω ct with the carrier frequency fc = 300 kHz (ωc = 2π ×
300,000). The following equipment is available in the stockroom: (i) a
sinewave generator of frequency 100 kHz; (ii) a ring modulator; (iii) a
bandpass filter with adjustable center frequency with the tuning range of 100
kHz to 500 kHz.
(a) Show how you can generate the desired signal.
(b) Explain how to tune the bandpass filter.

(c) If the output of the modulator must be 400 ·m(t) cos ωct, what should be
the amplifier gain to be used on the input m(t) to obtain the desired modulator
output signal amplitude?

3. Two signals m1(t) and m2(t), both band-limited to 5000 Hz, are to be
transmitted simultaneously over a channel by the multiplexing scheme shown
in the following figure. The signal at point b is the multiplexed signal, which
now modulates a carrier of frequency 20,000 Hz. The modulated signal at
point c is transmitted over a channel.
(a) Sketch signal spectra at points a, b, and c.
(b) What must be the bandwidth of the distortionless channel?
(c) Design a receiver to recover signals m1(t) and m2(t) from the modulated
signal at point c.

4. Sketch ϕAM(t) for modulation indices of μ =0.5 and μ =1, when 𝑚(𝑡) =
𝑏𝑐𝑜𝑠 𝜔𝑚𝑡. This case is referred to as tone modulation because the modulating
signal is a pure sinusoid (or tone).
5. Determineηand the percentage of the total power carried by the sidebands of
the AM wave for tone modulation when (a) μ = 0.5 and (b) μ = 0.3.

6. Sketch the AM signal [B+m(t)] cos ωct for the random binary signal m(t)
shown in the following figure, corresponding to the modulation index by
selecting a corresponding B: (a) μ = 0.5; (b) μ = 1; (c) μ = 2; (d) μ=∞.
Is there any pure carrier component for the case μ=∞?

7. In an amplitude modulation system, the message signal is given by the above


figure, and the carrier frequency is 1 kHz. The modulator output is
𝑠𝐴𝑀(𝑡) = 2[𝑏 + 0.5𝑚(𝑡)] 𝑐𝑜𝑠 𝜔𝑐𝑡
(a) Determine the average power in sAM(t) as a function of b and A.

(b) If b = A, determine the modulation index and the modulation power


efficiency.
(c) Find the minimum value of b such that the AM signal can still be
demodulated via envelope detection. Determine maximum modulation index
and maximum modulation power efficiency based on the resulting b.

8. For the AM signal with m(t) shown in the following figure and μ = 2:

(a) Find the amplitude and power of the carrier.


(b) Find the sideband power and the power efficiency η.
(c) Sketch the time domain AM signal corresponding to the AM modulation .
(d) If this modulated signal is applied at the input of an envelope detector,
show the output of the envelope detector is not m(t).

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