Institute of Aviation Engineering and Technology (IAET)

Course Name : Electrical Communications (1-A) Sheet No. : 3

Course Code : ECE 303 Dr. Mohamed Sobhy
Level & Semester : 3rd year & 1st Semester Sheet Title : Amplitude Modulation

AM Modulation
Review Questions
1. What are the main reasons of modulation?
2. Define the following :
i. Modulation process.
ii. Amplitude modulation (AM).
iii. AM modulation index.
3. Draw a block diagram (BD) of AM modulator and explain its operation?
4. What is meant by non-coherent demodulation?
5. Draw envelop detector, explain its operation? Illustrate your answer by drawing
the signal waveforms?
6. What are the advantages of non-coherent demodulation of AM?
7. Sketch the spectrum of AM signal?
8. Sketch the AM waveforms?
9. Discuss the power of the AM signal?
10. State the AM signal bandwidth?
11. Draw BD of coherent demodulation of AM and explain its operation?

Problem Set
1. Consider tone AM modulation where the modulating signal is 𝑚(𝑡) =
2 cos(103 𝜋𝑡) and the modulation index 𝜇 = 2⁄3.
i. Sketch the AM waveform.
ii. Find the carrier power, the sidebands power, the total power, and the power
efficiency.
iii. Show how the modulation index can be determined from the AM waveform.
iv. Sketch the spectrum of the tone AM signal and find its bandwidth (BW)
assuming the carrier frequency is 𝑓𝑐 = 500 𝑘𝐻𝑧.

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2. Consider the signal 𝑚(𝑡) which is a square wave of amplitude 𝐴 = 1 𝑣𝑜𝑙𝑡 and
period 𝑇 = 4 𝑚𝑠𝑒𝑐. This signal modulates a carrier using modulation index 𝜇 =
0.5.
i. Sketch the waveform of the AM signal.
ii. Calculate the modulation efficiency.
iii. Calculate the BW, the frequency range of the modulated signal assuming the
BW of 𝑚(𝑡) is five of its fundamental frequency and the carrier frequency
is 𝑓𝑐 = 500 𝑘𝐻𝑧.
3. Sketch the AM modulated signal for 𝑚(𝑡) = cos(2𝜋𝑓𝑐 𝑡) and calculate the power
efficiency for different modulation index.
i. 𝜇 = 0.5.
ii. 𝜇 = 1.
iii. 𝜇 = 2.
iv. 𝜇 = ∞, Comment your answer.
4. Determine the power efficiency 𝜂 and the percentage of the total power carried by
the sidebands of the AM wave for tone modulation for different modulation index.
i. 𝜇 = 1.
ii. 𝜇 = 0.5.
iii. 𝜇 = 0.3.
iv. Comment your answers.
5. The efficiency 𝜂 of AM is defined as the percentages of the total power carried by
the sidebands 𝜂 = 𝑃𝑠 ⁄𝑃𝑇 ∗ 100% where 𝑃𝑠 is the power carried by the sidebands
and 𝑃𝑇 is the total power of AM signal.
i. Find an expression for an AM single-tone 𝑚(𝑡) = cos(2𝜋𝑓𝑐 𝑡).
ii. Calculate 𝜂 for 𝜇 = 0.5 (50 % percent modulation).
iii. Find 𝜂𝑚𝑎𝑥 .
6. Show that a coherent (synchronous) demodulation in Fig. 1 can demodulate the
AM signal 𝑠𝐴𝑚 (𝑡) = [𝐴 + 𝑚(𝑡)] cos(2𝜋𝑓𝑐 𝑡) regardless of the value of A.

xAM t  y t 
LPF DC blocker

cos 2fct 
Fig. 1 : AM coherent detector.

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 DSB Modulation
Review Questions
1. Draw BD of coherent demodulation of DSB and explain its operation?
2. What are the advantages of DSB modulation scheme?
3. Draw BD of DSB modulator and explain its operation?
4. Sketch the DSB waveforms?
5. Sketch the spectrum of DSB signal?
6. State the DSB signal bandwidth?
7. Draw BD of Costas loop for generation of carrier of coherent demodulation?
8. Compare between AM and DSB modulation schemes?

Problem Set
1. For a modulating signal 𝑚(𝑡) is given by:
i. 𝑚(𝑡) = cos(200𝜋𝑡)
ii. 𝑚(𝑡) = cos(200𝜋𝑡) cos(500𝜋𝑡)
In each case
a. Sketch the spectrum of 𝑚(𝑡).
b. Sketch the spectrum of DSB-SC signal 𝑠𝐷𝑆𝐵 (𝑡) = 2𝑚(𝑡) cos(1000𝜋𝑡)
c. Identify the USB and LSB spectra.
d. Write an expression for USB signal 𝑠𝑈𝑆𝐵 (𝑡) and LSB signal 𝑠𝐿𝑆𝐵 (𝑡).

2. Verify that the message signal 𝑚(𝑡) is recovered from a modulated DSB by first
multiplying it by a local sinusoidal carrier and then passing the resultant signal
through a low pass filter (LPF), as shown in Fig. 2,
i. In the time domain
ii. In the frequency domain.
sDSB t  y1 t  y t 
LPF

cos 2fct 
Fig. 2 : Coherent demodulation.

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3. Fig. 3 shows a DSB-SC modulator. Explain whether it would be able to generate
the desired signal.
i. What kind of filter is required?
ii. Determine the spectra at points b and c and identify the frequency bands in
these spectra.
iii. What is the minimum usable value of 𝑓𝑐 .
iv. Would this scheme work if the carrier generator output were cos2 (2𝜋𝑓𝑐 𝑡)?
v. Would this scheme work if the carrier generator output were cos𝑛 (2𝜋𝑓𝑐 𝑡)
for any integer 𝑛 ≥ 2 ?
M f 

mt  kmt  cos2fct 

Filter
(a) (b) (c)

f
B
cos 2fct 
3 B
(a) (b)
Fig. 3: DSB modulator.

Quadrature Amplitude Modulation (QAM)

Review Questions
1. Draw BD of quadrature multiplexing system. Explain its operation.
2. Mention the advantages and disadvantages of quadrature multiplexing.
3. Consider quadrature multiplexing scheme whose the local oscillator generated in
the receiver has a phase error of 𝜃0 radians. Derive the formula of the received
signals and signal to cross-talk (XTK) ratio for both signals.
4. Consider quadrature multiplexing system of two signals show how the two signals
are recovered at the receiver output.

Problem Set
1. Consider a QAM communication system where the two modulating signals are
𝑚1 (𝑡) = 5 cos(𝜋 ∗ 104 𝑡) and 𝑚2 (𝑡) = 10 cos(6𝜋 ∗ 103 𝑡). If the locally
generated carrier has a phase shifted of 5° compared to the transmitter. Find the
received signals and signal to XTK ratio.

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2. Find the maximum phase error of demodulator carrier signal such that the signal
to interfering level for 𝑚1 (𝑡) is 40 𝑑𝐵 and in this case find the signal to interfering
level for 𝑚2 (𝑡) where:
𝑚1 (𝑡) = 3 cos(4𝜋 ∗ 103 𝑡)
𝑚2 (𝑡) = 10 cos(6𝜋 ∗ 103 𝑡)
SSB Modulation
Review Questions
1. State the advantages and disadvantages of SSB modulation?
2. Discuss the methods common used to generate SSB :
i. Selective filtering method.
ii. Phase shift method.
3. Compare between selective filtering method and phase shift method?
4. Compare among the following AM modulation schemes in tabular form
concerning power efficiency, bandwidth efficiency and complexity. justify your
answers
i. AM
ii. DSB
iii. SSB

Problem Set
1. Show that if the output of the phase-shift modulator in Fig. 4 is a SSB signal,
i. The difference of the signal at the summing output produces the upper
sideband (USB) signal.
ii. The sum of the signal at the summing output produces the lower sideband
(LSB) signal.

cos 2fct 
+ sSSB t 
mt 
 2 

sin 2fct 

mh t 
 2

Fig. 4: phase-shift method

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2. Show that an SSB signal can be demodulated by the synchronous detector of Fig.
5 by
i. Sketching the spectrum of the signal at each point.
ii. The time domain expression of the signal at each point.

sSSB t  y1 t  yt 
LPF

cos 2fct 
Fig. 5: Synchronous detector.

Vestigial Sideband (VSB) Modulation

1. For the modulating signal is 𝑚(𝑡) = 2 cos(4𝜋 ∗ 103 𝑡) + 5 cos(8𝜋 ∗ 103 𝑡) +
cos(𝜋 ∗ 104 𝑡). Find the following :
i. Write the waveform equation and sketch the spectrum of DSB signal.
ii. Write the waveform equation and sketch the spectrum of VSB signal.
iii. Find the power and the bandwidth of VSB Modulated.
Assuming the VSB filter characteristics as follows:
𝐻 (𝑓 )
0 for 𝑓 ≤ 9.996 𝑀𝐻𝑧
= {12 ∗ 10−6 (𝑓 − 10−7 ) + 0.5 for 9.996 𝑀𝐻𝑧 ≤ 𝑓 ≤ 10.004 𝑀𝐻𝑧
1 for 𝑓 ≥ 10.004 𝑀𝐻𝑧
And consider the carrier frequency is 𝑓𝑐 = 10 𝑀𝐻𝑧.
2. The carrier frequency of a certain VSB signal is 𝑓𝑐 = 20 𝑘𝐻𝑧 and baseband signal
of 6 𝑘𝐻𝑧. The VSB filter 𝐻v (𝑓 ) is shown in Figure. Find the output transfer
function.

Hv  f 

f  kHz 
18 20 22 26

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