Institute of Aviation Engineering and Technology (IAET)

Course Name : Electrical Communications (1-A) Sheet No. : 4

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

Review Questions
FM and PM
1. Define the following :
i. Angle modulation.
ii. Frequency modulation.
iii. Phase modulation.
iv. Frequency modulation index.
v. Frequency deviation.
2. State the relation between PM and FM.
3. What is the equivalence between PM and FM?
4. Discuss the average power of PM and FM.
5. Draw waveform of modulating signal, carrier signal, the instantaneous frequency,
FM and PM modulated signal.
Spectrum and Bandwidth of FM modulated signal
1. Sketch block diagram of NBFM modulator and explain its operation.
2. Derive an expression for tone NBFM signal. Sketch its spectrum and find its BW.
3. Derive an expression for tone WBFM signal. Derive and sketch its spectrum.
4. Compare between NBFM and WBFM.
5. State Carson’s rule.
FM generation and detection
1. Draw block diagram of Armstrong indirect FM transmitter. Discuss the function
of each block.
2. Draw block diagram of direct FM generation method. Explain its operation.
3. State the advantages and disadvantages of Armstrong method for FM generation.
4. Draw block diagram of a differentiator FM detector. Find the signal at the output
of each block until the modulating signal is recovered and find the condition for
no envelope distortion.
5. What are the advantages and disadvantages of FM compared to AM?

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 Problem Set
1. Suppose 𝑚1 (𝑡) and 𝑚2 (𝑡) be two message signals and let 𝑥𝑐1 (𝑡) and 𝑥𝑐2 (𝑡) be
the modulated signals corresponding to 𝑚1 (𝑡) and 𝑚2 (𝑡) respectively. Show
that the superposition property for :
i. DSB modulation
ii. PM
iii. FM
iv. Comment your results.
2. Consider the signal 𝑠(𝑡) = 10 cos(2𝜋103 𝑡 + sin 10𝜋𝑡)
i. Find and sketch the instantaneous frequency of signal 𝑠(𝑡).
ii. Assuming 𝑠(𝑡) is an FM signal, find 𝑘𝑓 and 𝑚(𝑡).
iii. Assuming 𝑠(𝑡) is a PM signal, find 𝑘𝑝 and 𝑚(𝑡).
iv. Find the power of the angle modulated signal 𝑠(𝑡).
3. Consider the signal 𝑚(𝑡) = 5 cos(8𝜋104 𝑡) angle modulates a carrier
signal 𝑐(𝑡) = 5 cos(106 𝜋𝑡). Find and sketch the modulated signal and calculate
the total frequency deviation in the following cases.
i. FM with 𝑘𝑓 = 25 kHz/V.
ii. PM with 𝑘𝑝 = 0.25𝜋 rad/V.
4. Consider the shown below triangular half wave symmetric signal angle modulates
a sinusoidal carrier of 5 volts peak amplitude and 1 MHz frequency.
i. Find and sketch the instantaneous frequency in both cases of FM with 𝑘𝑓 =
10 kHz/V and PM with 𝑘𝑝 = 0.8𝜋 rad/V.
ii. Sketch the PM waveform.
m t 
0.2 msec
5

t
5

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5. Sketch FM and PM waves for the digital modulating signal 𝑚(𝑡) shown below.
The constants 𝑘𝑓 = 100 kHz/V and 𝑘𝑝 = 0.5𝜋 rad/V and 𝑓𝑐 = 100 MHz.

m t 
1

1

6. For 𝑚(𝑡) shown below compute

i. BW of FM signal.
ii. BW of FM signal if 𝑚(𝑡) is multiplied by 2, i.e. its peak amplitude is
doubled. Comment your results.
iii. BW of FM signal if 𝑚(𝑡) is time-expanded by a factor of 2, i.e. new
period of 𝑚(𝑡) is 4*10-4 seconds.
m t 

0.2 msec
1

t
1

[Hint: BW of 𝒎(𝒕) is 𝑩 = 𝟏𝟓 kHz and 𝒌𝒇 = 𝟏𝟎𝟎 kHz/V].

7. A carrier signal of frequency 20 MHz is frequency modulated by a sinusoidal
signal of amplitude 5 volts and frequency 20 kHz. The frequency sensitivity of
the modulator is 10 kHz/V.
i. Write FM equation.
ii. Determine the approximate bandwidth of the FM signal using Carson’s
rule.

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 iii. Determine the bandwidth by transmitting only those side frequencies
whose amplitudes exceed 1 percent of unmodulated carrier amplitude
using the Bessel function table.
iv. Repeat your calculations assuming that the amplitude of the modulating
signal is doubled.
v. Repeat your calculations assuming that the modulation frequency is
doubled.
8. Calculate the carrier frequency 𝑓𝑐 and the peak frequency deviation ∆𝑓4 of the
output of Armstrong FM transmitter if 𝑓𝑐1 = 200 kHz, 𝑓𝑜𝑠𝑐 = 10.6 MHz, ∆𝑓1 =
30 Hz, 𝑛1 = 64 and 𝑛2 = 48.
9. Design (only the block diagram) an Armstrong indirect FM modulation to
generate an FM signal with carrier frequency 98.1 MHz and peak deviation ∆𝑓 =
75 kHz. A narrow band FM generator is available at carrier frequency 100 kHz
and frequency deviation ∆𝑓 = 10 Hz. The stock room has also an oscillator with
an adjustable frequency in the range of 10 to 11 MHz. There are also plenty of
frequency doublers, triplers, and quintuplers.

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