ES 442
HW # 5 - Chapter 5 - Angle Modulation
1- Given FM or PM modulators with the following parameters (assume the carrier signal Vc (Vpeak is one
volt):
Parameter
FM
PM
sensitivity constant
1.5 Khz/V
0.75 rad/V
carrier frequecy
500 Khz
500 Khz
modulating signal
2sin(2π⋅2000t)
2sin(2π⋅2000t)
maximum modulating signal
amplitude (Vm)
2 volt-peak
2 volt-peak
a) Determine the modulation index for FM and PM.
b) Sketch the output spectrum [S(f)] for FM and PM. For each case calculate the bandwidth using Carson’s
rule.
c) Explain how the FM and PM spectrums are different.
d) Find the total bandwidth for FM and PM.
e) Change the modulating signal amplitude for both modulations to 4Vp (instead of 2Vp). Repeat steps a-d.
f) Change the modulating signal frequency for both modulation to 1KHz (instead of 2KHz). Repeat steps a-d.
g) Summarize your answers in the table below (complete the table for calculated values of fm, and Vm):
Given
Vm=
fm=
Find
FM
PM
Modulation Index
Bandwidth
Vm=
fm=
Modulation Index
Bandwidth
Vm=
fm=
Modulation Index
Bandwidth
h) Based on the obtained frequency spectrums, clearly explain how it is possible to distinguish FM from PM
in frequency domain?
i) Using MATLAB plot the frequency spectrum of the output FM signal as you obtained in part (b). You can
use the Bessel function table here: http://www.electronics.dit.ie/staff/akelly/bessel-tables.pdf. HINT: your
plot should look similar to appendix A. Use the sample MATLAB code provided. Check the peak values
and make sure they are consistent with what you obtained for part (a)
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ES 442
HW # 5 - Chapter 5 - Angle Modulation
2-
NOTE: You must use MATLAB for this problem. Show your code and two plots for part (a) and (b).
On each plot show m(t) and s(t). In each case identify where maximum deviations in s(t) occur.
3-
4a) Find the transmission bandwidth by using Carson’s rule.
b) Find the expression for normalized average power: 〈s2(t)〉 = ½ 〈 | g(t)2 | 〉 in terms of modulation
index.
c) Assuming we use Carson’s rule, calculate the normalized average power using part (b) - HINT:
Assume n=3.
d) If the bandwidth is infinite (n approaching infinity) what will be the normalized average power?
e) comparing parts (c) and (d). Exactly what percentage of power can be captured by Carson’t rule?
5- An FM transmitter has the block diagram shown in figure below. The audio frequency
response is flat over the 20-Hz-to-15-kHz audio band. The FM output signal is to have a carrier
frequency of 103.7 MHz and a peak deviation of 75 kHz.
(a) Find the bandwidth and center frequency required for the bandpass filter.
(b) Calculate the frequency fo of the oscillator.
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ES 442
APPENDIX:
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HW # 5 - Chapter 5 - Angle Modulation