The Hong Kong Polytechnic University
CM071A, 071B, 071C
Department of Electronic and Information Engineering
Communication Laboratory
Frequency Modulation
Objective
To study the operation of an FM Modulator.
Background Knowledge
(1) Concepts of Frequency Modulation
As in amplitude modulation, a carrier signal is modulated by the information that is being
sent. The amplitude of the carrier is varied in time with the modulation source.
Alternatively, an FM wave is a sine wave with a periodically varying instantaneous
frequency and a constant amplitude.
+
Modulating signal
=
Carrier signal
Modulated signal
Figure 1: Illustration the formation of Frequency Modulation.
When no modulating signal is being applied, the carrier is at its nominal frequency (the
carrier frequency). The modulating signal causes the frequency to deviate (to move above
and below its nominal value). With the greatest possible deviation, the minimum
frequency could be near zero and, the maximum frequency would then be about twice the
carrier frequency. However, this would take a very large amount of frequency spectrum
and the bandwidth would have no relationship to the modulating signal bandwidth. A set
of limits is normally made on the amount that the carrier can deviate from its nominal
frequency and this is called the maximum deviation.
Bandwidth of an FM Signal
It is important that we can understand and estimate the bandwidth of the transmitted
signal so that the transmission parameters can be chosen to fit into the available
spectrum. Clearly the bandwidth must be at least equal to twice the deviation, as the
carrier actually moves above and below its nominal frequency by that amount. But it also
depends on how fast the frequency is being changed, i.e. on the bandwidth of the
modulating signal. An FM signal has sidebands far above and below the maximum
deviation. The sidebands appear in pair. However the power in these sidebands decreases
quickly as they become further away from the carrier and it can be shown that, for
practical purposes, a good approximation to the bandwidth is given by:
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The Hong Kong Polytechnic University
B=2 ( Fd + Fm )
CM071A, 071B, 071C
where B is the bandwidth,
Fd is maximum carrier frequency deviation,
Fm is the modulation frequency.
This is sometimes called Carson’s Rule, and the bandwidth B can be viewed as
containing the majority of the transmitted power, certainly sufficient for successful
demodulation.
As we have seen, the bandwidth of an FM signal depends on both the deviation and the
modulation bandwidth. It might be though that, in order to keep the bandwidth as narrow
as possible, all FM systems should be operated with a very small deviation. However,
there are significant advantages to operating with a wide deviation. The main one is an
apparent improvement in noise performance.
Actually, a specific bandwidth can be the result of wide deviation with a low modulation
bandwidth or a narrow deviation with a large modulation bandwidth. The ratio of
deviation to modulation bandwidth is called the modulation index and is an important
parameter in describing an FM system.
Modulation index is given by:
β = Fd / Fm
where β is the modulation index.
In the practical, a frequency modulator is formed from a Voltage-Controlled Oscillator
(VCO). A voltage is applied to it from a control on the hardware board and the oscillator
output can be examined on the oscilloscope and spectrum analyser. Using this
configuration, the fundamental concept of an oscillator frequency being changed by an
external signal can be understood.
(2) A Frequency Modulator
In this practical, a sine wave signal is used to frequency-modulate a carrier so that you
can investigate the appearance of such signals in both the time and frequency domains.
You can adjust the amount of deviation and hence change the modulation index. Notice
that the appearance of an FM signal on the spectrum analyser is similar to that of an AM
signal when the modulation index is small.
(3) FM Spectrum with a Large Modulation Index
In this practical, the modulation frequency has been reduced to about 5kHz. Since the
maximum deviation is the same as the previous practicals, the modulation index is much
greater. From the equation B=2 ( Fd + Fm ), if Fm is small compared with Fd, then the
modulation index is high and resulting in B=2Fd.
On the analyser, the spectrum appears to be continuous but in reality it is made up of a
large number of sidebands spaced at 5 kHz intervals from the carrier up to Fd. This
practical simply shows how when the modulation index is large, the bandwidth is
determined almost exclusively by the deviation.
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The Hong Kong Polytechnic University
CM071A, 071B, 071C
Reference
1. Ferrel G. Stremler, Introduction to Communication Systems 3rd, Addison Wesley
2. Noise Reduction in Frequency Modulation
http://www.arrakis.com.au/ais_users/tudor/signal/theory.html
3. Frequency Modulation
http://www.rfcafe.com/references/electrical /frequency_modulation.htm
4. Angle Modulation
http://www.williamson-labs.com/home.htm (select RF sub-topic)
Equipment
1. PC Interface Box (RAT 53-100)
2. FM Board 53-140
3. Oscilloscope
4. Feedback Power Supply 01-100
5. PC with Discovery Software
Preliminary Preparation
1. Connect the equipment as the following Figure 2 and DO NOT turn on any power at
this moment.
Oscilloscope
Monitor
Computer
Keyboard
Interface
RAT 53-100
FM Board 53-140
Power
Supply
Figure 2: Setting.
2. Switch on the Oscilloscope and set it as follows:
Vert. Amp
0.5V/Div
Hori. Amp
5µs/Div
3. Turn on the Computer first and connect FM Board to the Interface before switching
on the FEEDBACK Power Supply 01-100.
Note: Connect the voltages of the FM Board to that of the Interface carefully,
otherwise, the Board will be burnt!
4. In DOS Prompt mode, type <CD\FBTP> and then <START>.
5. Turn on the power.
6. Use the Mouse to click at the <System> in the Menu Bar and then select <Index>.
7. Click <3> in the list for Assignment 3 and then select <Yes> for this experiment.
8. Click at the <Practicals> in the Menu Bar, and select <Practical 1> for Practical 1
experiment and so on.
9. Click at <Conditions> in the Menu Bar and select <Spectrum Analyser>.
10. Click at <Conditions> in the Menu Bar and select <Change size>. Then the spectrum
analyser will be in large size.
11. Use Channel 1 of the Oscilloscope to monitor any point on the FM Board.
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The Hong Kong Polytechnic University
CM071A, 071B, 071C
Experimental Procedures & Questions
(1) Practical 1 (Concepts of Frequency Modulation)
In this part, you can see how the oscillator frequency can be controlled by an external
signal. The hardware is configured as shown below:
Oscilloscope
0.08
Volts dc
Variable
Voltage
16
Frequency
Modulator
4
Figure 3: Practical 1 configuration.
1.
2.
3.
4.
5.
6.
7.
8.
Select <Practical 1> from the <Practicals> menu in Assignment 3.
Connect point <4> on the FM Board to the oscilloscope.
Connect point <4> to the <spectrum analyser> on the monitor at the same time.
Set the <carrier level> (or the <modulator output level>) to about half scale.
Set the <manual frequency> to the minimum.
Record the d.c. voltages at <16> displayed on the monitor.
Record the time period at <4> from the oscilloscope.
Record the frequency and the amplitude at <4> from the <spectrum analyser> with a
large size on the monitor.
9. Increase the <manual frequency> and monitor at <16>. You can observe that the d.c.
voltage applied is increasing.
10. Repeat step 5 to 8 for the different d.c. voltages and also complete the table below.
d.c. voltage at <16>
(in Volts)
(min)
Time Period at <4>
(in µs)
Frequency at <4>
(in kHz)
Amplitude at <4>
(in dB)
(half scale)
0.00
(max)
Question 1: Use the column 2 of the above table to calculate the total frequency range of
the oscillator.
Question 2: What is the total frequency range of the oscillator obtained in the column 3
of the above table?
Question 3: Is it easier to measure the frequency range on the oscillator or on the
spectrum analyser?
Question 4: Use the data obtained in the column 1 and the column 3 of the above table to
calculate the “frequency slope” of the oscillator in kilohertz per volt.
Question 5: Can you see any amplitude variation over the frequency range from the
column 4 of the above table? Should there be any?
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The Hong Kong Polytechnic University
CM071A, 071B, 071C
(2) Practical 2 (A Frequency Modulator)
In this practical, the variable voltage used to control the VCO frequency has been
replaced by a sine wave oscillator. This sine wave now frequency-modulates the carrier.
Oscilloscope
Modulation
Source
3
Frequency
Modulator
4
Figure 4: Practical 2 configuration.
1.
2.
3.
4.
5.
Select <Practical 2> from the <Practicals> menu in Assignment 3.
Set the <carrier level> on the FM Board to about half scale.
Set the <modulation level> to the minimum.
Look at the signal at <4> with the <oscilloscope> at large size.
Increase the <modulation level> and observe that the frequency is changing. Note
where the output at <4> has a higher frequency.
Question 6: Draw the waveforms observed and decide where has a higher frequency.
Question 7: As the modulation level varies, how constant are:
a) the carrier-frequency component of the modulated signal?
b) the amplitude of the modulated signal?
6. Monitor point <3> with the oscilloscope.
7. Adjust the <modulation level> and observe how the instantaneous frequency depends
on the instantaneous value of the modulating signal.
Question 8: Conclude the observation from point <3> and point <4>.
8. Connect point <4> to the <spectrum analyser> at large size in order to examine the
sidebands of the signal.
9. Adjust the <modulation level> until only the sidebands at Fc – Fm and Fc+ Fm are
present. It is a FM signal that has sidebands with low deviation.
Question 9: Draw the spectrum with low frequency deviation and label Fc, Fc – Fm and
Fc+ Fm.
10. Try to adjust the <modulation level> again until the higher-order sidebands appear at
higher deviation, i.e. a larger modulation index.
Question 10: Draw the spectrum with high frequency deviation and label Fc, Fc – Fm and
Fc+ Fm.
Question 11: Can you estimate the frequency of the modulating signal from the
waveforms obtained? Explain briefly.
Question 12: Would it be equally easy to estimate the bandwidth of the modulating signal
from the spectrum if the modulating signal were complex, having many frequencies?
5
The Hong Kong Polytechnic University
CM071A, 071B, 071C
(3) Practical 3 (FM Spectrum with a Large Modulation Index)
In this practical, the modulation index has been set to 5kHz. This means that the
modulation index can be very high. This enables you to see that under these conditions
the bandwidth of a FM signal is almost equal to twice the deviation. The hardware is
configured as shown below:
Figure 5: Practical 3 configuration.
1. Select <Practical 3> from the <Practicals> menu in Assignment 3.
2. Set the <Carrier level>to about half scale.
3. Turn the <5kHz level> up and down and observe the bandwidth changing. Note that
the bandwidth is almost proportional to the frequency deviation.
Question 13: Draw the spectrum observed.
Question 14: If the modulating frequency is 5kHz and the frequency deviation is 50kHz,
calculate the modulation index.
Question 15: Calculate the signal bandwidth using Carson’s rule. Comment on the
answer.
Question 16: If a bandpass filter were to be added at the input of a FM detector, what is
the bandwidth required?
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