Communications I
Laboratory #4
1
Generation of Frequency Modulated Signals
FM Modulation
OBJECTIVES
The purpose of this experiment is to show how the frequency-modulated signals
are generated and the importance of it. Also, in this experiment you will be able to see
the modulated signal in the oscilloscope and its power spectrum.
EQUIPMENT LIST
1. Spectrum Analyzer
2. Arbitrary waveform generator
3. Oscilloscope
4. Audio Input Module and Microphone
5. 47  resistor
6. ANACOM 2 Trainer
7. Power supply
8. N to BNC connector adapter
9. Cables
10. Two oscilloscope probes
11. HP-VEE
DISCUSSION
Modulation is a process that causes a shift of the range of frequencies in a signal.
It is used to facilitate transmission over a given channel. Baseband signals produced by
various information sources are not always suitable for direct transmission over a given
channel. These signals are usually further modified to facilitate transmission. This
conversion process is known as modulation. In this process the baseband signal is used
to modify some parameter of a high frequency carrier signal.
A carrier is a sinusoid of high frequency, and one of the parameters such as
amplitude, frequency or phase is varied in proportion to the baseband signal m(t). In FM
modulation the frequency of the carrier is modify in proportion to the baseband signal. A
baseband signal is used to designate the band of frequencies of the signal delivered by
the source.
Another advantages of modulation are the ease of radiation of electromagnetic
energy allowing antenna sizes to be reasonable and simultaneous transmission of several
signals over the same channel.
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Rev. 10/22/01
Communications I
Laboratory #4
2
Frequency Modulation
Another means of encoding a wave of information is by producing a complex
wave whose frequency is varied in proportion to the instantaneous amplitude of the
information wave. Such an encoding is frequency modulation. The result of this
encoding or modulation process is a complex modulated wave whose instantaneous
frequency is a function of the amplitude of the modulating wave and differs from the
frequency of the carrier from instant to instant as the amplitude of the modulating wave
varies.
The following equation provides the equivalent formula for FM:
v(t )  A sin(  c t  M f sin(  i t ))
where
v(t) is the instantaneous voltage
A is the peak value of the carrier
c is the carrier angular velocity
Mf is the modulation index
i is the modulating signal angular velocity
The FM formula is really complex. In figure 1 is the waveform of a FM signal. To solve
for the frequency components of an FM wave requires the use of the Bessel functions.
They show that frequency-modulating carrier with a pure sine actually generates an
infinite number of sidebands spaced at multiples of the intelligence frequency, fm, above
and below the carrier. Fortunately, the amplitude of these sidebands approaches a
negligible level the farther away they are from the carrier, which allow FM transmission
within finite bandwidths.
Figure 1: FM Signal Representation
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Rev. 10/22/01
Communications I
Laboratory #4
3
The Bessel functions solution to the FM equation is
1
2

 



f c (t )  J 0 ( M f ) cos( c t )  J 1 ( M f )cos(( c   i )t )  cos(( c   i )t )
3


 J 2 ( M f )cos(( c  2 i )t )  cos(( c  2 i )t )
4


 J 3 ( M f )cos(( c  3 i )t )  cos(( c  3 i )t )  ....
where
1 = carrier component
2 = component at ± fi around the carrier
3 = component at ± 2fi around the carrier
4 = component at ± 3fi around the carrier
To solve for the amplitude of any side-frequency component, Jn is equal to
2

( M f 2) 4 ( M f 2) 6
 M f   1 ( M f 2)
   
J N ( M f )  n  


 ...
 2   n! 1!(n  1)! 2!(n  2)! 3!(n  3)!

In figure 2 is an example of a FM spectrum
Figure 2: FM Spectrum
Center Frequency
The center frequency is that frequency assigned to the carrier, but during
modulation the carrier is not always present in the complex modulated wave and the
instantaneous frequency of the complex modulated wave varies above and below the
frequency assigned to the carrier. This assigned frequency, then, is the “center” about
which the instantaneous frequencies of the modulated wave vary.
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Rev. 10/22/01
Communications I
Laboratory #4
4
Frequency Deviation
In FM the shift in frequency is proportional to the amplitude of the modulating
wave. A weak modulating wave will have a small peak amplitude, which will produce a
small peak frequency variation. A strong modulating wave whose peak amplitude is the
maximum that the modulating system is designed to handle will produce the maximum
peak frequency variation. Any of these peak variations from the center frequency is
called the frequency deviation (fd).
 f  fc 
f d  max  max

 f c  f min 
The maximum value of the frequency deviation (fD) is a system constant, and
when it is intended that the modulated wave be radiated, its magnitude is established by
law.
Frequency Swing
The overall extreme of the excursion of instantaneous frequencies from maximum
negative to maximum positive is called the frequency swing. Frequency swing,
therefore, is equal to twice the maximum design frequency deviation. In FM the
frequency swing is a system constant and is usually expressed in terms of the maximum
frequency deviation as ±fD.
Deviation Ratio
Any modulating system is intended to accommodate some specific band of
modulating frequencies. Therefore the lower limit and especially the upper limit of this
band are of importance in the design of the equipment. The upper frequency is the most
important because it determines the maximum bandwidth requirements. In FM, the
highest modulating frequency (fM) is a system constant. The ratio of the maximum
frequency deviation (fD) to the highest modulating frequency (fM) is called the deviation
ratio (D).
f
D D
fM
The deviation ratio is strictly an equipment characteristic and is a quantity used to set the
circuit bandwidth of a modulating system.
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Rev. 10/22/01
Communications I
Laboratory #4
5
Modulation Index
There is a very important signal characteristic that resembles the deviation ratio
and under certain circumstances is equal to it. It is the ratio,
f
Mf  d
fm
Notice, however, that fd is any frequency deviation, not necessarily maximum and fm is
any modulating frequency, not necessarily the highest. There are system restrictions that
apply; for example fd cannot exceed fD and fm cannot be greater than fM.
Bandwidth Calculations
Since the sidebands are separated by multiples of the modulating frequency, the
frequency of the highest important sidebands is given by
f m ( M f  1)
The overall bandwidth from the highest to the lowest side frequency whose amplitude is
15 % (or greater) of the unmodulated carrier is twice this value. In figure 3 is the
commercial FM bandwidth allocation for two adjacent stations
BW  2 f m ( M f  1)
Mf 
fd
fm
 f

BW  2 f m  d  1
 fm

BW  2( f d  f m )
Figure 3: Commercial FM bandwidth allocation for two adjacent stations
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Rev. 10/22/01
Communications I
Laboratory #4
6
FM Generation Circuit (Reactance Modulator)
The reactance modulator is a very popular means of FM generation and is shown
in figure 4. The reactance modulator is an amplifier designed so that its input impedance
has a reactance that varies as a function of the amplitude of the applied input voltagemodulating signal).
Figure 4: FM Reactance Modulator
PROCEDURE
1.
Connect the power supply to the trainer with all equipment turned off. Follow the
following diagram.
+12 V
Power Supply
+12 V
0V
0V
-12 V
-12 V
ANACOM 2
2.
Select the following conditions in the trainer
a. Mixer/Amplifier Amplitude dial :
Maximum clockwise direction
b. VCO switch (PLL detector block):
OFF position
c. Modulation switch
:
Reactance
3.
Turn on the power supply. Connect the oscilloscope to test point 1. Turn Audio
Oscillator amplitude dial to the maximum position. Using the oscilloscope adjust
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Rev. 10/22/01
Communications I
Laboratory #4
7
the Audio Oscillator frequency to 2 kHz
modulating signal.
(fm = 2 kHz). This signal is the
4.
Using a cable jumper, connect the Audio Oscillator output to the Modulator
Circuits audio input.
5.
The output of the Reactance modulator can be measured in test point 13, but to
avoid the capacitive effect of the probe, connect the oscilloscope’s probe to test
point 34. The input impedance of the mixer/amplifier block is high enough to get
a good measurement.
6.
Turn the REACTANCE MODULATOR CARRIER FREQUENCY dial to the
middle position.
7.
Turn the Audio Oscillator amplitude dial to the minimum position.
8.
Connect the oscilloscope to test point 34 and measure the frequency, peak to peak
voltage and average voltage of the carrier. Record in table 1.
9.
Disconnect the oscilloscope and connect the universal (frequency) counter to test
point 34 to measure the carrier frequency. Start changing the modulating signal
amplitude and determine the maximum and minimum frequency measured in the
frequency counter. What’s the frequency deviation (fd)? Did you see a significant
change in the carrier frequency? What’s the signal bandwidth? Record in table 2.
10.
Disconnect the frequency counter and connect the spectrum analyzer to test point
34. Set the spectrum analyzer center frequency with the frequency determined in
step 8 and span of 20 kHz. Start changing the modulating signal amplitude and
see what happen with the FM spectrum. Print out the frequency spectrum with a)
Audio Oscillator amplitude dial in the minimum position, b) middle position and
c) maximum position. What happen with the frequency spectrum?
11.
Turn the power off and disconnect the Audio Oscillator from the modulator, then
connect the microphone Audio Input Module’s output to the Audio Input socket in
the Modulator Circuits block. Turn the power on and connect the oscilloscope to
test point 34 and start talking into the microphone. See how your frequency
modulated voice looks like, then connect the spectrum analyzer at the same point.
Examine the signal spectrum.
12.
Connect the waveform generator to the 50  as illustrated in the diagram.
Waveform
Generator
Output
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Circuit
Board
Rev. 10/22/01
Communications I
Laboratory #4
8
13.
Run HP-VEE program in the computer and call up the function generator control
panel from the I/O instruments menu. Set the following parameters in the
instrument using HP-VEE.
Main Panel:
Function:
Sinusoid
Freq:
15 kHz
Amplitude: 5 Vp-p
Load:
50 
Modulation Pan:
Frequency Panel
Function:
Sinusoid
Freq:
1 Hz
Deviation:
5 kHz
FM State:
ON
14.
Connect the oscilloscope probe in parallel with the resistance. Measure the
maximum and minimum frequency, deviation factor and modulation index.
What’s the signal bandwidth? Record in table 3.
15.
Disconnect the oscilloscope and connect the spectrum analyzer. Set center
frequency to 15 kHz and span of 20 kHz. What’s the signal bandwidth? What did
you see?
BW  ________________
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Rev. 10/22/01
Communications I
Laboratory #4
9
RESULTS
Table 1: Carrier Frequency
Carrier Signal
fc
Vp-p
Vavg
Table 2: Modulated Signal (Part 1)
Modulated Signal
fmax
fmin
fd
Mf
BW
Table 3: Modulated Signal (Part 2)
Modulated Signal
fmax
fmin
fd
Mf
BW
QUESTIONS
1.
2.
3.
4.
5.
Which of the two cases require a greater bandwidth? Why?
Which system provides a greater voice quality at the receiver end? Why?
Explain how the frequency-modulated signals are generated.
Which system the AM or FM provides better noise immunity? Why?
Explain the relationship between bandwidth and voice quality.
By: Prof. Rubén Flores Flores and Prof. Caroline González Rivera
Rev. 10/22/01