Dept of Electrical & Electronic Engineering

Course # EEE-307
Experiment # 04
Frequency modulation

Preliminary discussion
A disadvantage of the AM, DSBSC and SSB communication systems is that they are susceptible
to picking up electrical noise in the transmission medium (the channel). This is because noise
changes the amplitude of the transmitted signal and the demodulators of these systems are
affected by amplitude variations.

As its name implies, frequency modulation (FM) uses a message’s amplitude to vary the
frequency of a carrier instead of its amplitude. This means that the FM demodulator is designed
to look for changes in frequency instead. As such, it is less affected by amplitude variations and
so FM is less susceptible to noise. This makes FM a better communications system in this
regard.

There are several methods of generating FM signals but they all basically involve an oscillator
with an electrically adjustable frequency. The oscillator uses an input voltage to affect the
frequency of its output. Typically, when the input is 0V, the oscillator outputs a signal at its rest
frequency (also commonly called the free-running or centre frequency). If the applied voltage
varies above or below 0V, the oscillator’s output frequency deviates above and below the rest
frequency. Moreover, the amount of deviation is affected by the amplitude of the input voltage.
That is, the bigger the input voltage, the greater the deviation.

Figure 1 below shows a simple message signal (a bipolar squarewave) and an unmodulated carrier.
It also shows the result of frequency modulating the carrier with the message.
Figure 1
There are a few things to notice about the FM signal. First, its envelopes are flat – recall that
FM doesn’t vary the carrier’s amplitude. Second, its period (and hence its frequency) changes
when the amplitude of the message changes. Third, as the message alternates above and below
0V, the signal’s frequency goes above and below the carrier’s frequency. (Note: It’s equally
possible to design an FM modulator to cause the frequency to change in the opposite direction
to the change in the message’s polarity.)

Before discussing FM any further, an important point must be made here. A squarewave message
has been used in this discussion to help you visualise how an FM carrier responds to its message.
In so doing, Figure 1 suggests that the resulting FM signal consists of only two sinewaves (one at
a frequency above the carrier and one below). However, this isn’t the case. Spectral composition
of the FM signal in Figure 1 is much more complex than implied.

This highlights one of the important differences between FM and the modulation schemes
discussed earlier. The mathematical model of an FM signal predicts that even for a simple
sinusoidal message, the result is a signal that potentially contains many sinewaves. In contrast,
for the same sinusoidal message, an AM signal would consist of three sinewaves, a DSBSC signal
would consist of two and an SSBSC signal would consist of only one. This doesn’t automatically
mean that the bandwidth of FM signals is wider than AM, DSBSC and SSBSC signals (for the
same message signal). However, in the practical implementation of FM communications, it usually
is.

Finally, when reading about the operation of an FM modulator you may have recognised that
there is a module on the Emona Telecoms-Trainer 101 that operates in the same way - the VCO
module. In fact a voltage-controlled oscillator is sometimes used for FM modulation (though
there are other methods with advantages over the VCO).

The experiment
In this experiment you’ll generate a real FM signal using MATLAB. First, you’ll set up an
unmodulated carrier at a known frequency. Then you’ll observe the effect of frequency
modulating its output with a squarewave then speech. You’ll also use the speech signal to
demonstrate the effect that a message’s amplitude has on an FM modulator. Finally, you’ll use a
sinewave to observe the spectral composition of an FM signal (in the time domain).

Procedure

Part A – Frequency modulating a squarewave

1. First generate a carrier in matlab having amplitude of 2V and frequency 50kHz. Take
time array such that 20 cycle of the carrier is within the array.

2. Now generate a square wave in matlab having a frequency of 5kHz. I can be done by the
code below:
m = square(2*pi*fm*t);
 3. Now, use the following equation of frequency of the carrier to generate the frequency
modulated signal.

4. We will use the value of kf as 10000Hz / V.

5. Observe the modulated carrier and change the value of kf and observe it’s effect.

Figure 2

Figure 3

The set-up in Figure 3 can be represented by the block diagram in Figure 4 below. The Master
Signals module is used to provide a 2kHz squarewave message signal and the VCO module is the
FM modulator with a 10kHz carrier.
 Figure 4

Question 1
How does the frequency of the carrier change?

Question 2
Can you determine the frequency when the square wave is positive? What is the value of
the frequency when the square wave is negative?

Part B – Generating an FM signal using speech

1. Now replace the message signal by a speech signal. We will use the same file used in
experiment – 1. Here, we will take samples from the middle of the voice signal. The
number of samples should be equal to the length of the time array or the length of the
carrier signal array.

2. Don’t forget that the audio file should be in the same folder as the code.

3. For better understanding, amplify the audio signal amplitude by 3.

4. Observe the effect of the FM signal.

Question 3
What is the relationship between the FM signal’s frequency deviation and the amplitude
of the message?

Part C – Considering the spectral composition of FM signals

Figure 6

You should now see a display that looks similar to Figure 7 below.
 Figure 7

Post-lab:
1. Write a code in MATLAB to generate FM signal using the following analytical
expressions (show the plots in different figures with appropriate legend, xlabel,
ylabel):
k
u (t ) = A J
n=− k
c n (  f ) cos 2 ( f c + nfm )t

u (t ) = Ac cos2f ct +  sin(2f mt )
Carrier signal amplitude, Ac = last 2digits of your ID in volt, frequency, fc = last 2digits of
your ID in KHz, fm = last 2digits of your ID *100Hz, and
last digit of SID, if last digit of SID  5
 =
2 * last digit of SID, otherwise
last digit of SID, if last digit of SID  6
k =
2 * last digit of SID, otherwise

2. Use the MATLAB built-in function ‘fmmod’, to produce u(t). Search the internet to
find out how to use fmmod. Compare the results with your plots in the lab.

3. Mention the advantages and disadvantages of FM modulation along with its