IT300 Virtual Lab
Part 2: Frequency and Phase Modulation
George Mason University
Student Name: ________________________________________ GMU ID: _______________
Date: ___________________
Objectives:
Section 1.0 of this lab is intended to give the student a basic understanding of how to
use MATLAB for fundamental math calculations and graph plotting. During section 1.0, the student will
learn how enter and plot basic sinusoidal equations. Parts 2.0, 3.0 and 4.0 cover AM, FM, and PM
methods respectively.
Student tasking (i.e., multiple choice questions and the copy/paste of plots) appear in blue print and are
to be submitted for VLAB grading purposes. Multiple choice questions are to be answered directly into
the VLAB multiple choice questions assignment in the VLAB folder. Plots that must be pasted and
submitted by students are also identified in blue print and must be pasted into the “IT300 Virtual Lab
Plot Submission v13” doc and submitted in a separate assignment also located in the VLAB folder.
Students are highly encouraged to change the values of variables during each part of the lab in order to
observe changes in the signal plots.
Students will be given the basic MATLAB formulas to work with; however, students will need to modify
the values of some variables so that signal plot changes can be observed.
Part 3
Section 3.0: FM Modulation
message or modulating signal:
carrier:
FM modulation index:
FM modulation formula:
m(t) = Amcos(2πfmt)
c(t) = Ac cos(2πfct)
h = ∆f/fm = k*Am/fm, where k is in Hz to voltage (i.e., how
many Hz per volt)
s(t) = Ac cos[2πfct + h sin(2πfmt)]
Step 3.1 Enter the following into the MATLAB editor. We will compare AM and FM techniques.
%AM Modulation;
clear;
Ac=5;
Am=5;
fc=10000;
fm=1000;
t=0:0.00001:0.003;
m=Am*cos(2*pi*fm*t);
c=Ac*cos(2*pi*fc*t);
1
mi = Am/Ac;
s=Ac*(1+mi*cos(2*pi*fm*t)).*cos(2*pi*fc*t);
subplot(2,2,1);
plot(t,s);
xlabel('time');
ylabel('amplitude');
title('AM modulation');
subplot(2,2,4);
yyaxis left;
plot(t,m);
yyaxis right;
plot(t,s);
title('combined message and AM signal');
xlabel('time');
ylabel('amplitude');
%FM
kvco=1000;
beta=(kvco*Am)/fm;
sFM=Ac*cos((2*pi*fc*t)+beta*sin(2*pi*fm*t));
subplot(2,2,2);
plot(t,sFM);
xlabel('time');
ylabel('amplitude');
title('FM modulation');
%combined FM and m(t) plot
subplot(2,2,3);
yyaxis left;
plot(t,m);
yyaxis right;
plot(t,sFM);
title('combined message and FM signal');
xlabel('time');
ylabel('amplitude');
Definition of above MATLAB formula:
kvco: Hz/volts, represents the frequency change per message amplitude change, and is
called the frequency to voltage gain
beta: FM Modulation Index is the amount of frequency change possible over the center
frequency of the message signal. βFM = ∆f/fm = (kvco*Am)/fm
sFM: FM modulated signal
Select the "Run" icon. A window should open showing graphical plots for the modulated carrier
wave or signal, and the message or modulating wave.
Question 3.1 Select the correct statement regarding the difference between the FM
modulated signal waveform and the AM modulated signal waveform.
2
a. The FM signal wave changes frequency according to the message wave m(t). The "peak"
amplitude of the FM signal, Ac=5, remains constant. This is because m(t) does not modulate
the amplitude of the carrier wave when using FM techniques.
b. There is no difference between the FM and AM signal waves because they are both
modulated by the same message wave, m(t) = Amcos(2πfmt)
c. The AM signal wave frequency changes with the message wave m(t) while the amplitude of
the FM signal changes with m(t).
d. All statements are correct.
Plot 3.1 - FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 3.1 above
into the “IT300 Virtual Lab Plot Submission” .
Question 3.2 By observing the combined AM and FM plots, we see that both AM and FM
signals appear to represent the original message signal.
a. True
b. False
Step 3.3 Change the message amplitude to 1, and plot.
Question 3.3 Select the statement that best describes the resultant wave forms.
a. Regarding FM modulation, with Am=1, the FM Index becomes very small, resulting in a
modulated carrier signal that barely changes as the message changes.
b. Regarding AM modulation, the AM index is between 0 and 1, and therefore, it can be seen
that the AM modulated carrier signal represents the message.
c. Both statements are correct
d. Neither statement is correct.
Plot 3.3 - FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 3.3 above
into the “IT300 Virtual Lab Plot Submission” .
Step 3.4 Change the message amplitude to 10, and answer the following questions.
Question 3.4 Select the statement that best describes your observation.
a. The FM modulated carrier signal appears to change with the message
b. The AM modulated carrier shows distortion since the AM index is >1
c. In both the AM and FM cases, Am = 10v and Ac = 5v
d. All of the statements are correct
Plot 3.4 - FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 3.4 above
into the “IT300 Virtual Lab Plot Submission” .
3
4.0 PM Modulation
message or modulating signal:
carrier:
PM modulation index:
PM modulation formula:
m(t) = Amcos(2πfmt)
c(t) = Ac cos(2πfct)
μp=kp*Am), where kp is a constant that represents radians per
volt
s(t) = Ac cos [2πfct + μp cos (2πfmt )]
Step 4.1 Enter the following into the MATLAB editor. We will compare AM, FM and PM
techniques.
%AM Modulation;
clear;
Ac=5;
Am=5;
fc=10000;
fm=1000;
t=0:0.00001:0.003;
m=Am*cos(2*pi*fm*t);
c=Ac*cos(2*pi*fc*t);
mi = Am/Ac;
s=Ac*(1+mi*cos(2*pi*fm*t)).*cos(2*pi*fc*t);
subplot(2,2,1);
plot(t,s);
xlabel('time');
ylabel('amplitude');
title('AM modulation');
subplot(2,2,2);
plot(t,m);
xlabel('time');
ylabel('amplitude');
title('Message');
%FM
kvco=1000;
beta=(kvco*Am)/fm;
sFM=Ac*cos((2*pi*fc*t)+beta*sin(2*pi*fm*t));
subplot(2,2,4);
yyaxis left;
plot(t,m);
yyaxis right;
plot(t,sFM);
title('combined message and FM signal');
xlabel('time');
ylabel('amplitude');
%PM
kp=0.8;
t=0:0.000001:0.002;
m=Am*cos(2*pi*fm*t);
mp=kp*Am;
sPM=Ac*cos((2*pi*fc*t)+mp*cos(2*pi*fm*t));
4
subplot(2,2,3);
yyaxis left;
plot(t,m);
yyaxis right;
plot(t,sPM);
title('combined message and PM signal');
xlabel('time');
ylabel('amplitude');
Step 4.2 Select the "Run" icon. Another window should open showing graphical plots for the
modulated carrier wave or signal, and the message or modulating wave.
Question 4.2 Select the statement that best describes the PM wave.
a. The PM signal clearly does not change phases with the message wave. In this case, the PM
signal will not be received.
b. The PM signal appears to change frequency with the message wave since both PM and FM
are considered angular modulation techniques. However, the message in a PM wave is only
captured in phase changes vice frequency changes.
c. Since both PM and FM signals are considered angular modulation techniques, PM can be
demodulated using FM demodulation techniques.
d. All statements are correct.
Plot 4.2 - PM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 4.2 above
into the “IT300 Virtual Lab Plot Submission” .
Step 4.3 Now change kp to π/200.
Question 4.3 What is your observation?
a. The PM signal can still be received since kp does not influence the PM index.
b. kp is too high, therefore PM modulation will overlap sampling times and the message will be
lost.
c. kp is very small, therefore the PM index is very small, and changes in the message wave will
be difficult to detect in the PM signal. This will require a highly sensitive receiver capable of
detecting small phase changes.
d. All statements are incorrect.
Plot 4.3 - PM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 4.3 above
into the “IT300 Virtual Lab Plot Submission” .
5