IT 300 James Madison University Frequency and Phase Modulation Lab Report

IT300 Virtual Lab 2 v22Frequency and Phase Modulation
Student Name: ___________________ GMU ID: ____________Date: _____________
Objectives.
VLAB2 covers part 1: frequency modulation (FM) and part 2: phase modulation (PM) analog signaling techniques.
As you read through this procedure, you will find multiple choice questions appearing in blue text. You are
required to answer these questions in a separate VLAB assignment which will appear in the VLAB folder. The
question format is similar to that of a homework assignment (i.e., select the correct answers and submit). In
addition, you will be asked to copy and submit plots that you create using MatLab. These will also be identified by
blue text within the procedures. A document “plot submission” template will be available for you to paste
requested copies for submission into the VLAB assignment.
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.
Note: Each procedure step depends upon the previous values entered in previous steps; therefore, you must execute
the procedures on a step-by-step basis unless otherwise instructed. This ensures that your variables and plots are
correct!
Part 1. FM Modulation
message or modulating signal:
carrier:
modulation index:
FM modulation formula:
m(t) = Amcos(2πfmt),
m=Am*cos(2*pi*fm*t),
MatLab equation
c(t) = Ac cos(2πfct),
c=Ac*cos(2*pi*fc*t) ,
MatLab equation
β = ∆f/fm = kvco*Am/fm,
beta=(kvco*Am)/fm,
MatLab equation
s(t) = Ac cos[2πfct + β sin(2πfmt)]
sFM=Ac*cos((2*pi*fc*t)+beta*sin(2*pi*fm*t)) , MatLab equation
Step 1.1 Use the following MATLAB code and create plots.
%AM Modulation;
clear;
clc;
clf;
Ac=3;
Am=3;
fc=11000;
fm=1200;
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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(2,2,3);
yyaxis left;
plot(t,m);
yyaxis right;
plot(t,s);
title(‘combined message and AM signal’);
xlabel(‘time’);
ylabel(‘amplitude’);
%FM
kvco=2500;
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(2,2,4);
yyaxis left;
plot(t,m);
ylim([-8 9])
yyaxis right;
plot(t,sFM);
ylim([-8 9])
title(‘combined message and FM signal’);
xlabel(‘time’);
ylabel(‘amplitude’);
Question 1. Select the correct statement regarding the difference between the FM and the AM modulated
signal waveforms.
a. 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)
b. The AM modulated signal accurately represents the message; the FM modulated signal does not accurately
represent the message wave
c. Neither AM nor FM modulated signals accurately represents the message wave
d. The AM modulated signal accurately represents the message; the FM modulated signal accurately represents
the message wave
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Plot 1 – FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 1.1 above into the
“IT300 Virtual Lab Plot Submission” .
Step 1.2 Plot the following equations:
m(t) = 7cos(2π*800Hz*t)
c(t) = 5cos(2π*8kHz*t)
Kvco = 800
Question 2. Select the statement that best describes the resultant wave forms.
a. The AM signal begins to distort because the AM index is too high
b. The FM signal appears to faithfully represent m(t)
c. Both AM and FM signals represent the message accurately.
d. both a and b are true
Plot 2 – FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 1.2 above into the
“IT300 Virtual Lab Plot Submission” .
Step 1.3 Plot the following equations:
m(t) = 5cos(2π*800Hz*t)
c(t) = 5cos(2π*10kHz*t)
Kvco = 100
Question 3. Select the statement that best describes your observation.
a. Kvco is large enough to faithfully represent the modulated carrier s(t)
b. By viewing the AM modulated plot, distortion can easily be seen, which is caused by a large AM index.
c. Kvco is very small, which means that the FM index is very small, thus the FM modulated carrier does not
faithfully represent m(t).
d. b and c are correct
Plot 3 – FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 1.3 above into the
“IT300 Virtual Lab Plot Submission” .
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Part 2. PM Modulation
message or modulating signal:
carrier:
modulation index:
PM modulation formula:
m(t) = Amcos(2πfmt),
m=Am*cos(2*pi*fm*t),
MatLab equation
c(t) = Ac cos(2πfct),
c=Ac*cos(2*pi*fc*t) ,
MatLab equation
μp=kp*Am ,
kp (radians/volt) ,
MatLab equation
s(t) = Ac cos [2πfct + μp cos (2πfmt )],
sPM=Ac*cos((2*pi*fc*t)+mp*cos(2*pi*fm*t)) ,
MatLab equation
Step 2.1 Enter the following into the MATLAB editor. We will compare AM, FM and PM techniques.
%AM Modulation;
clear;
clc,
clf;
Ac=6;
Am=5;
fc=9000;
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=1800;
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);
ylim([-12 12])
yyaxis right;
plot(t,sFM);
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ylim([-12 12])
title(‘combined message and FM signal’);
xlabel(‘time’);
ylabel(‘amplitude’);
%PM
kp=pi/2;
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));
subplot(2,2,3);
yyaxis left;
plot(t,m);
ylim([-12 12])
yyaxis right;
plot(t,sPM);
ylim([-12 12])
title(‘combined message and PM signal’);
xlabel(‘time’);
ylabel(‘amplitude’);
Question 4. Select the statement that best describes the PM wave.
a. Carrier phase angle changes represent the PM modulated signal, however, unlike FM and AM modulated
carriers, it is not always easy to see these phase changes in the plot.
b. The FM signal accurately represents the message.
c. Although PM and FM techniques are classified as angular modulation techniques, they cannot be used
interchangeably (i.e., modulated with FM and demodulated with PM, and visa versa).
d. All statements are correct.
Plot 4 – PM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 2.1 above into the
“IT300 Virtual Lab Plot Submission” .
Step 2.2 Now change kp to pi/7.
Step 2.2 Plot the following equations:
m(t) = 6cos(2π*1000Hz*t)
c(t) = 3cos(2π*9kHz*t)
Kvco=1000, Kp = pi/7
Question 5. What is your observation?
a. The PM modulated signal remains unchanged since kp does not influence the PM index.
b. kp only effects FM modulated signals, therefore our PM modulated signal remains
unchanged.
c. kp changes and therefore the PM Index also changes. This will impact the quality of the
phase modulated signal.
d. All statements are incorrect.
Plot 5 – PM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 2.2 above into
the “IT300 Virtual Lab Plot Submission” .
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IT300 Virtual Lab 2 v22
Frequency and Phase Modulation
Student Name: ___________________ GMU ID: ____________Date: _____________
Plot 1 – FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 1.1 above into the
“IT300 Virtual Lab Plot Submission” .
Plot 2 – FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 2 above into the “IT300
Virtual Lab Plot Submission” .
Plot 3 – FM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 3 above into the “IT300
Virtual Lab Plot Submission” .
Plot 4 – PM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 2.1 above into the
“IT300 Virtual Lab Plot Submission” .
Plot 5 – PM Signal Plot Submission: Submit (i.e., copy/paste) the MATLAB plots from step 2.2 above into
the “IT300 Virtual Lab Plot Submission” .