Generating Phase Modulated wave in matlab

1. 1
Lab Report 06:
Generating PM wave at a different modulation
index
Submitted By :
Syed Abuzar Hussain Shah
Reg # :
SP15-BEE-096
Submitted To:
Sir Atiq-ul-Anam
Class:
BEE-5A
Dated: 19/06/2017

2. 2
Statement of Problem
Generate PM wave at different modulation index. Verify whether the
modulation index depends on the bandwidth of PM modulated wave or the
power of entire pm waves including side bands
Literature Background
Phase modulation (PM) is a modulation process that encodes information as
variations in the instantaneous phase of a carrier wave. Consider the modulating
signal:
Mathematically:
Baseband’s Equation:
= Vm sin (ωmt ) (1)
Carrier’s Equation:
= Vc sin (ωct ) (2)
Modulated wave Equation:
= Vc sin (ωct + mp cos ωmt) (3)
Figure 1: Carrier, baseband and PM modulated signal

3. 3
Deviation:
The amount by which the signal frequency varies is termed as daviation.
Normally measured in kiloHertz (kHz).
Band width:
The difference of highest and lowest frequencies which contain 90%
energy of the signal is called bandwidth.
Where bandwidth of an FM is given by:
B.W=2 x x No. of side bands (4)
Power of a Signal:
Power is a time average of energy.
∫ | | (5)
In MATLAB we can use this formula to calculate power:
∑ | |
(6)
Phase modulation works by modulating the phase of the signal, i.e. changing the
rate at which the point moves around the circle. This changes the phase of the
signal from what it would have been if no modulation was applied. In other
words the speed of rotation around the circle is modulated about the mean
value.

4. 4
Procedure:
First of all we generate a carrier wave fc and single frequency modulating signal
fm by using MatLab. Generating PM wave using the derived equation of PM
given in eq. 3 at modulation index 0, 0.5, 1, and 2.
Matlab code:
clc
clear all
close all
t=0:1:300;
fm=100; %modulated freq
fc=20*fm; %carrier freq
fs=5*fc; %sampling freq
ts=t/fs; %sampling time
Vm=5;
Vc=10;
Mp=1;
PM =Vc*cos(2*pi*fc*ts+Mp*cos(2*pi*fm*ts));
plot(ts*1000,PM)
title('PM wave in time domain')
xlabel('time (ms)')
ylabel('Vc')
grid on;
figure
z=fft(PM);
z=abs(z(1:length(z)/2+1));
frq=(0:length(z)-1)*fs/length(z)/2;
plot(frq/1000,z)
title('PM wave in Frequency domain')
xlabel(['F= ' num2str(fc/1000) 'kHz'])
grid on
power=sum(PM.^2)/length(t) %for calculating power
in entire FM wave

5. 5
Analysis:
Mp = 0
Figure 2: PM wave in time domain
Figure 3: PM wave in Frequency domain
power = 50.1661

6. 6
Mp = 1
Figure 4: PM wave in time domain
Figure 5: PM wave in Frequency domain
power = 49.9309

7. 7
Mp = 2
Figure 6: PM wave in time domain
Figure 7: PM wave in Frequency domain
power = 49.8914

8. 8
Table No 1:
Serial Number Modulation Index Power in entire
PM wave
Band width in
Hertz
1 0 50.1661 1
2 1 49.9309 600
3 2 49.8914 800
Questions and answers:
Q1) What will happen to the power of PM including side bands (increasing
or decreasing) with the increase of modulation index? Give mathematical
reasoning.
Ans) Power of the PM wave increases slightly with the increase of modulation
index (negligible) because power does not depends on modulation index.
Mathematically:
So there will be no change in power of PM signal by changing Mp.
Q2) What will happen to the band width of the PM wave (increasing or
decreasing) with the increase of modulation index? Give mathematical
reasoning.
Ans ) Band width will increase with the increase of modulation index, because
Here band width is depending on as well as on no of side bands.
Increase in Mp, sidebands increases so Bandwidth also increses.

9. 9
Q3) At what modulation index of PM the bandwidth of AM and PM
remains same?
Ans) When Modulation indexis zero, the band width of AM and PM are equal.
Conclusion:
 Band width depends on the Modulation index.
 Power is independent of Modulation index.
 Bw(AM) = Bw(PM) at M=0.