Generation of Amplitude modulated wave at different modulation indexes in MATLAB.

1. 1
Lab Report 04:
Generating AM 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: 23/05/2017

2. 2
Statement:
Generate AM wave (Amplitude Modulation) at a different modulation index.
Verify whether the modulation index depends on the band width of AM
modulated wave or the power of side bands?
Literature Background:
Amplitude Modulation:
The amplitude modulation is a technique in which the amplitude of the carrier
changes according to the instantaneous amplitude of the baseband signal.
( ) ( ) (1)
Power of a Signal:
Power is energy over a time period.
∫ | | (2)
In MATLAB power is calculated by:
∑ | |
(3)
Band width:
Difference of highest and lowest frequencies which contain 90% energy of the
signal.
Where bandwidth of an AM is given by
B.W=2*fm (4)
“fm” is the highest frequency of baseband signal.
Procedure:
MATLAB Coding:
clc
clear all
close all

3. 3
t=0:1:200;
fm=500;
fc=20*fm;
Vc=10;
MA=1;
Vm=MA*Vc;
phase =0;
fs=10*fc;
ts=t/fs;
Xm=Vm*cos(2*pi*fm*ts+phase);
plot(ts*1000,Xm)
title('baseband signal')
xlabel('time in ms')
ylabel('Vm')
grid on;
figure
Xc=Vc*cos(2*pi*fc*ts+phase);
plot(ts*1000,Xc)
title('carrier signal')
xlabel('time in ms')
ylabel('Vc')
grid on;
figure
Y=Xc+Xm.*cos(2*pi*fc*ts+phase);
plot(ts*1000,Y)
title('Amplitude Modulated wave')
xlabel('time in ms')
ylabel('Vc+Vm')
grid on;
figure
z=fft(Y);
z=abs(z(1:length(z)/2+1));
frq=(0:length(z)-1)*fs/length(z)/2;
plot(frq/1000,z);
title('FFT of Modulated Wave')
xlabel('F in kHz')
ylabel('Amplitude')
grid on;

4. 4
carrier_power = sum(Xc.^2)/length(t);
display(carrier_power);
entire_power = sum(Y.^2)/length(t);
display(entire_power);
sideband_power = entire_power-carrier_power;
display(sideband_power);
Analysis:
= 0
Figure 1: Baseband signal with fm=500Hz, =0V
Figure 2: Carrier signal with fc=10kHz =10V

5. 5
Figure 3: Amplitude Modulated Signal
Figure 4: AM Wave in Frequency Domain
carrier_power =
50.2488
entire_power =
50.2488
sideband_power =
0

6. 6
= 0.5
Figure 5: Baseband signal with fm=500Hz, =5V
Figure 6: Carrier signal with fc=10kHz, =10V

7. 7
Figure 7: Amplitude Modulated Signal
Figure 8: AM Wave in Frequency Domain
carrier_power =
50.2488
entire_power =
57.0896
sideband_power =
6.8408

8. 8
= 1
Figure 9: Baseband signal with fm=500Hz, =10V
Figure 10: Carrier signal with fc=10kHz, =10V

9. 9
Figure 11: Amplitude Modulated Signal
Figure 12: AM Wave in Frequency Domain
carrier_power =
50.2488
entire_power =
76.6169
sideband_power =
26.3682

10. 10
= 1.5
Figure 13: Baseband signal with fm=500Hz, =15V
Figure 14: Carrier signal with fc=10kHz, =10V

11. 11
Figure 15: Amplitude Modulated Signal
Figure 16: AM Wave in Frequency Domain
carrier_power =
50.2488
entire_power =
108.8308
sideband_power =
58.5821

12. 12
Table # 01:
S.No Modulation
Index
Power in
entire AM
Wave
Power in
side bands
only
Bandwidth
in Hz
1 0 50.2488 0 1
2 0.5 57.0896 6.8408 1000
3 1 76.6169 26.3682 1000
4 1.5 108.8303 58.5821 1000
Questions:
Q1) What will happen to the power of side bands (increasing or
decreasing) with the increase of modulation index? Give mathematical
reasoning?
Ans: Relation for Power of the side bands is
(5)
is power of sidebands
is power of carrier wave
is Modulation index
From eq(5) it is clearly seen that power of the sidebands is directly proportional
to the Modulation index. With the increase in Modulation index, power of the
side bands also increases.
Q2) What will happen to the band width of AM wave (increasing or
decreasing) with the increase of modulation index? Give mathematical
reasoning?
Ans: The band width of AM wave does not depends on Modulation index.
If Modulation index is increased or decreased, the bandwidth of AM will
remains same.

13. 13
Mathematically:
Bw=2*fm (6)
From eq(6) we clearly see that bandwidth depends on the higher frequency of
baseband signal not on Modulation index.
Q3) Why the modulation index in AM is not greater than 1?
Ans: Maximum value of Modulation index for AM is 1 because when
Modulation index is greater than 1, over modulation occurs and distortion
created in signal and information will be lost.
Mathematically:
(7)
When = , =1
If is further increased, Over Modulation occurs which will cause distortion
in transmitted signal.
Conclusion:
 Transmitted Power and Power of side bands increases with increase in
Modulation index.
 Band width of AM is independent of Modulation index.
 Band width of AM depends on the highest frequency of baseband signal.
Bw=2*fm
 Bandwidth is 1Hz when Modulation index is 0 because and =0.
 Transmitted Signal will be distorted when Modulation index >1.