Analog Communication - Practical 1

Aim

To study the amplitude modulation and demodulation for different modulation indices.

Theory

Amplitude Modulation (AM) is a technique used in communication systems where the amplitude of a high-frequency carrier signal is varied in proportion to the instantaneous amplitude of the message signal.

The modulation index (m) determines the extent of modulation and is defined as the ratio of the amplitude of the message signal to the amplitude of the carrier signal. The modulation index influences the characteristics of the AM signal:

Under-Modulation: When m < 1, the message is fully represented in the modulated signal.
Perfect Modulation: When m = 1, the carrier is fully utilized.
Over-Modulation: When m > 1, distortion occurs due to overlapping of sidebands.

The demodulation process retrieves the original message signal from the modulated signal. This is achieved using an envelope detector or by using digital signal processing techniques like the Hilbert transform.

MATLAB Code

% MATLAB Code for AM and Demodulation
fs=8000;
fm=20;
fc=500; 
Am=1;
Ac=1;
t=[0:.1*fs]/fs;
m=Am*cos(2*pi*fm*t);
c=Ac*cos(2*pi*fc*t);
ka=0.5;
u=ka*Am;
s1=Ac*(1+u*cos(2*pi*fm*t)).*cos(2*pi*fc*t);
subplot(4,3,1:3);
plot(t,m);
title('Modulating or Message signal(fm=20Hz)');
subplot(4,3,4:6);
plot(t,c);
title('Carrier signal(fc=500Hz)');
subplot(4,3,7);
plot(t,s1);
title('Under Modulated signal(ka.Am=0.5)');
Am=2;
ka=0.5;
u=ka*Am;
s2=Ac*(1+u*cos(2*pi*fm*t)).*cos(2*pi*fc*t);
subplot(4,3,8);
plot(t,s2);
title('Exact Modulated signal(ka.Am=1)');
Am=5;
ka=0.5;
u=ka*Am;
s3=Ac*(1+u*cos(2*pi*fm*t)).*cos(2*pi*fc*t);
subplot(4,3,9);
plot(t,s3);
title('Over Modulated signal(ka.Am=2.5)');
r1= s1.*c;
[b a] = butter(1,0.01);
mr1= filter(b,a,r1);
subplot(4,3,10);
plot(t,mr1);
r2= s2.*c;
[b a] = butter(1,0.01);
mr2= filter(b,a,r2);
subplot(4,3,11);
plot(t,mr2);
r3= s3.*c;
[b a] = butter(1,0.01);
mr3= filter(b,a,r3);
subplot(4,3,12);
plot(t,mr3);

Expected Output

The MATLAB code generates three plots demonstrating the process of modulation and demodulation:

Message Signal: A sinusoidal wave representing the original message signal.
Modulated Signal: A high-frequency carrier wave whose amplitude varies based on the message signal. The variation is governed by the modulation index.
Demodulated Signal: The retrieved message signal using the envelope of the modulated wave, ideally resembling the original message.

These plots visually validate the modulation and demodulation process and showcase the impact of the modulation index on the AM signal's characteristics.