Analog Communication - Practical 2

Aim

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

Theory

Frequency Modulation (FM) is a technique where the frequency of the carrier signal is varied in accordance with the instantaneous amplitude of the message signal. Unlike AM, the amplitude of the carrier remains constant.

The modulation index (β) in FM is defined as the ratio of the frequency deviation (Δf) to the frequency of the modulating signal (fm):

β = Δf / fm

The modulation index determines the bandwidth of the FM signal, governed by Carson's rule:

Bandwidth = 2(Δf + fm)

Demodulation of FM signals involves recovering the original message signal by detecting changes in the instantaneous frequency of the modulated signal. This can be achieved using techniques such as frequency discriminators or phase-locked loops (PLLs).

MATLAB Code

%The frequency modulation(FM)waveform in time and frequency domain.
%fm=35HZ,fc=500HZ,Am=1V,Ac=1V,B=10
functionfmdm
fs=10000;
Ac=1;
Am=1;
fm=35;
fc=500;
B=10;
t=(0:.1*fs)/fs;
wc=2*pi*fc;
wm=2*pi*fm;
m_t=Am*cos(wm*t);
subplot(5,1,1);
plot(t,m_t);
title('Modulating or Message signal(fm=35Hz)');
c_t=Ac*cos(wc*t);
subplot(5,1,2);
plot(t,c_t);
title('Carrier signal(fm=500Hz)');
s_t=Ac*cos((wc*t)+B*sin(wm*t));
subplot(5,1,3);
plot(t,s_t);
title('Modulated signal');
d=demod(s_t,fc,fs,'fm');
subplot(5,1,4);
plot(t,d);
title('demodulated signal');

Expected Output

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

Message Signal: A sinusoidal wave representing the original message signal.
Frequency Modulated Signal: A sinusoidal signal where the frequency varies according to the amplitude of the message signal.
Demodulated Signal: The recovered message signal derived from changes in the frequency of the modulated wave.

The results validate the FM modulation and demodulation process, highlighting the effect of the modulation index on the FM signal's bandwidth.