FM

EXP NO: 4 GENERATION AND DETECTION OF FM

AIM: To write a program for Frequency Modulation and Demodulation using SCILAB and to observe and measure the frequency deviation and the modulation index of FM.

EQUIPMENTS REQUIRED

• Computer with i3 Processor • SCI LAB

THEORY:

Frequency modulation is a type of modulation in which the frequency of the high frequency (carrier) is varied in accordance with the instantaneous value of the modulating signal. FREQUENCY DEVIATION f and MODULATION INDEX m f : The frequency deviation f represents the maximum shift between the modulatedsignal frequency, over and under the frequency of the carrier.

We define modulation index m f the ratio between f and the modulating frequency m= f / fm

FREQUENCY MODULATION GENERATION: The circuits used to generate a frequency modulation must vary the frequency of a high frequency signal (carrier) as function of the amplitude of a low frequency signal (modulating signal). In practice there are two main methods used to generate FM. Algorithm

1. Define Parameters: • Fs: Sampling frequency. • T: Duration of the signal. • Fc: Carrier frequency. • Fm: Frequency of the modulating signal. • Beta: Modulation index, which controls the extent of frequency deviation.

2. Generate Signals: • Modulating signal: Sinusoidal signal used for modulation. • Carrier signal: The high-frequency carrier signal. • Modulated signal: FM modulated signal calculated by varying the carrier frequency according to the modulating signal.

3. FM Modulation: • Modulated signal is obtained by modulating the carrier signal with the modulating signal.

4. FM Demodulation: • Differentiation: Computes the derivative of the modulated signal to extract frequency variations. • Envelope Detection: Takes the absolute value to retrieve the envelope of the signal. • Low-pass Filtering: Applies a Butterworth low-pass filter to smooth the envelope and recover the original modulating signal.

5. Visualization: • Plots the modulating signal, carrier signal, FM modulated signal, and demodulated signal for analysis.

PROCEDURE

• Refer Algorithms and write code for the experiment. • Open SCILAB in System • Type your code in New Editor • Save the file • Execute the code • If any Error, correct it in code and execute again Verify the generated waveform using Tabulation and Model Waveform

MODEL GRAPH:

Program

Am=12.5;
Ac=25;
fm=919;
fc=9190;
fs=91900;
b=5
t=0:1/fs:2/fm;
m=Am*cos(2*3.14*fm*t);
subplot(3,1,1);
plot(t,m);
c=Ac*cos(2*3.14*fc*t);
subplot(3,1,2);
plot(t,c);
s=Ac*cos(2*3.14*fc*t + B*sin(2*3.14*fm*t));
subplot(3,1,3);
plot(t,s)

Output Waveform

Tabulation

Calculation

Frequency Deviation Practical =

Modulation Index Practical =

Modulation Index Theoretical =

RESULT:

Thus, the frequency modulation and demodulation is successfully done and the output is experimentally verified.