I need to present frequency modulation of 2 armonic signals, using only traditional formulas (no fmmod), the modulated signal doesn't look right. Can someone help?

This is my code, I have a modulating signal a carrier signal and I need to show FM using a BETA=0.1 (modulation index). These are the only formulas present in my UNI Course :

y=cos(2*pi*Fc*t+B*sin(2*pi*Fm*t)) //GENERAL FORMULA

y=Ac.*cos(Oc*t)-B*Ac.*sin(Wm*t).*sin(Oc*t) //B=0.1

y=Ac.*cos(Oc*t)-(B*Ac)/2.*cos((Oc-Wm)*t)+(B*Ac)/2.*cos((Oc+Wm)*t).

//top is modulating signal,middle is carrier,bottom is modulated

Using these formulas I get the exact same result; I can see that the modulation is not happening, as the modulated signal 'y' has a constant frequency and looks similar to the carrier.

Is there a problem with the formulas, or is my code missing something?

(I am new to MATLAB coding and the teacher told us this problem was difficult, so I am assuming there are extra steps I need to take.)

//CODE STARTS HERE

clc

close all

format long

Fm=10;%modulating frequency

Fc=100;%carrier frequency

Am=3;

Ac=3;

Fs=10000;

B=0.1;%B<0.4

Oc=Fc*2*pi;

Wm=Fm*2*pi;

Ts = 1/Fs;

t = 0 : Ts : 0.2;

xm=Am*sin(2*pi*Fm*t);%modulating signal

xc=Ac*cos(2*pi*Fc*t);%carrier signal

%y=cos(2*pi*Fc*t+B*sin(2*pi*Fm*t)) ; //B<0.4

%y=Ac.*cos(Oc*t)-B*Ac.*sin(Wm*t).*sin(Oc*t);

y=Ac.*cos(Oc*t)-(B*Ac)/2.*cos((Oc-Wm)*t)+(B*Ac)/2.*cos((Oc+Wm)*t)

figure

subplot(3,1,1)

plot(t,xm,'r')

subplot(3,1,2)

plot(t,xc,'b');

subplot(3,1,3)

plot(t,y,'g');

grid

//CODE ENDS HERE

Answer 1

[Vishwa]

Hi Stefan,

Only your first equation is for frequency modulation rest two are for amplitude modulation, so use that only.

y=cos(2*pi*Fc*t+B*sin(2*pi*Fm*t)) //GENERAL FORMULA

Also it just so happens that your modulation index is very low (B=0.1), so your modulated waveform is visibily indistinguishable from your carrier.

Here is your code with value of modulation index equal to 5.

clc
close all 
format long
Fm=10;%modulating frequency
Fc=100;%carrier frequency
Am=3;
Ac=3;
Fs=10000;
B=5;%B<0.4
Oc=Fc*2*pi;
Wm=Fm*2*pi;
Ts = 1/Fs;
t = 0 : Ts : 0.2;
xm=Am*sin(2*pi*Fm*t);%modulating signal
xc=Ac*cos(2*pi*Fc*t);%carrier signal
y=cos(2*pi*Fc*t+B*sin(2*pi*Fm*t)) ;  %B<0.4 
figure
subplot(3,1,1)
plot(t,xm,'r')
subplot(3,1,2)
plot(t,xc,'b');
subplot(3,1,3)
plot(t,y,'g');
grid

Hope it helps.