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Exp.(6) Frequency modulation(fm). Done by: BASIL Z. BARZAQ 120070737 BASSAM H. SALLOUHA 120071676 MOHAMED A. ELSHAER 120071709. Supervised by: Eng.: Mohammed Kamel AbuFoul. May 2010. OBJECTIVES.

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exp 6 frequency modulation fm

Exp.(6)Frequency modulation(fm)

Done by:

BASIL Z. BARZAQ 120070737

BASSAM H. SALLOUHA 120071676

MOHAMED A. ELSHAER 120071709

Supervised by:

Eng.: Mohammed Kamel AbuFoul

May 2010

objectives
OBJECTIVES
  • Understanding frequency modulation and demodulation by direct differentiation ,slope detection.
  • Using MATLAB m-file and simulink to implement FM modulation ,demodulation.
frequency modulation
Frequency modulation
  • Definition: it’s a form of modulation which represents information as variations in the instantaneous frequency of a carrier wave.
  • Note:

1)In analog applications,the

carrier frequency is varied

in direct proportion to

changes in the amplitude

of an input signal.

slide4

2) The FM-modulated signal has its instantaneous frequency that varies linearly with the amplitude of the message signal.

Now we can get the FM-modulation by:

Where:

Kƒ is the sensitivity factor, and represents the frequency deviation rate as a result of message amplitude change.

The instantaneous frequency is:

slide5

The maximum deviation of Fc (which represents the max. shift away from Fc in one direction) is:

Note:

The FM-modulation is implemented by controlling the instantaneous freq. of a voltage-controlled oscillator(VCO).

The amplitude of the input signal controls the oscillation freq. of the VCO output signal.

fm demodulation
Fm demodulation
  • In the FM demodulation what we need to recover is the variation of the instantaneous frequency of the carrier, either above or below the center frequency.
  • The detecting device must be constructed so that its output amplitude will vary linearly according to the instantaneous freq. of the incoming signal.
fm demodulation by direct differentiation
Fm demodulation by direct differentiation
  • In this method we differentiate the FM signal to get an AM signal, then we use an envelope detector.
matlab codes
Matlab codes
  • The code of plotting m(t) and FM modulated signal:

clear all

fc=100;

ts=1/(10*fc);

fs=(1/ts);

kf=80;

wc=2*pi*fc;

t=0:ts:2;

m=sin(2*pi*t);

y=cos(wc*t+(kf*2*pi*cumsum(m)).*ts);

figure(1)

subplot(211)

plot(t,m)

title(\'input signal\')

subplot(212)

plot(t,y)

title(\'fm modulation of input signal\')

slide9

The code of magnitude spectrum of m(t) and the FM signal:

mf=fftshift(fft(m))*ts;

delta=fs/length(mf);

f=-fs/2:delta:fs/2-delta;

figure(2)

subplot(211)

plot(f,abs(mf))

title(\'magnitude spectrum

of input signal\')

a=fftshift(fft(y))*ts;

delta=fs/length(a);

f=-fs/2:delta:fs/2-delta;

subplot(212)

plot(f,abs(a))

title(\'magnitude spectrum of the fm\')

slide10

The plot of the output signal after differentiator:

E=diff(y)/ts;

figure(3)

plot(E)

title(\'the differentiation of fm \')

slide11

The plot of the output signal from the envelope detector:

vout(1)=E(1);

t1=(0:length(E)-1)*ts;

R=[10^5,10^4,10^3,10^2]*3.2;

c=10^-6;

for n=1:4

for i =2:length(E)

if E(i)>vout(i-1)

vout(i)=E(i);

else

vout(i)=vout(i-1).*exp(-ts/(R(n)*c));

end

end

figure(4)

subplot(4,1,n)

plot(t1,vout,t1,E)

title(\' the AM signal and envelope signal \')

end

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