# Amplitude modulation DSB-LC (full AM)

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Amplitude modulation DSB-LC (full AM)
Islamic University of Gaza Electrical Engineering Department Communication I laboratory Amplitude modulation DSB-LC (full AM) Submitted by: Adham Abu-Shamla Mohammed Hajjaj Submitted to: Eng. Mohammed kamel Abu-Foul

Contents: The objective of this experiment.
Quick review about the AM modulation and (DSB-LC) Part 1 code and its comments and results (step by step) Part 2 code and its comment and results Conclusion.

Objective: Understanding AM modulation, Double Side Band-Large Carrier (DSB-LC) “known as Full AM”. Using MATLAB to plot the modulated signal. To simulate coherent demodulator and an envelope detector to obtain the real signal using MATLAB.

Quick review about the AM modulation and (DSB-LC)
What is AM modulation It’s a type of modulation, that’s used to transmit the signal with high frequency. Why Modulation FDM(frequency division multiplexing) Hard ware limitation (λ=c/f),(L(Antenna Hight)=λ/10)

Type of AM Modulation DSB-SC DSB-LC SSB VSB

(AM) and (FM) :

Part 1 Use MATLAB to simulate this block (AM block) (f(t)=cos(2π2000t),Ac=4,m=0.25,fc=20Khz) f(t) m Ac.cos(2.π.fct) S(t)=Ac[1+mf(t)] .cos(2.π.fct) X +

Part 1 (a) code: the input signal
Sampling period Carrier freqyancy DC shift Modulation index µ=mp/A Sampling frequancy fc=20000; % Carrier frequency ts=1/(10*fc); t=[0:2000]*ts; fs=1/ts; % Sampling frequency m=.25; % Modulation index Ac=4; % DC shift x=cos(2*pi*2000*t); % the original signal figure(1) subplot(211) plot(t,x) title('plot of baseband signal x(t)') xlabel('time (t)') ylabel('x(t)') plot the real signal Comment: In the above code we chose ts =1/(10*fs) to avoid overlapping in signal, then we make Fourier transform to plot the magnitude spectrum.

Code cont. Xf=fftshift(fft(x)); Xf=Xf/length(Xf);
deltax=fs/length(Xf); fx=-fs/2:deltax:fs/2-deltax; subplot(212) plot(fx,abs(Xf)) title('the fourier transform of x(t)') xlabel('frequency (f)') ylabel('X(f)') Fourier Transform of a real signal Plot the magnitude spectrum

Two Sym. pulses on the signal frequency
The results (part 1a) Two Sym. pulses on the signal frequency

Code (part 1b): modulated signal
y=(1+m*x)*Ac.*cos(2*pi*fc*t); % (Modulated signal) figure(2) subplot(211) plot(t,y) title('the modulated signal y(t)=(1+m*x)*Ac.*cos(2*pi*fc*t)') xlabel('time (t)') ylabel('y(t)') yf=fftshift(fft(y));

Code (part 1b): modulated signal cont.
yf=yf/length(yf); delta=fs/length(yf); f=-fs/2:delta:fs/2-delta; subplot(212) plot(f,abs(yf)) title('the fourier transform of the modulated signal Y(f)') xlabel('frequency (f)') ylabel('Y(f)') Plot the magnitude spectrum

The same signal shifted at fc and the magnitude divided by 2
The results (part 1b) The same signal shifted at fc and the magnitude divided by 2

Coherent detector S(t) w(t) ) LPH v(t) cos(2.π.fc.t)

Code (Part 1c-1) coherent demodulator “before filtering”.
w=y.*cos(2*pi*fc*t); % Coherent demodulated signal figure(3) subplot(211) plot(t,w) title('plot of demodulated signal w(t) before LPF') xlabel('time (t)') ylabel('w(t)') wf=fftshift(fft(w));

Code (Part 1c-1) coherent demodulator “before filtering”.
wf=wf/length(wf); delta=fs/length(wf); f=-fs/2:delta:fs/2-delta; subplot(212) plot(f,abs(wf)) title('fourier transform of the demodulated signal W(f)') xlabel('frequency (f)') ylabel('W(f)')

The results (part 1c-1) The modulated signal shifted at 2*fc and the magnitude divided by 2 There are a signal in 0 as real signal

Code (Part 1c-2) coherent demodulator “after filtering”.
Fn. that return the order of the filter and the cutt off frequency Fn. that return the transfer function of the Butterworth filter losses due to rippels The Upper frequency of the transient region ( must be between 0 and 1 ) the lower frequency of the transient region ( must be between 0 and 1 ) Wp=5000/fs; Ws=20000/fs; Rp=-1; Rs=-100; [N, Wn] = BUTTORD(Wp, Ws, Rp, Rs); % [num,den]=butter(N,Wn); %

Code (Part 1c-2) coherent demodulator “after filtering”.
Filtering process v=filter(num,den,w); figure(4) subplot(211) plot(t,v) title('the demodulated signal after LPF v(t)') xlabel('time (t)') ylabel('v(t)')

Code (Part 1c-2) coherent demodulator “after filtering”.
Vf=fftshift(fft(v)); Vf=Vf/length(Vf); deltav=fs/length(Vf); fv=-fs/2:deltav:fs/2-deltav; subplot(212) plot(fv,abs(Vf)) title('the fourier transform of v(t)') xlabel('frequency (f)') ylabel('V(f)')

There are a signal in 0 as real signal only
The results (part 1c-2) There are a signal in 0 as real signal only

Envelope detector

Code (part 1d) %C=0.1e-6F,R=3.2e2%%%%% c=0.1e-6; r=3.2e2; RC=r*c;
Vc=ones*(1:length(y)); Vc(1)=y(1); for i=2:length(y) if y(i)>=Vc(i-1)

We can explain this code by the following flow chart
Code (part 1d) Vc(i)=y(i); else Vc(i)=Vc(i-1).*exp(-ts/RC); end figure(5) plot(t,y,t,Vc) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% We can explain this code by the following flow chart

Vc(i)=Vc(i-1).*exp(-ts/RC);
start Vc(1)=y(1) i=2 Y(i)>=Vc(i-1) YES NO Vc(i)=y(i) Vc(i)=Vc(i-1).*exp(-ts/RC); i=length(Y) NO YES start

The results (C=0.1e-6F,R=3.2e2)

If we change R R=3.2e(3) R=3.2e(4)

we will show the results of this part and comment the reason
Repeat part 1 with Ac=1, m = 2 After we make the simulation, the result is the same in part 1, but we saw some difference in the envelope detector . we will show the results of this part and comment the reason

Result of envelope overlap

Result of envelope Not as real signal

Comment in part 2 The reason of part 2 become like this becouse the Ac is not enough to alternate the signal up to zero so envelope detector can’t get the real signal

Conclusion The experiment is a good simulate for AM signals.
We must make sure of the code because any error causes fail in compiling

Thank you