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**Intelligent Islamic Electrical Engineers (IIEE)**

Communications LAB I Amplitude Modulation DSB-LC (Full AM) presentation UNDER SUBERVISION: Eng. Mohammed k. Abu Foul Design by : Intelligent Islamic Electrical Engineers (IIEE) presentation by: Mahmood A. El-Tatar Islame E. Ashoor Mohaned H. Eqdeeh

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**Signals in Communications**

Base band Bandpass Amplitude modulation Angle Phase MOD. PM Frequency MOD. FM DSB-SC MOD. DSB+C MOD. SSB MOD. VSB MOD.

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**Analog Communication system**

Information source Signal modulator Propagation channel Signal demodulator Information output

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**Amplitude Modulation:**

There are 4 main types of AM signals: Full Am – 2 sidebands and carrier. Double sideband suppressed carrier (DSB-SC). Single sideband AM (SSB). Vestigial sideband AM (VSB).

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**Amplitude Modulation DSB-LC (Full AM)**

Full AM is sometimes referred to as Double Side Band – Large Carrier (DSLC) clearly indicating its main feature as having a large amplitude carrier component added to the signal spectrum. Type of modulators : 1-multiplier mod. 2-nonlinear mod. 3- switching mod.

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Modulating a signal Block diagram : Equations :

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Process of modulation

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**Modulation index If we consider : We defined modulation index to be**

f(t)= Am cos(wm*t), c(t)= Ac cos(wc*t) Φ(t)= (Am+Ac) cos(wm*t) cos(wc*t) We defined modulation index to be M= Am/Ac Thus we have: Φ(t)= Ac(1+m cos(wm*t))* cos(wc*t) In order to detect the signal with no distortion we require m ≤1

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**Matlap code fc=20000; ts=1/(10*fc); t=[0:2000]*ts; fs=1/ts; m=.25;**

Ac=4; x = (cos(2*pi*2000*t)).^3 figure(1) subplot(221) plot(t,x) title('plot of baseband signal x(t)') xlabel('time (t)') ylabel('x(t)') Xf=fftshift(fft(x))/length(t); deltax=fs/length(Xf); fx=-fs/2:deltax:fs/2-deltax; subplot(222) plot(fx,abs(Xf)) title('the fourier transform of x(t)') xlabel('frequency (f)') ylabel('X(f)') y=(1+m*x)*Ac.*cos(2*pi*fc*t); subplot(223) plot(t,y) %%title('the modulated signal y(t)=(1+m*x)*Ac.*cos(2*pi*fc*t)') ylabel('y(t)') yf=fftshift(fft(y))/length(t); delta=fs/length(yf); f=-fs/2:delta:fs/2-delta; subplot(224) plot(f,abs(yf)) ylabel('Y(f)')

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**Demodulation of Full AM**

(1) Coherent Demodulation: consists of multiplying received signal with a local carrier and filtering out unwanted components centered around 2wc.

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**Filters Types Of Filters:**

We will use the Butterworth filter in our study . Types Of Filters: LPF BPF HPF BRF

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HOW TO MAKE LPF To get the Butterworth filter order and cutoff frequency we use this code : Wp=5000/fs; Ws=20000/fs; Rp=-1; Rs=-100; [N, Wn] = BUTTORD(Wp, Ws, Rp, Rs) [num,den]=butter(N,Wn) v=filter(num,den,w) Where: Wp :Passband corner frequency. Ws: Stopband corner frequency . Rp&Rs : ripple factor . N : Filter order Wn: cutoff frequency num, den: filter transfer function

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**Matlap code w=y.*cos(2*pi*fc*t) 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)); 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)') Wp=5000/fs; Ws=20000/fs; Rp=-1; Rs=-100; [N, Wn] = BUTTORD(Wp, Ws, Rp, Rs) [num,den]=butter(N,Wn) v=filter(num,den,w) figure(4) plot(t,v) title('the demodulated signal after LPF v(t)') ylabel('v(t)') Vf=fftshift(fft(v))/length(t); deltav=fs/length(Vf); fv=-fs/2:deltav:fs/2-deltav; plot(fv,abs(Vf)) title('the fourier transform of v(t)') ylabel('V(f)')

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(2) Envelope Detector The output of the detector follows the envelope of the modulated signal. On positive half-cycle of RF input signal Φ(t), the diode is forward biased and the capacitor C charges up rapidly to the peak value of RF input signal When RF input falls below the output voltage then the diode becomes reversebiased and the capacitor C discharges through the load resistor RL

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**1/fc << RC<< 1/B**

RC effective Choice of R and C: 1/fc << RC<< 1/B Where B is the highest frequency in f(t) (original signal) Where fc is the carrier frequency

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**Matlap code R=3.2e3; C=01e-6; RC=R*C; Vout(1)=y(1); for i=2:length(y);**

if y(i)>Vout(i-1) Vout(i)=y(i); else Vout(i)=Vout(i-1)*exp(ts/RC); end figure(3) plot(t,Vout,t,y) xlabel('time (t)') ylabel('v(t)')

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RC effective by Matlap RC too large RC too small

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conclusion Clearly, main advantage of Full AM modulation is very simple and cost effective demodulation of the signal at the receiving end. But AM is as wasteful of spectrum as DSB-SC and requires a large carrier amplitude which in turns require more overall power to be transmitted. (Transmission of carrier is a waste of power since it does not carry information except its phase and frequency).

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GUI TOOL This tool is used to give a simple understanding of this experiment and generally of the amplitude modulation. You can use it ENJOY

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**Intelligent Islamic Electrical Engineers**

IIEE Soon … in Al-Aqsa

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Standard Amplitude Modulation (AM)

Standard Amplitude Modulation (AM)

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