lab4 am modulation
TRANSCRIPT
LAB REPORT
EXPERIMENT
INTRODUCTION TO AMPLITUDE MODULATION
INTRODUCTION TO AMPLITUDE MODULATION
Purpose: The objectives of this laboratory are: 1. To introduce the spectrum analyzer as used in frequency domain analysis. 2. To implement theoretically functional blocks using the Communications Simulink Block.
Equipment List: 1. PC with Matlab and Simulink 2. Theoretical basis about equation of the AM, FM
Pre questions befor pactices:
1. DFT, FFT theoretical 2. Spectrum of sinus waveform 3. Spectrum of sinus waveform multiplication
A: Exersices.(All exersices must be completed) Exersice 1. Implement and sketch an a simple sine wave and spectrum of Sine wave form. Exersice 2. Implement and sketch an output y = kmcos(2f1t)*cos(2f2t) and spectrum of this wave form. Exersice 3. Implement and sketch the output signal of AM modulation.
Exersice 3. Implement and sketch the output signal of FM modulation. The carrier signal is represented by c(t) = A cos(wct)
The modulating signal is represented by m(t) = B sin(wmt)
Then the final modulated signal is A cos(wct + m(t)) = A cos(wct + B sin(wmt))
B: Theoretical Experiment.
I Spectrum Analyzer and Function Generator. This section deals with looking at the spectrum of simple waves. We first look at the spectrum of a simple sine wave. To Start Simulink: Start Matlab then type simulink on the command line. A Simulink Library Window opens up as shown in figure 1.
Figure 1.1
ttaky m )10000(2cos())1000(2cos(1(
Spectrum of a simple sine wave: - Figure 1.2 shows the design for viewing the spectrum of a simple sine wave.
Figure 1.2 Figure 1.3 shows the time-domain sine wave and the corresponding frequency domain is shown in figure 1.4. The frequency domain spectrum is obtained through a buffered-FFT scope, which comprises of a Fast Fourier Transform of 128 samples which also has a buffering of 64 of them in one frame. The property block of the B-FFT is also displayed in figure 1.5.
Figure 1.3 Figure 1.4
Figure 1.5
This is the property box of the Spectrum Analyzer
From the property box of the B-FFT scope the axis properties can be changed and the Line properties can be changed. The line properties are not shown in the above. The Frequency range can be changed by using the frequency range pop down menu and so can be the y-axis the amplitude scaling be changed to either real magnitude or the dB (log of magnitude) scale. The upper limit can be specified as shown by the Min and Max Y-limits edit box. The sampling time in this case has been set to 1/5000. Note: The sampling frequency of the B-FFT scope should match with the sampling time of the input time signal. Also as indicated above the FFT is taken for 128 points and buffered with half of them for an overlap. Calculating the Power: The power can be calculated by squaring the value of the voltage of the spectrum analyzer. Note: The signal analyzer if chosen with half the scale, the spectrum is the single-sided analyzer, so the power in the spectrum is the total power. Similar operations can be done for other waveforms � like the square wave, triangular. These signals can be generated from the signal generator block.
II Waveform Multiplication (Modulation) The implementation of the output y = kmcos2(2ft), when km = 1 was shown below.
Figure 1.6 The following figure demonstrates the waveform multiplication. A sine wave of f1kHz is generated using a sine wave generator and multiplied with a replica signal. The input signal, the output and output of the multiplier are shown in figures Figure 1.6. It can be seen that the output of the multiplier in time domain is basically a sine wave but doesn�t have the negative sides. Since they get canceled out in the multiplication.
Figure 1.7
The spectral output of the spectrum is shown below. It can be seen that there are two side components in spectrum and a central impulse.
If a DC component was present in the input waveform, then y = km*(cos(21000t) + Vdc)2
= km*(cos2(21000t) + 2cos(21000t)*Vdc + Vdc2) The effect of adding a dc component to the input has the overall effect of raising the amplitude of the 2KHz component and decreases the 2KHz component and adding the 1KHz component. Figure shows the multiplication of two difference signal waveform. The Signals are at 1kHz and 10kHz.
The output is shown below. It can be seen that the output consists of just two side bands at +(fc + fm) and the other at �(fc + fm) , i.e. at 9kHz and 11kHz.
By multiplying the carrier signal and the message signal, we achieve modulation.
Y*m(t) = [km cos (21000t)*cos (210000t)] We observe the output to have no 10KHz component i.e., the carrier is not present. The output contains a band at 9KHz (fc-fm) and a band at 11KHz (fc+fm). Note: By varying the multiplication of two difference sinus waveform we observe that the 2 sidebands move according to the equation fcfm. Amplitude Modulation: This experiment is the amplitude modulation for modulation index a = 0.5. From the equation of the AM
The representation of the signal in both time-domain and frequency domain when km=1 for a=0.5 were found to be as shown in figures. The experimental set up for generating an AM signal looks like this:
The waveforms at various levels of modulation are shown in the following figures.
ttaky m )10000(2cos())1000(2cos(1(
The results from the experiment were shown. The results from the experiment are pretty much the same as in the theoretical ones except there are 2 other peaks at 0 and 1000kHz. This is the same as earlier experiment. The cause of this problem is probably the multiplier.
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AM waveform when a=0.5
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Appendix
PRE LAB
INTRODUCTION TO AMPLITUDE MODULATION
III. Sketch the time and frequency domain representations(magnitude only) of the following: A. Cos 2ft f = 1kHz Sine Wave The time and frequency domain of the input signal is shown as below.
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subplot(2,1,1); x = -5:0.001:5; t = 0:1/4000:1; time = cos(2*3.14*1000*t); y1 = cos(2*3.14*1000*x); plot(x,y1) axis([-5 5 -3 3]); grid on zoom on
Spectrum Analyzer
SCOPE
xlabel('Time domain'); ylabel('Amplitude'); % now create a frequency vector for the x-axis and plot the magnitude and phase subplot(2,1,2); fre = abs(fft(time)); f = (0:length(fre) - 1)'*4000/length(fre); plot(f,fre); %axis([0 1 -1 10]); %axis([0 0.75 -2 2]); grid on zoom on xlabel('Freq domain'); ylabel('Amplitude'); B. Square wave period = 1msec, amplitude = 1v Square Wave
CODE: subplot(2,1,1); x = -5:0.001:5; Fs = 399; t = 0:1/Fs:1; time = SQUARE(2*3.14*1000*t); y1 = SQUARE(2*3.14*1000*x); plot(x,y1) axis([-5 5 -3 3]); grid on zoom on xlabel('Time domain'); ylabel('Amplitude'); % now create a frequency vector for the x-axis and plot the magnitude and phase subplot(2,1,2); fre = abs(fft(time)); f = (0:length(fre) - 1)'*Fs/length(fre); plot(f,fre); %axis([0 1 -1 10]); %axis([0 0.75 -2 2]);
Spectrum Analyzer
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grid on zoom on xlabel('Freq domain'); ylabel('Amplitude');
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C. Cos2(2ft) f = 1kHz subplot(2,1,1); x = -5:0.001:5; Fs = 1699; t = 0:1/Fs:1; time = cos(2*3.14*1000*t).*cos(2*3.14*1000*t); y1 = cos(2*3.14*1000*x).*cos(2*3.14*1000*x); plot(x,y1) axis([-5 5 -3 3]); grid on zoom on xlabel('Time domain'); ylabel('Amplitude'); % now create a frequency vector for the x-axis and plot the magnitude and phase subplot(2,1,2); fre = abs(fft(time)); f = (0:length(fre) - 1)'*Fs/length(fre); plot(f,fre); %axis([0 1 -1 10]);
%axis([0 0.75 -2 2]); grid on zoom on xlabel('Freq domain'); ylabel('Amplitude');
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II A carrier Cos 2(5000)t is modulated by a single tone Cos 2(1000)t. The time and freq domain representation are shown. A. Double side-band � suppressed carrier modulation
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% Modulating the single tone message signal. Ts = 199; subplot(4,1,1); t = 0:1/Ts:1; m = cos(2*3.14*1000*t); plot(t,m); grid on zoom on % plot of the carrier signal subplot(4,1,2); c = cos(2*3.14*5000*t); plot(t,c); grid on zoom on % plot of the DSB signal with Suppresed carrier intime domain subplot(4,1,3); d = m.*c; plot(t,d); grid on zoom on % freq. domain of the DSB signal. subplot(4,1,4); fre = abs(fft(d)); f = (0:length(fre) - 1)'*Ts/length(fre); plot(f,fre); %axis([0 1 -1 10]); axis([0 100 0 50]); grid on
zoom on xlabel('Freq domain'); ylabel('Amplitude'); B. 100% AM modulation ( modulation index = 1) % Modulating the single tone message signal. Ts = 199; K = 1; a = 1; subplot(4,1,1); t = -1:1/Ts:1; m = cos(2*3.14*1000*t); plot(t,m); grid on zoom on % plot of the carrier signal subplot(4,1,2); c = cos(2*3.14*5000*t); plot(t,c); grid on zoom on % plot of the DSB signal with Suppresed carrier intime domain subplot(4,1,3); d = (K + a*m).*c; plot(t,d); grid on zoom on % freq. domain of the DSB signal. subplot(4,1,4); fre = abs(fft(d)); f = (0:length(fre) - 1)'*4000/length(fre); plot(f,fre); %axis([0 1 -1 10]); %axis([0 0.75 -2 2]); grid on zoom on xlabel('Freq domain'); ylabel('Amplitude'); %axis([0 2000 0 205]);
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C. 50% AM modulation (modulation index = 0.5) Ts = 199; K = 1; a = 1; subplot(4,1,1); t = -1:1/Ts:1; m = cos(2*3.14*1000*t); plot(t,m); grid on zoom on % plot of the carrier signal subplot(4,1,2); c = cos(2*3.14*5000*t); plot(t,c); grid on zoom on % plot of the DSB signal with Suppresed carrier intime domain subplot(4,1,3); d = (K + a*m).*c; plot(t,d); grid on zoom on % freq. domain of the DSB signal. subplot(4,1,4); fre = abs(fft(d)); f = (0:length(fre) - 1)'*4000/length(fre); plot(f,fre);
%axis([0 1 -1 10]); %axis([0 0.75 -2 2]); grid on zoom on xlabel('Freq domain'); ylabel('Amplitude'); %axis([0 2000 0 205]); Single Side Band Modulation (lower side band)
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The single side band waveform can be obtained by filtering the DSB signal. Filtering out the lower side band give the upper side � i.e. the SSB signal with the upper side bands. So by low passing the DSB signal we get the lower side band of the SSB signal.
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D. By changing the modulating signal in frequency the distance between the carrier and
the side bands change as shown in figure for a increase and decrease in the frequency of the modulating signal.
Increasing the frequency f = 4000Hz.
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Decreasing the Frequency f = 990Hz
III Two Tone (1kHz and 2kHz) modulating a carrier of 5kHz. A. Double side band suppressed carrier
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B. 100% AM modulation ( modulation index = 1) % Modulating the single tone message signal. Ts = 199; K = 1; a = 1s; subplot(4,1,1); t = -1:1/Ts:1; m = cos(2*3.14*1000*t) + cos(2*3.14*2000*t); plot(t,m); title('2 tone Double side band - suppressed carrier modulation'); xlabel('Time'); ylabel('Amplitude'); grid on zoom on % plot of the carrier signal subplot(4,1,2); c = cos(2*3.14*5000*t); plot(t,c); grid on zoom on % plot of the DSB signal with Suppresed carrier intime domain
subplot(4,1,3); d = (K + a*m).*c; plot(t,d); grid on zoom on % freq. domain of the DSB signal. subplot(4,1,4); fre = abs(fft(d)); f = (0:length(fre) - 1)'*4000/length(fre); plot(f,fre); %axis([0 1 -1 10]); %axis([0 0.75 -2 2]); grid on zoom on xlabel('Freq domain'); ylabel('Amplitude'); %axis([0 2000 0 205]);
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C.50% AM modulation (modulation index = 0.5)
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