Generating AM wave
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1. The document describes an experiment to generate AM waves at different modulation indices and analyze the effect on sideband power and bandwidth. 2. The results show that sideband power increases with increasing modulation index, while bandwidth remains constant at 1000Hz regardless of modulation index. 3. The maximum modulation index for AM is 1, as overmodulation leading to signal distortion can occur if the index exceeds 1.
Generating AM wave
- 1. 1 Lab Report 04: Generating AM wave at a different modulation index Submitted By : Syed Abuzar Hussain Shah Reg # : SP15-BEE-096 Submitted To: Sir Atiq-ul-Anam Class: BEE-5A Dated: 23/05/2017
- 2. 2 Statement: Generate AM wave (Amplitude Modulation) at a different modulation index. Verify whether the modulation index depends on the band width of AM modulated wave or the power of side bands? Literature Background: Amplitude Modulation: The amplitude modulation is a technique in which the amplitude of the carrier changes according to the instantaneous amplitude of the baseband signal. ( ) ( ) (1) Power of a Signal: Power is energy over a time period. ∫ | | (2) In MATLAB power is calculated by: ∑ | | (3) Band width: Difference of highest and lowest frequencies which contain 90% energy of the signal. Where bandwidth of an AM is given by B.W=2*fm (4) “fm” is the highest frequency of baseband signal. Procedure: MATLAB Coding: clc clear all close all
- 3. 3 t=0:1:200; fm=500; fc=20*fm; Vc=10; MA=1; Vm=MA*Vc; phase =0; fs=10*fc; ts=t/fs; Xm=Vm*cos(2*pi*fm*ts+phase); plot(ts*1000,Xm) title('baseband signal') xlabel('time in ms') ylabel('Vm') grid on; figure Xc=Vc*cos(2*pi*fc*ts+phase); plot(ts*1000,Xc) title('carrier signal') xlabel('time in ms') ylabel('Vc') grid on; figure Y=Xc+Xm.*cos(2*pi*fc*ts+phase); plot(ts*1000,Y) title('Amplitude Modulated wave') xlabel('time in ms') ylabel('Vc+Vm') grid on; figure z=fft(Y); z=abs(z(1:length(z)/2+1)); frq=(0:length(z)-1)*fs/length(z)/2; plot(frq/1000,z); title('FFT of Modulated Wave') xlabel('F in kHz') ylabel('Amplitude') grid on;
- 4. 4 carrier_power = sum(Xc.^2)/length(t); display(carrier_power); entire_power = sum(Y.^2)/length(t); display(entire_power); sideband_power = entire_power-carrier_power; display(sideband_power); Analysis: = 0 Figure 1: Baseband signal with fm=500Hz, =0V Figure 2: Carrier signal with fc=10kHz =10V
- 5. 5 Figure 3: Amplitude Modulated Signal Figure 4: AM Wave in Frequency Domain carrier_power = 50.2488 entire_power = 50.2488 sideband_power = 0
- 6. 6 = 0.5 Figure 5: Baseband signal with fm=500Hz, =5V Figure 6: Carrier signal with fc=10kHz, =10V
- 7. 7 Figure 7: Amplitude Modulated Signal Figure 8: AM Wave in Frequency Domain carrier_power = 50.2488 entire_power = 57.0896 sideband_power = 6.8408
- 8. 8 = 1 Figure 9: Baseband signal with fm=500Hz, =10V Figure 10: Carrier signal with fc=10kHz, =10V
- 9. 9 Figure 11: Amplitude Modulated Signal Figure 12: AM Wave in Frequency Domain carrier_power = 50.2488 entire_power = 76.6169 sideband_power = 26.3682
- 10. 10 = 1.5 Figure 13: Baseband signal with fm=500Hz, =15V Figure 14: Carrier signal with fc=10kHz, =10V
- 11. 11 Figure 15: Amplitude Modulated Signal Figure 16: AM Wave in Frequency Domain carrier_power = 50.2488 entire_power = 108.8308 sideband_power = 58.5821
- 12. 12 Table # 01: S.No Modulation Index Power in entire AM Wave Power in side bands only Bandwidth in Hz 1 0 50.2488 0 1 2 0.5 57.0896 6.8408 1000 3 1 76.6169 26.3682 1000 4 1.5 108.8303 58.5821 1000 Questions: Q1) What will happen to the power of side bands (increasing or decreasing) with the increase of modulation index? Give mathematical reasoning? Ans: Relation for Power of the side bands is (5) is power of sidebands is power of carrier wave is Modulation index From eq(5) it is clearly seen that power of the sidebands is directly proportional to the Modulation index. With the increase in Modulation index, power of the side bands also increases. Q2) What will happen to the band width of AM wave (increasing or decreasing) with the increase of modulation index? Give mathematical reasoning? Ans: The band width of AM wave does not depends on Modulation index. If Modulation index is increased or decreased, the bandwidth of AM will remains same.
- 13. 13 Mathematically: Bw=2*fm (6) From eq(6) we clearly see that bandwidth depends on the higher frequency of baseband signal not on Modulation index. Q3) Why the modulation index in AM is not greater than 1? Ans: Maximum value of Modulation index for AM is 1 because when Modulation index is greater than 1, over modulation occurs and distortion created in signal and information will be lost. Mathematically: (7) When = , =1 If is further increased, Over Modulation occurs which will cause distortion in transmitted signal. Conclusion: Transmitted Power and Power of side bands increases with increase in Modulation index. Band width of AM is independent of Modulation index. Band width of AM depends on the highest frequency of baseband signal. Bw=2*fm Bandwidth is 1Hz when Modulation index is 0 because and =0. Transmitted Signal will be distorted when Modulation index >1.