1. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 43 2nd order Filters MATLAB BodePlt

2. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 2 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Signal Filters  The FOUR Basic Filter Types: Lowpass filters PASS LOW frequencies and attenuate high frequencies. Highpass filters PASS HIGH frequencies and attenuate low frequencies. Bandpass filters PASS A CERTAIN BAND of frequencies, and attenuate all else Bandstop (also called bandREJECT or NOTCH) filters ATTENUATE A CERTAIN BAND of frequencies, and pass all else

3. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 3 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis IDEAL Signal Filters  Ideal Filters Characteristics: The lowpass filter passes all frequencies below f c. The highpass filter passes all frequencies above f c. The bandpass filter passes all frequencies between f c1 and f c2. The bandstop (or Notch) filter attenuates all frequencies between f c1 and f c2.

4. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 4 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC LOWpass Filter  Last Time We analyzed the RLC BAND-pass Filter  ReArrange the RLC Series Ckt to Produce LOW-passBehavior

5. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 5 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC LOWpass Filter  Using Frequency Domain Voltage- Divider Analysis:  As before use:  With Enough Complex Algebra find:

6. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 6 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC LoPass Performance Don’t Like the Humps, Take Q≈1 u = logspace(-1,3,500); % u = f/f0 H_5 = 20*log10(abs((-j*0.5*(1./u))./(1+j*0.5*(u-1./u)))); H1 = 20*log10(abs((-j*1*(1./u))./(1+j*1*(u-1./u)))); H2 = 20*log10(abs((-j*2*(1./u))./(1+j*2*(u-1./u)))); H5 = 20*log10(abs((-j*5*(1./u))./(1+j*5*(u-1./u)))); semilogx(u,H_5, u,H1, u,H2, u,H5, 'LineWidth',3), grid axis([0.1 100 -80 20]) LoPasslegend = legend('Q=0.5','Q=1','Q=2','Q=5'); xlabel('f/f_{0}') ylabel(' RLC LoPass |H(f)| (dB)‘)

7. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 7 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC HIGHpass Filter  Last Time We analyzed the RLC BAND-pass Filter  ReArrange the RLC Series Ckt to Produce HIGH-passBehavior

8. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 8 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC HIGHpass Filter  Using Frequency Domain Voltage- Divider Analysis:  As before use:  With Enough Complex Algebra find:

9. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 9 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC HiPass Performance Don’t Like the Humps, Take Q≈1 u = logspace(-1,3,500); % u = f/f0 H_5 = 20*log10(abs((j*0.5*u)./(1+j*0.5*(u-1./u)))); H1 = 20*log10(abs((j*1*u)./(1+j*1*(u-1./u)))); H2 = 20*log10(abs((j*2*u)./(1+j*2*(u-1./u)))); H5 = 20*log10(abs((j*5*u)./(1+j*5*(u-1./u)))); semilogx(u,H_5, u,H1, u,H2, u,H5, 'LineWidth',3), grid axis([0.1 100 -40 20]) LoPasslegend = legend('Q=0.5','Q=1','Q=2','Q=5'); xlabel('f/f_{0}') ylabel(' RLC LoPass |H(f)| (dB)')

10. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 10 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC NOTCH (BandReject) Filter  Last Time We analyzed the RLC Band-PASS Filter  ReArrange the RLC Series Ckt to Produce BandREJECT Behavior

11. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 11 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC BandReject (notch) Filter  Using Frequency Domain Voltage- Divider Analysis:  As before use:  With Enough Complex Algebra find:

12. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 12 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC Notch Performance u = logspace(-2,2,1500); % u = f/f0 H_5 = 20*log10(abs((j*0.5*(u-1./u))./(1+j*0.5*(u-1./u)))); H1 = 20*log10(abs((j*1*(u-1./u))./(1+j*1*(u-1./u)))); H2 = 20*log10(abs((j*2*(u-1./u))./(1+j*2*(u-1./u)))); H5 = 20*log10(abs((j*5*(u-1./u))./(1+j*5*(u-1./u)))); semilogx(u,H_5, u,H1, u,H2, u,H5, 'LineWidth',2), grid axis([0.01 100 -50 10]) LoPasslegend = legend('Q=0.5','Q=1','Q=2','Q=5'); xlabel('f/f_{0}') ylabel(' RLC Notch |H(f)| (dB)‘)

13. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 13 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis RLC bandPASS Performance u = logspace(-2,2,1500); % u = f/f0 H_5 = 20*log10(abs((j*0.5*(u-1./u))./(1+j*0.5*(u- 1./u)))); H1 = 20*log10(abs((j*1*(u-1./u))./(1+j*1*(u-1./u)))); H2 = 20*log10(abs((j*2*(u-1./u))./(1+j*2*(u-1./u)))); H5 = 20*log10(abs((j*5*(u-1./u))./(1+j*5*(u-1./u)))); semilogx(u,H_5, u,H1, u,H2, u,H5, 'LineWidth',2), grid axis([0.01 100 -50 10]) LoPasslegend = legend('Q=0.5','Q=1','Q=2','Q=5'); xlabel('f/f_{0}') ylabel(' RLC Notch |H(f)| (dB)‘)

14. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 14 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis WhiteBoard Work  The RLC Notch Filter has the disadvantage of Using an INDUCTOR L’s are Large & Heavy relative to R’s & C’s  An Alternative is the “dual-T” Notch Filter Which Eliminates the Inductor

15. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 15 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis WhiteBoard Work  For the Dual-T Notch Filter Use Hand-Analysis to Derive the TRANSFER FUNCTION Use MATLAB to Create the BODE PLOT for the case where R = 2kΩ & C=120nF

16. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 16 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis dualT Notch Filter Magnitude

17. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 17 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis dualT Notch Filter Phase

18. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 18 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis MATLAB Code % Bruce Mayer, PE % ENGR43 17Jul11 % Lec6c_Dual_T_NotchFilter_1107.m % w = logspace(1,6,1500); % w = 2*pi*f % syms K HK = ((1+1/K)+ K*(1+K))/(2*(1+K)^2*(1+1/K)-K*(1+K)-(1+1/K)) Hsimp = simplify(HK) % C = 120e-9; R = 2000; H = (1-C^2*R^2*w.^2)./((1-C^2*R^2*w.^2) + j*4*w*C*R); Hmag = 20*log10(abs(H)); Hphi = angle(H)*180/(2*pi); semilogx(w,Hmag, 'LineWidth',3), grid axis([10 1e6 -50 10]) xlabel('\omega = 2\pif (rad/s)') ylabel('|H(f)| (dB)') title('Dual-T Notch Filter: R=2k, C=120n') % PAUSE Coming disp('showing MAG plot; hit ANY KEY to continue') pause % Plot Phase Angle semilogx(w,Hphi, 'LineWidth',3), grid axis([10 1e6 -50 50]) xlabel('\omega = 2\pif (rad/s)') ylabel('Angle H(f) (°)') title('Dual-T Notch Filter: R=2k, C=120n')

19. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 19 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis All Done for Today Butterworth’s Original 1930 Work

20. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 20 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 43 Appendix

21. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 21 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

22. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 22 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

23. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 23 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

24. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 24 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

25. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 25 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

26. BMayer@ChabotCollege.edu ENGR-43_Lec-06c_2ndOrder-Filter_MATLAB-BodePlots.pptx 26 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis