1 / 26

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

Engineering 43. 2 nd order Filters MATLAB BodePlt. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. Signal Filters. The FOUR Basic Filter Types: Low pass filters PASS LOW frequencies and attenuate high frequencies.

ramya
Download Presentation

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Engineering 43 2nd order FiltersMATLAB BodePlt Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. 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. IDEAL Signal Filters • Ideal Filters Characteristics: • The lowpass filter passes all frequencies below fc. • The highpass filter passes all frequencies above fc. • The bandpass filter passes all frequencies between fc1 and fc2. • The bandstop (or Notch) filter attenuates all frequencies between fc1 and fc2.

  4. RLC LOWpass Filter • Last Time We analyzed the RLC BAND-pass Filter • ReArrange the RLC Series Ckt to Produce LOW-passBehavior

  5. RLC LOWpass Filter • Using Frequency Domain Voltage-Divider Analysis: • As beforeuse: • With Enough Complex Algebra find:

  6. 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. RLC HIGHpass Filter • Last Time We analyzed the RLC BAND-pass Filter • ReArrange the RLC Series Ckt to Produce HIGH-passBehavior

  8. RLC HIGHpass Filter • Using Frequency Domain Voltage-Divider Analysis: • As beforeuse: • With Enough Complex Algebra find:

  9. 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. RLC NOTCH (BandReject) Filter • Last Time We analyzed the RLC Band-PASS Filter • ReArrange the RLC Series Ckt to Produce BandREJECT Behavior

  11. RLC BandReject (notch) Filter • Using Frequency Domain Voltage-Divider Analysis: • As beforeuse: • With Enough Complex Algebra find:

  12. 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. 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. 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 FilterWhichEliminatestheInductor

  15. 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. dualT Notch Filter Magnitude

  17. dualT Notch Filter Phase

  18. % Bruce Mayer, PE % ENGR43 • 17Jul11 % Lec6c_Dual_T_NotchFilter_1107.m % w = logspace(1,6,1500); % w = 2*pi*f % symsK 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') MATLAB Code

  19. All Done for Today Butterworth’sOriginal1930 Work

  20. Engineering 43 Appendix Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

More Related