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Frequency response:

Frequency response:. Let. Then. and. Therefore;. +. Overall db gain =sum of individual db gains. +. =. +. Overall phase =sum of individual phases. +. =. Bode plot. Plot of db magnitude vs. Log frequency. Plot of phase vs. Log frequency. Bode Diagram. Magnitude (dB).

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Frequency response:

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  1. Frequency response: Bode plots

  2. Let Then and Bode plots

  3. Therefore; Bode plots

  4. + Overall db gain =sum of individual db gains + = Bode plots

  5. + Overall phase =sum of individual phases + = Bode plots

  6. Bode plot Plot of db magnitude vs. Log frequency Plot of phase vs. Log frequency Bode plots

  7. Bode Diagram Magnitude (dB) Phase (deg) -1 0 1 2 10 10 10 10 Frequency (rad/sec) Semi-log paper 1 decade 1 octave Bode plots

  8. Procedure • Factorize the transfer function in to “simple” factors • Obtain magnitude(db) versus frequency and phase versus frequency characteristics for each • Obtain overall magnitude(db) versus frequency characteristics by adding those of factors • Obtain overall phase versus frequency characteristics by adding those of factors Bode plots

  9. Constant multiplier Origin zero Origin pole Finite real zero Finite real pole Conjugate zero pair Conjugate pole pair “simple” factors Bode plots

  10. Constant multiplier K 20logK Bode plots

  11. w log Origin zero: s =1 Slope = 20 db/decade Bode plots

  12. w log Origin pole: =1 Slope = -20 db/decade Bode plots

  13. Finite real zero As As Bode plots

  14. Asymptotes Bode plots

  15. Deviations from actual 1 octave 1 db 1 db 3 db 1 octave Bode plots

  16. =10z =z =z/10 Finite real zero:Phase vs. Frequency 1 decade 1 decade Bode plots

  17. =z 0 1 decade 1 decade 0.1 rad 0.1 rad Bode plots

  18. Finite real pole Bode plots

  19. 1 db 3 db 1 db 1 octave 1 octave Bode plots

  20. =z 0 1 decade 1 decade Finite real pole:Phase vs. Frequency 0.1 rad 0.1 rad Bode plots

  21. Conjugate zero pair: Bode plots

  22. Bode plots

  23. 1 octave 1 octave 6 db 1 db Magnitude vs. frequency Bode plots

  24. Phase vs. frequency  0 Bode plots

  25. Conjugate pole pair: Bode plots

  26. Bode plots

  27. 1 octave 1 octave Magnitude vs. frequency Bode plots

  28. Phase vs. frequency 0 - Bode plots

  29. T3 T1 T2 T4 Example Bode plots

  30. Magnitude (dB) Phase (deg) 0 -20 -40 -60 90 0 -90 -180 0.1 1 10 100 Frequency (rad/sec) Bode plots

  31. 20 0 Magnitude (dB) -20 -40 -60 -45 -90 Phase (deg) -135 -180 -1 0 1 2 10 10 10 10 Frequency (rad/sec) Bode plots

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