2. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 1 Frequency response:

3. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 2 Let Then and

4. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 3 Therefore;

5. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 4 Overall db gain =sum of individual db gains + +=

6. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 5 Overall phase =sum of individual phases + +=

7. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 6 Bode plot Plot of db magnitude vs. Log frequency Plot of phase vs. Log frequency

8. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 7 Semi-log paper Bode Diagram Frequency (rad/sec) Phase (deg) Magnitude (dB) 10 10 0 1 2 1 decade 1 octave

9. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode 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

10. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 9 “simple” factors Origin zero Constant multiplier Origin pole Finite real zero Finite real pole Conjugate zero pair Conjugate pole pair

11. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 10 Constant multiplier K 20log K

12. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 11 =1=1 Slope = 20 db/decade  log Origin zero: s

13. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 12 =1=1  log Slope = -20 db/decade Origin pole:

14. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 13 As Finite real zero

15. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 14 Asymptotes

16. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 15 Deviations from actual 3 db 1 octave 1 db 1 octave 1 db

17. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 16 Finite real zero: Phase vs. Frequency  =10z  =z/10  =z 1 decade

18. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 17 1 decade  =z 0 0.1 rad

19. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 18 Finite real pole

20. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 19 Asymptotes

21. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 20 3 db 1 octave 1 db 1 octave 1 db

22. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 21 Finite real pole: Phase vs. Frequency 1 decade  =z 0 0.1 rad

23. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 22 Conjugate zero pair:

24. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 23

25. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 24 1 octave Magnitude vs. frequency 6 db 1 db

26. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 25 0  Phase vs. frequency

27. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 26 Conjugate pole pair:

28. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 27

29. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 28 1 octave Magnitude vs. frequency

30. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 29 0 ---- Phase vs. frequency

31. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 30 T4T4 T3T3 T2T2 T1T1 Example

32. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 31 Frequency (rad/sec) Phase (deg) Magnitude (dB) 0.1110100 0 -20 -40 -60 90 0 -90 -180

33. Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 32 -60 -40 -20 0 20 Magnitude (dB) 10 10 0 1 2 -180 -135 -90 -45 Phase (deg) Frequency (rad/sec)