1. Fundamentals of PWM Dc-to-Dc Power Conversion Dynamic Performance of PWM Dc-to-Dc Converters

2. 2 Performance of PWM Dc-to-Dc Converters Dc-to-Dc Converter Performance ● Static performance: ● Dynamics performance Stability Frequency-domain response: Time-domain response:

3. 3 Buck Converter Example Stability

4. 4 Stability of Buck Converter Stability

5. 5 Loop Gain Stability

6. 6 Stability of Buck Converter Stability

7. 7 Input-to-Output Frequency Response: ● Input-to-output transfer function: : Laplace transformation of ac component of : Laplace transformation of ac component of Frequency-Domain Performance Criteria

8. 8 Audio-Susceptibility Time-Domain Performance Criteria Audio-susceptibility

9. 9 Input-to-Output Frequency Response Frequency-Domain Performance Criteria

10. 10 Load Current-to-Output Transfer Function: ● Load current-to-output transfer function: : : Laplace transformation of ac component of : Laplace transformation of ac component of Frequency-Domain Performance Criteria

11. 11 Output Impedance Time-Domain Performance Criteria Output impedance

12. 12 Load Current-to-Output Frequency Response Time-Domain Performance Criteria Output impedance

13. 13 Step Load Response ● Transient response of the output voltage due to step change in the input voltage Time-Domain Performance Criteria

14. 14 Output Impedance and Step Load Response Time-Domain Performance Criteria Output impedanceStep load response

15. 15 Step Input Response Time-Domain Performance Criteria ● Transient response of the output voltage due to step change in load current

16. 16 Audio-Susceptibility and Step Input Response Time-Domain Performance Criteria Audio-susceptibility Step input response

17. 17 Definition of Stability ● Stability of transfer function T(s) or stability of an LTI system having T(s) as its transfer function ● T(s) or LTI system is stable if and only if all the roots of the characteristic equation are located in the left-half plane(LHP) of the s-plane Stability Definition

18. 18 Nyquist (Stability) Criterion ● Nyquist(Stability) Criterion: Graphical method to determine the number of RHP roots in 1+T m (s)=0 Nyquist Criterion

19. 19 Application Example ● ● Characteristic equation Nyquist Criterion

20. 20 Stability Analysis of PWM Converters Nyquist Criterion

21. 21 Nyquist Analysis on 1+T m (s)=0 Nyquist Criterion

22. 22 Absolute Stability Nyquist Criterion

23. 23 Stability Analysis Using Bode Plot Nyquist Criterion

24. 24 Marginally Stable Buck Converter

25. 25 Marginally Stable Buck Converter

26. 26 Conditionally Stable System Marginally Stable Buck Converter

27. 27 Effect of Gain and Phase Delay Relative Stability

28. 28 Gain Margin ● Gain margin : the amount of gain increase that can be added to before the system becomes unstable, Stability Margins

29. 29 Phase Margin ● Phase margin : the amount of phase delay that can be added to before the system becomes unstable, Stability Margins

30. 30 Gain Margin and Phase Margin Stability Margins

31. 31 Stability Margins and Closed-Loop Performance ● Proximity to (-1,0) point Small stability margin Nearness of poles to imaginary axis:

32. 32 Buck Converter Example Stability Margins and Closed-Loop Performance

33. 33 Buck Converter Example Stability Margins and Closed-Loop Performance

34. 34 Buck Converter Example: Step Load Response Stability Margins and Closed-Loop Performance