1. Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion Outline of discussion DIRECT MODELING APPROACH 1.How small-signal variations in the switching frequency affect the spectrum of the switch network output voltage v s1 (t) 2.Passing the frequency-modulated voltage v s1 (t) through the tank transfer function H(s) leads to amplitude modulation of the output voltage v(t) 3.How to recover the envelope of the output voltage and determine the small-signal control-to-output-envelope transfer function G env (s) PHASOR TRANSFORMATION APPROACH 1.Equivalent circuit modeling via the phasor transform 2.PSPICE simulation of G env (s) using the phasor transform

2. Fundamentals of Power Electronics 2 Chapter 19: Resonant Conversion Conventional phasor definition (sinusoidal steady state)

3. Fundamentals of Power Electronics 3 Chapter 19: Resonant Conversion Equivalent device models in phasor domain in sinusoidal steady-state

5. Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion Applying the conventional definition to amplitude and angle-modulated waveforms

7. Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion Extending the phasor definition

8. Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion Applying the generalized phasor definition to amplitude and angle-modulated waveforms

9. Fundamentals of Power Electronics 9 Chapter 19: Resonant Conversion Equivalent device models in phasor domain using generalized phasor definition

10. Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion Equivalent device models in phasor domain using generalized phasor definition

11. Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion Large signal phasor models of circuit elements

12. Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion Linearizing the device models

13. Fundamentals of Power Electronics 13 Chapter 19: Resonant Conversion Linearizing the device models

14. Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion Inductor equivalent circuit model

15. Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion Inductor equivalent circuit model

16. Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion Inductor equivalent circuit model

17. Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion Linearizing the device models

18. Fundamentals of Power Electronics 18 Chapter 19: Resonant Conversion Small-signal phasor models of circuit elements

19. Fundamentals of Power Electronics 19 Chapter 19: Resonant Conversion Some insight

20. Fundamentals of Power Electronics 20 Chapter 19: Resonant Conversion Modelling the switch network

21. Fundamentals of Power Electronics 21 Chapter 19: Resonant Conversion One way

22. Fundamentals of Power Electronics 22 Chapter 19: Resonant Conversion More general – model the switch network with an equivalent transformer

23. Fundamentals of Power Electronics 23 Chapter 19: Resonant Conversion Steps

24. Fundamentals of Power Electronics 24 Chapter 19: Resonant Conversion Steps

25. Fundamentals of Power Electronics 25 Chapter 19: Resonant Conversion Steps

26. Fundamentals of Power Electronics 26 Chapter 19: Resonant Conversion The generalized phasor transformer model

27. Fundamentals of Power Electronics 27 Chapter 19: Resonant Conversion Power balance in the phasor transformer model

28. Fundamentals of Power Electronics 28 Chapter 19: Resonant Conversion Power balance in the phasor transformer model

29. Fundamentals of Power Electronics 29 Chapter 19: Resonant Conversion Linearization of the transformer model