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 Phasor analysis

5. Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion Total output voltage and envelope

6. Fundamentals of Power Electronics 6 Chapter 19: Resonant Conversion Intepretation: time-varying phasor representation of output voltage

7. Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion 3. Extract expression for envelope

8. Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion Square and linearization

9. Fundamentals of Power Electronics 9 Chapter 19: Resonant Conversion Square root and linearization

10. Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion Result: Small-signal expression for envelope

11. Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion What is G env (s)?

12. Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion The poles G env (s)

13. Fundamentals of Power Electronics 13 Chapter 19: Resonant Conversion The poles G env (s)

14. Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion The numerator of G env (s)

15. Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion The DC gain G env (s)