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 1. Spectrum of v s1 (t)

4. Fundamentals of Power Electronics 4 Chapter 19: Resonant Conversion

5. Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion Spectra of frequency-modulated signal

8. Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion Spectra of frequency-modulated signal via Bessel functions

9. Fundamentals of Power Electronics 9 Chapter 19: Resonant Conversion Dynamic analysis of resonant inverters

10. Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion Assumptions so far

11. Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion 2. Effect of the tank transfer function narrowband

12. Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion One way

13. Fundamentals of Power Electronics 13 Chapter 19: Resonant Conversion Phasor analysis

14. Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion Total output voltage and envelope

15. Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion Intepretation: time-varying phasor representation of output voltage

16. Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion 3. Extract expression for envelope

17. Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion Square and linearization

18. Fundamentals of Power Electronics 18 Chapter 19: Resonant Conversion Square root and linearization

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

20. Fundamentals of Power Electronics 20 Chapter 19: Resonant Conversion The transfer function G env (s)