1. Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion Announcements Prof. Erickson PDF slides on AC modeling posted on website. Some comments on handwritten notes / slides Some comments on HW #4 (due for on-campus students Mon. Feb 18) G env = G env,vin “Root Locus” Salient features Algebra

2. Fundamentals of Power Electronics 2 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

3. Fundamentals of Power Electronics 3 Chapter 19: Resonant Conversion Phasor analysis

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

11. Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion Result: Small-signal expression for envelope

12. Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion What is G env (s)?

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

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

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

16. Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion The DC gain G env (s)

17. Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion Phasor representation of amplitude and frequency modulated signals For amplitude modulation: For frequency and amplitude modulation (traditional phasor definition): For frequency and amplitude modulation (modified phasor definition):

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