Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion Outline of discussion DIRECT MODELING APPROACH 1.How small-signal variations in the.

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Outline of discussion DIRECT MODELING APPROACH

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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

Fundamentals of Power Electronics 2 Chapter 19: Resonant Conversion 1. Spectrum of v s1 (t)

Fundamentals of Power Electronics 4 Chapter 19: Resonant Conversion

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

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

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

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

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

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

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

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

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

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

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

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

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

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