1. Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion For both on-campus and CAETE students: A DVD of recorded lectures from Professor Erickson’s Spring ’06 class will be mailed to you sometime next week. These will not be available on the CAETE website CUAnywhere.colorado.edu For on-campus students: You will not have access to this semesters recorded lectures on the CAETE website For CAETE students: By popular request, scanned and e-mailed homework will be accepted provided the submissions meet the following requirements: Black and white (no color, no grayscale) 200 – 300 dpi All problems scanned into ONE PDF file for the whole assignment PDF file is easy to read, easy to open, and easy to print ECEN 5817 Housekeeping update

2. Fundamentals of Power Electronics 2 Chapter 19: Resonant Conversion Chapter 19 Resonant Conversion Introduction 19.1Sinusoidal analysis of resonant converters 19.2Examples Series resonant converter Parallel resonant converter 19.3Soft switching Zero current switching Zero voltage switching 19.4Load-dependent properties of resonant converters 19.5 Exact characteristics of the series and parallel resonant converters

3. Fundamentals of Power Electronics 3 Chapter 19: Resonant Conversion Equivalent circuit of rectifier Rectifier input port: Fundamental components of current and voltage are sinusoids that are in phase Hence rectifier presents a resistive load to tank network Effective resistance R e is With a resistive load R, this becomes Rectifier equivalent circuit Loss free resistor

4. Fundamentals of Power Electronics 4 Chapter 19: Resonant Conversion 19.1.4 Solution of converter voltage conversion ratio M = V/V g Eliminate R e :

5. Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion Conversion ratio M So we have shown that the conversion ratio of a resonant converter, having switch and rectifier networks as in previous slides, is equal to the magnitude of the tank network transfer function. This transfer function is evaluated with the tank loaded by the effective rectifier input resistance R e.

6. Fundamentals of Power Electronics 6 Chapter 19: Resonant Conversion 19.2.2 Subharmonic modes of the SRC Example: excitation of tank by third harmonic of switching frequency Can now approximate v s (t) by its third harmonic: Result of analysis:

7. Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion Subharmonic modes of SRC Not often used - reduced switch utilization and decreased voltage conversion ratio Still need to be aware their existence

8. Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion 19.2 Examples 19.2.1 Series resonant converter

9. Fundamentals of Power Electronics 9 Chapter 19: Resonant Conversion Model: series resonant converter

10. Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion Construction of Z i – Resonant (high Q) case C = 0.1 μF, L = 1 mH, R e = 10 Ω

11. Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion Construction of H = V / V g – Resonant (high Q) case C = 0.1 μF, L = 1 mH, R e = 10 Ω Buck characteristic

12. Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion Construction of Z i

13. Fundamentals of Power Electronics 13 Chapter 19: Resonant Conversion Construction of H

14. Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion Model: series resonant converter

15. Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion Construction of Z i – Non-resonant (low Q) case C = 0.1 μF, L = 1 mH, R e = 1 kΩ

16. Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion Construction of H – Non-resonant (low Q) case C = 0.1 μF, L = 1 mH, R e = 1 kΩ

17. Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion 19.2.3 Parallel resonant dc-dc converter Differs from series resonant converter as follows: Different tank network Rectifier is driven by sinusoidal voltage, and is connected to inductive-input low-pass filter Need a new model for rectifier and filter networks

18. Fundamentals of Power Electronics 18 Chapter 19: Resonant Conversion Model of uncontrolled rectifier with inductive filter network – input port Fundamental component of i R (t) :

19. Fundamentals of Power Electronics 19 Chapter 19: Resonant Conversion Model of uncontrolled rectifier with inductive filter network – output port Output inductor volt second balance: dc voltage is equal to average rectified tank output voltage

20. Fundamentals of Power Electronics 20 Chapter 19: Resonant Conversion Effective resistance R e Again define In steady state, the dc output voltage V is equal to the average value of | v R | : For a resistive load, V = IR. The effective resistance R e can then be expressed

21. Fundamentals of Power Electronics 21 Chapter 19: Resonant Conversion Equivalent circuit model of uncontrolled rectifier with inductive filter network Dependent voltage source based on rectified tank voltage. Vs. SRC, dependent current source based on rectified tank current.

22. Fundamentals of Power Electronics 22 Chapter 19: Resonant Conversion Equivalent circuit model Parallel resonant dc-dc converter

23. Fundamentals of Power Electronics 23 Chapter 19: Resonant Conversion 2 different ways to construct transfer function H

24. Fundamentals of Power Electronics 24 Chapter 19: Resonant Conversion Construction of Z i – Resonant (high Q) case C = 0.1 μF, L = 1 mH, R e = 1 kΩ

25. Fundamentals of Power Electronics 25 Chapter 19: Resonant Conversion Construction of H = V / V g – Resonant (high Q) case C = 0.1 μF, L = 1 mH, R e = 1 kΩ Buck-boost characteristic

26. Fundamentals of Power Electronics 26 Chapter 19: Resonant Conversion Construction of Z o

27. Fundamentals of Power Electronics 27 Chapter 19: Resonant Conversion Construction of H

28. Fundamentals of Power Electronics 28 Chapter 19: Resonant Conversion Dc conversion ratio of the PRC At resonance, this becomes PRC can step up the voltage, provided R > R 0 PRC can produce M approaching infinity, provided output current is limited to value less than V g / R 0

29. Fundamentals of Power Electronics 29 Chapter 19: Resonant Conversion Comparison of approximate and exact characteristics Series resonant converter Below resonance: 0.5 < F < 1 Above resonance: 1 < F

30. Fundamentals of Power Electronics 30 Chapter 19: Resonant Conversion Comparison of approximate and exact characteristics Parallel resonant converter Exact equation: solid lines Sinusoidal approximation: shaded lines