1. Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion Upcoming Assignments Preparation for Lecture 2: Read Section 19.1, Sinusoidal analysis of resonant converters Preparation for Lecture 3: Read Section 19.2, Examples Homework assignment, due Lecture 5: Homework set #1, Review

2. Fundamentals of Power Electronics 2 Chapter 19: Resonant Conversion Derivation of a resonant dc-dc converter Rectify and filter the output of a dc-high-frequency-ac inverter The series resonant dc-dc converter

3. Fundamentals of Power Electronics 3 Chapter 19: Resonant Conversion Resonant conversion: advantages The chief advantage of resonant converters: reduced switching loss Zero-current switching Zero-voltage switching Turn-on or turn-off transitions of semiconductor devices can occur at zero crossings of tank voltage or current waveforms, thereby reducing or eliminating some of the switching loss mechanisms. Hence resonant converters can operate at higher switching frequencies than comparable PWM converters Zero-voltage switching also reduces converter-generated EMI Zero-current switching can be used to commutate SCRs In specialized applications, resonant networks may be unavoidable High voltage converters: significant transformer leakage inductance and winding capacitance leads to resonant network

4. Fundamentals of Power Electronics 4 Chapter 19: Resonant Conversion Resonant conversion: disadvantages Can optimize performance at one operating point, but not with wide range of input voltage and load power variations Significant currents may circulate through the tank elements, even when the load is disconnected, leading to poor efficiency at light load Quasi-sinusoidal waveforms exhibit higher peak values than equivalent rectangular waveforms These considerations lead to increased conduction losses, which can offset the reduction in switching loss Resonant converters are usually controlled by variation of switching frequency. In some schemes, the range of switching frequencies can be very large Complexity of analysis

5. Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion Analysis of resonant converters Series resonant dc-dc converter example Complex! Small ripple approximation is not valid Need new approaches: Sinusoidal approximation State plane analysis

6. Fundamentals of Power Electronics 6 Chapter 19: Resonant Conversion Outline of course 1. Analysis of resonant converters using the sinusoidal approximation Classical series, parallel, LCC, and other topologies Sinusoidal model Zero voltage and zero current switching Resonant converter design techniques based on frequency response 2. Sinusoidal analysis: small-signal ac behavior with frequency modulation Spectra and envelope response Phasor transform method 3. State-plane analysis of resonant converters Fundamentals of state-plane and averaged modeling of resonant circuits Exact analysis of the series and parallel resonant dc-dc converters

7. Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion Outline, p. 2 4. State plane analysis of resonant switch and other soft-switching converters Quasi-resonant topologies and their analysis via state-plane approach Quasi-square wave converters Zero voltage transition converter Soft switching in forward and flyback converters Multiresonant and class E converter 5. Server systems, portable power, and green power issues (time permitting) Modeling efficiency vs. load, origins of loss Variable frequency approaches to improving light-load efficiency –DCM –Burst mode Effects of parallel modules DC transformers

8. Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion Outline, p. 2 4. Resonant switch and related converters Quasi-resonant topologies and their analysis via state-plane approach Quasi-square wave converters Zero voltage transition converter Soft switching in forward and flyback converters Multiresonant and class E converter 5. Server systems, portable power, and green power issues Modeling efficiency vs. load, origins of loss Variable frequency approaches to improving light-load efficiency –DCM –Burst mode Effects of parallel modules DC transformers

9. Fundamentals of Power Electronics 9 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

10. Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion 19.1 Sinusoidal analysis of resonant converters A resonant dc-dc converter: If tank responds primarily to fundamental component of switch network output voltage waveform, then harmonics can be neglected. Let us model all ac waveforms by their fundamental components.

11. Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion Input impedance

12. Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion The sinusoidal approximation Tank current and output voltage are essentially sinusoids at the switching frequency f s. Neglect harmonics of switch output voltage waveform, and model only the fundamental component. Remaining ac waveforms can be found via phasor analysis.

13. Fundamentals of Power Electronics 13 Chapter 19: Resonant Conversion 19.1.1 Controlled switch network model If the switch network produces a square wave, then its output voltage has the following Fourier series: The fundamental component is So model switch network output port with voltage source of value v s1 (t)

14. Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion Model of switch network input port Assume that switch network output current is It is desired to model the dc component (average value) of the switch network input current.

15. Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion Switch network: equivalent circuit Switch network converts dc to ac Dc components of input port waveforms are modeled Fundamental ac components of output port waveforms are modeled Model is power conservative: predicted average input and output powers are equal

16. Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion 19.1.2 Modeling the rectifier and capacitive filter networks Assume large output filter capacitor, having small ripple. v R (t) is a square wave, having zero crossings in phase with tank output current i R (t). If i R (t) is a sinusoid: Then v R (t) has the following Fourier series:

17. Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion Sinusoidal approximation: rectifier Again, since tank responds only to fundamental components of applied waveforms, harmonics in v R (t) can be neglected. v R (t) becomes Actual waveformswith harmonics ignored

18. Fundamentals of Power Electronics 18 Chapter 19: Resonant Conversion Rectifier dc output port model Output capacitor charge balance: dc load current is equal to average rectified tank output current Hence

19. Fundamentals of Power Electronics 19 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

20. Fundamentals of Power Electronics 20 Chapter 19: Resonant Conversion 19.1.3 Resonant tank network Model of ac waveforms is now reduced to a linear circuit. Tank network is excited by effective sinusoidal voltage (switch network output port), and is load by effective resistive load (rectifier input port). Can solve for transfer function via conventional linear circuit analysis.

21. Fundamentals of Power Electronics 21 Chapter 19: Resonant Conversion Solution of tank network waveforms Transfer function: Ratio of peak values of input and output voltages: Solution for tank output current: which has peak magnitude

22. Fundamentals of Power Electronics 22 Chapter 19: Resonant Conversion 19.1.4 Solution of converter voltage conversion ratio M = V/V g

23. Fundamentals of Power Electronics 23 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.

24. Fundamentals of Power Electronics 24 Chapter 19: Resonant Conversion 19.2 Examples 19.2.1 Series resonant converter

25. Fundamentals of Power Electronics 25 Chapter 19: Resonant Conversion Model: series resonant converter

26. Fundamentals of Power Electronics 26 Chapter 19: Resonant Conversion Construction of Z i – Resonant (high Q) case C = 0.1 μ F, L = 1 mH, R e = 10 Ω

27. Fundamentals of Power Electronics 27 Chapter 19: Resonant Conversion Construction of H = V / V g – Resonant (high Q) case C = 0.1 μ F, L = 1 mH, R e = 10 Ω

28. Fundamentals of Power Electronics 28 Chapter 19: Resonant Conversion Construction of Z i

29. Fundamentals of Power Electronics 29 Chapter 19: Resonant Conversion Construction of H

30. Fundamentals of Power Electronics 30 Chapter 19: Resonant Conversion Model: series resonant converter

31. Fundamentals of Power Electronics 31 Chapter 19: Resonant Conversion Construction of Z i – Non-resonant (low Q) case C = 0.1 μ F, L = 1 mH, R e = 1 kΩ

32. Fundamentals of Power Electronics 32 Chapter 19: Resonant Conversion Construction of H – Non-resonant (low Q) case C = 0.1 μ F, L = 1 mH, R e = 1 kΩ

33. Fundamentals of Power Electronics 33 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:

34. Fundamentals of Power Electronics 34 Chapter 19: Resonant Conversion Subharmonic modes of SRC Reduced switch utilization Possible instability in CL