1. Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion 19.3.1 Operation of the full bridge below resonance: Zero-current switching Series resonant converter example Current bi-directional switches ZCS vs. ZVS depends on tank current zero crossings with respect to transistor switching times = tank voltage zero crossings Operation below resonance: input tank current leads voltage Zero-current switching (ZCS) occurs

2. Fundamentals of Power Electronics 2 Chapter 19: Resonant Conversion Tank input impedance Operation below resonance: tank input impedance Z i is dominated by tank capacitor.  Z i is negative, and tank input current leads tank input voltage. Zero crossing of the tank input current waveform i s (t) occurs before the zero crossing of the voltage v s (t) – before switch transitions

3. Fundamentals of Power Electronics 3 Chapter 19: Resonant Conversion Switch network waveforms, below resonance Zero-current switching Conduction sequence: Q 1 –D 1 –Q 2 –D 2 Tank current is negative at the end of each half interval – antiparallel diodes conduct after their respective switches Q1 is turned off during D1 conduction interval, without loss

4. Fundamentals of Power Electronics 4 Chapter 19: Resonant Conversion Classical but misleading example: Transistor switching with clamped inductive load (4.3.1) Buck converter example transistor turn-off transition Loss:

5. Fundamentals of Power Electronics 5 Chapter 19: Resonant Conversion ZCS turn-on transition: hard switching Q 1 turns on while D 2 is conducting. Stored charge of D 2 and of semiconductor output capacitances must be removed. Transistor turn-on transition is identical to hard- switched PWM, and switching loss occurs.

6. Fundamentals of Power Electronics 6 Chapter 19: Resonant Conversion

7. Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion 19.3.2 Operation of the full bridge above resonance: Zero-voltage switching Series resonant converter example Operation above resonance: input tank current lags voltage Zero-voltage switching (ZVS) occurs

8. Fundamentals of Power Electronics 8 Chapter 19: Resonant Conversion Tank input impedance Operation above resonance: tank input impedance Z i is dominated by tank inductor.  Z i is positive, and tank input current lags tank input voltage. Zero crossing of the tank input current waveform i s (t) occurs after the zero crossing of the voltage v s (t) – after switch transitions

9. Fundamentals of Power Electronics 9 Chapter 19: Resonant Conversion Switch network waveforms, above resonance Zero-voltage switching Conduction sequence: D 1 –Q 1 –D 2 –Q 2 Tank current is negative at the beginning of each half-interval – antiparallel diodes conduct before their respective switches Q 1 is turned on during D 1 conduction interval, without loss – D 2 already off!

10. Fundamentals of Power Electronics 10 Chapter 19: Resonant Conversion ZVS turn-off transition: hard switching? When Q 1 turns off, D 2 must begin conducting. Voltage across Q 1 must increase to V g. Transistor turn-off transition is identical to hard-switched PWM. Switching loss may occur… but….

11. Fundamentals of Power Electronics 11 Chapter 19: Resonant Conversion Classical but misleading example: Transistor switching with clamped inductive load (4.3.1) Buck converter example transistor turn-off transition Loss:

12. Fundamentals of Power Electronics 12 Chapter 19: Resonant Conversion Soft switching at the ZVS turn-off transition Introduce small capacitors C leg across each device (or use device output capacitances). Introduce delay between turn-off of Q 1 and turn-on of Q 2. Tank current i s (t) charges and discharges C leg. Turn-off transition becomes lossless. During commutation interval, no devices conduct. So zero-voltage switching exhibits low switching loss: losses due to diode stored charge and device output capacitances are eliminated. Also get reduction in EMI.

13. Fundamentals of Power Electronics 13 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

14. Fundamentals of Power Electronics 14 Chapter 19: Resonant Conversion 19.4 Load-dependent properties of resonant converters Resonant inverter design objectives: 1. Operate with a specified load characteristic and range of operating points With a nonlinear load, must properly match inverter output characteristic to load characteristic 2. Obtain zero-voltage switching or zero-current switching Preferably, obtain these properties at all loads Could allow ZVS property to be lost at light load, if necessary 3. Minimize transistor currents and conduction losses To obtain good efficiency at light load, the transistor current should scale proportionally to load current (in resonant converters, it often doesn’t!)

15. Fundamentals of Power Electronics 15 Chapter 19: Resonant Conversion Topics of Discussion Section 19.4 Inverter output i-v characteristics Two theorems Dependence of transistor current on load current Dependence of zero-voltage/zero-current switching on load resistance Simple, intuitive frequency-domain approach to design of resonant converter Example Analysis valid for resonant inverters with resistive loads as well as resonant converters operating in CCM

16. Fundamentals of Power Electronics 16 Chapter 19: Resonant Conversion CCM PWM vs. resonant inverter output characteristics CCM PWM Low output impedance – neglecting losses, output voltage function of duty cycle only, not of load Steady-state IV curve looks like voltage source Resonant inverter (or converter operating in CCM) Higher output impedance – output voltage strong function of both control input and load current (load resistance) What does steady-state IV curve look like? (i.e. how does || v || depend on || i ||?)

17. Fundamentals of Power Electronics 17 Chapter 19: Resonant Conversion Analysis of inverter output characteristics – simplifying assumptions Load is resistive –Load does not change resonant frequency –Can include any reactive components in tank Resonant network is purely reactive (neglect losses)

18. Fundamentals of Power Electronics 18 Chapter 19: Resonant Conversion Thevenin equivalent of tank network output port Voltage divider Sinusoidal steady-state

19. Fundamentals of Power Electronics 19 Chapter 19: Resonant Conversion Output magnitude

20. Fundamentals of Power Electronics 20 Chapter 19: Resonant Conversion Inverter output characteristics

21. Fundamentals of Power Electronics 21 Chapter 19: Resonant Conversion Inverter output characteristics Let H  be the open-circuit ( R→  ) transfer function: and let Z o0 be the output impedance (with v i → short-circuit). Then, The output voltage magnitude is: with This result can be rearranged to obtain Hence, at a given frequency, the output characteristic (i.e., the relation between ||v o || and ||i o | |) of any resonant inverter of this class is elliptical.

22. Fundamentals of Power Electronics 22 Chapter 19: Resonant Conversion Inverter output characteristics General resonant inverter output characteristics are elliptical, of the form This result is valid provided that (i) the resonant network is purely reactive, and (ii) the load is purely resistive. with

23. Fundamentals of Power Electronics 23 Chapter 19: Resonant Conversion Matching ellipse to application requirements Electronic ballastElectrosurgical generator

24. Fundamentals of Power Electronics 24 Chapter 19: Resonant Conversion Example of gas discharge lamp ignition and steady-state operation from CoPEC research LCC resonant inverter Vg = 300 V I ref = 5 A

25. Fundamentals of Power Electronics 25 Chapter 19: Resonant Conversion Example of repeated lamp ignition attempts with overvoltage protection LCC resonant inverter Vg = 300 V I ref = 5 A Overvoltage protection at 3500 V

26. Fundamentals of Power Electronics 26 Chapter 19: Resonant Conversion 19.4 Load-dependent properties of resonant converters Resonant inverter design objectives: 1. Operate with a specified load characteristic and range of operating points With a nonlinear load, must properly match inverter output characteristic to load characteristic 2. Obtain zero-voltage switching or zero-current switching Preferably, obtain these properties at all loads Could allow ZVS property to be lost at light load, if necessary 3. Minimize transistor currents and conduction losses To obtain good efficiency at light load, the transistor current should scale proportionally to load current (in resonant converters, it often doesn’t!)

27. Fundamentals of Power Electronics 27 Chapter 19: Resonant Conversion Input impedance of the resonant tank network where

28. Fundamentals of Power Electronics 28 Chapter 19: Resonant Conversion Z N and Z D Z D is equal to the tank output impedance under the condition that the tank input source v s1 is open-circuited. Z D = Z o  Z N is equal to the tank output impedance under the condition that the tank input source v s1 is short-circuited. Z N = Z o 

29. Fundamentals of Power Electronics 29 Chapter 19: Resonant Conversion Magnitude of the tank input impedance If the tank network is purely reactive, then each of its impedances and transfer functions have zero real parts, and the tank input and output impedances are imaginary quantities. Hence, we can express the input impedance magnitude as follows:

30. Fundamentals of Power Electronics 30 Chapter 19: Resonant Conversion A Theorem relating transistor current variations to load resistance R Theorem 1: If the tank network is purely reactive, then its input impedance || Z i || is a monotonic function of the load resistance R. So as the load resistance R varies from 0 to , the resonant network input impedance || Z i || varies monotonically from the short-circuit value || Z i0 || to the open-circuit value || Z i  ||. The impedances || Z i  || and || Z i0 || are easy to construct. If you want to minimize the circulating tank currents at light load, maximize || Z i  ||. Note: for many inverters, || Z i  || < || Z i0 || ! The no-load transistor current is therefore greater than the short-circuit transistor current.

31. Fundamentals of Power Electronics 31 Chapter 19: Resonant Conversion Proof of Theorem 1  Derivative has roots at: Previously shown:  Differentiate: So the resonant network input impedance is a monotonic function of R, over the range 0 < R < . In the special case || Z i0 || = || Z i  ||, || Z i || is independent of R.

32. Fundamentals of Power Electronics 32 Chapter 19: Resonant Conversion Z i0 and Z i  for 3 common inverters