1. 1 Parameters for various resonant switch networks

2. 2 Salient features of small-signal transfer functions, for basic converters

3. 3 Half-wave ZCS quasi-resonant buck Low frequency model: set tank elements to zero

4. 4

5. 5

6. 6 Half-wave ZCS quasi-resonant boost Low frequency model: set tank elements to zero

7. 7

8. 8

9. 9 Quasi-square-wave ZVS converters A quasi-square-wave ZVS buck Resonant transitions but transistor and diode conduction intervals are similar to PWM Tank capacitor is in parallel with all semiconductor devices, hence all semiconductors operate with ZVS Peak currents are increased, and are similar to DCM Peak voltages applied to semiconductors are same as PWM Magnetics are small, and are similar to DCM

10. 10 Goal: Find steady-state solution for this resonant switch cell Approach: State plane analysis followed by averaging of terminal waveforms

11. 11 Interval 1 Q1 conduction Begins when Q1 starts to conduct For ZVS operation, this occurs when D1 had been previously conducting Circuit Initial conditions Dynamics What ends interval Endpoints Length of interval

12. 12 State plane

13. 13 Interval 2 Dead time Circuit Initial conditions Dynamics What ends interval Endpoints Length of interval

14. 14 Interval 3 D2 conduction Circuit Initial conditions Dynamics What ends interval Endpoints Length of interval

15. 15 Interval 4 Dead time Circuit Initial conditions Dynamics What ends interval Endpoints Length of interval

16. 16 Interval 5 (1) D1 conduction Circuit Initial conditions Dynamics What ends interval Endpoints Length of interval

17. 17 Waveforms

18. 18 Average switch input current

19. 19 Average output current

20. 20 Average output current, p. 2

21. 21 Control input: transistor/diode conduction angle 

22. 22

23. 23 A way to solve and plot the characteristics

24. 24 Solving, p 2

25. 25 Results: Switch conversion ratio µ vs. F

26. 26 Switch conversion ratio µ vs.  Course website contains Excel spreadsheet (with function macros) that evaluates the above equations and can plot the above characteristics.

27. 27 Characteristics: 1 transistor version µ vs. F

28. 28 Soft-switching converters with constant switching frequency With two or more active switches, we can obtain zero-voltage switching in converters operating at constant switching frequency Often, the converter characteristics are nearly the same as their hard- switched PWM parent converters The second switch may be one that is already in the PWM parent converter (synchronous rectifier, or part of a half or full bridge). Sometimes, it is not, and is a (hopefully small) auxiliary switch Examples: Two-switch quasi-square wave (with synchronous rectifier) Two-switch multiresonant (with synchronous rectifier) Phase-shifted bridge with zero voltage transitions Forward or other converter with active clamp circuit These converters can exhibit stresses and characteristics that approach those of the parent hard-switched PWM converter (especially the last two), but with zero-voltage switching over a range of operating points

29. 29 Quasi-square wave buck with two switches Q2 can be viewed as a synchronous rectifier Additional degree of control is possible: let Q2 conduct longer than D2 would otherwise conduct Constant switching frequency control is possible, with behavior similar to conventional PWM Can obtain µ < 0.5 See Maksimovic PhD thesis, 1989 Original one-switch version Add synchronous rectifier

31. 31 State plane Remaining details of analysis left as homework problem

32. 32 Waveforms and definition of duty cycle, 2 transistors Here, the controller duty cycle D c is defined as the duty cycle that would be chosen by a conventional PWM chip. The resonant transitions are “dead times” that occur at the beginning of the DT s and D’T s intervals.

33. 33 Constant-frequency control characteristics two switch quasi-resonant buck converter Constant frequency, duty cycle control: Low output impedance, µ doesn’t depend much on J Very similar to conventional PWM CCM buck converter, but exhibits ZVS over a range of operating points

35. 35 ZVS boundary Reducing F = f s /f 0 leads to ZVS over a wider range of µ and J