1. Fundamentals of Power Electronics 1 Chapter 20: Quasi-Resonant Converters Chapter 20 Quasi-Resonant Converters Introduction 20.1The zero-current-switching quasi-resonant switch cell 20.1.1Waveforms of the half-wave ZCS quasi-resonant switch cell 20.1.2The average terminal waveforms 20.1.3The full-wave ZCS quasi-resonant switch cell 20.2Resonant switch topologies 20.2.1The zero-voltage-switching quasi-resonant switch 20.2.2The zero-voltage-switching multiresonant switch 20.2.3Quasi-square-wave resonant switches 20.3Ac modeling of quasi-resonant converters 20.4Summary of key points

2. Fundamentals of Power Electronics 2 Chapter 20: Quasi-Resonant Converters

3. Fundamentals of Power Electronics 3 Chapter 20: Quasi-Resonant Converters The resonant switch concept A quite general idea: 1.PWM switch network is replaced by a resonant switch network 2.This leads to a quasi-resonant version of the original PWM converter Example:realization of the switch cell in the buck converter

4. Fundamentals of Power Electronics 4 Chapter 20: Quasi-Resonant Converters Two quasi-resonant switch cells Insert either of the above switch cells into the buck converter, to obtain a ZCS quasi-resonant version of the buck converter. L r and C r are small in value, and their resonant frequency f 0 is greater than the switching frequency f s.

5. Fundamentals of Power Electronics 5 Chapter 20: Quasi-Resonant Converters 20.1 The zero-current-switching quasi-resonant switch cell Tank inductor L r in series with transistor: transistor switches at zero crossings of inductor current waveform Tank capacitor C r in parallel with diode D 2 : diode switches at zero crossings of capacitor voltage waveform Two-quadrant switch is required: Half-wave: Q 1 and D 1 in series, transistor turns off at first zero crossing of current waveform Full-wave: Q 1 and D 1 in parallel, transistor turns off at second zero crossing of current waveform Performances of half-wave and full-wave cells differ significantly.

6. Fundamentals of Power Electronics 6 Chapter 20: Quasi-Resonant Converters Averaged switch modeling of ZCS cells It is assumed that the converter filter elements are large, such that their switching ripples are small. Hence, we can make the small ripple approximation as usual, for these elements: In steady state, we can further approximate these quantities by their dc values: Modeling objective: find the average values of the terminal waveforms  v 2 (t)  T s and  i 1 (t)  T s

7. Fundamentals of Power Electronics 7 Chapter 20: Quasi-Resonant Converters The switch conversion ratio µ In steady state: A generalization of the duty cycle d(t) The switch conversion ratio µ is the ratio of the average terminal voltages of the switch network. It can be applied to non-PWM switch networks. For the CCM PWM case, µ = d. If V/V g = M(d) for a PWM CCM converter, then V/V g = M(µ) for the same converter with a switch network having conversion ratio µ. Generalized switch averaging, and µ, are defined and discussed in Section 10.3.

8. Fundamentals of Power Electronics 8 Chapter 20: Quasi-Resonant Converters 20.1.1 Waveforms of the half-wave ZCS quasi-resonant switch cell The half-wave ZCS quasi-resonant switch cell, driven by the terminal quantities  v 1 (t)  Ts and  i 2 (t)  Ts. Waveforms: Each switching period contains four subintervals

9. Fundamentals of Power Electronics 9 Chapter 20: Quasi-Resonant Converters Subinterval 1 Diode D 2 is initially conducting the filter inductor current I 2. Transistor Q 1 turns on, and the tank inductor current i 1 starts to increase. So all semiconductor devices conduct during this subinterval, and the circuit reduces to: Circuit equations: with i 1 (0) = 0 Solution: where This subinterval ends when diode D 2 becomes reverse-biased. This occurs at time  0 t = , when i 1 (t) = I 2.

10. Fundamentals of Power Electronics 10 Chapter 20: Quasi-Resonant Converters

11. Fundamentals of Power Electronics 11 Chapter 20: Quasi-Resonant Converters Subinterval 2 Diode D 2 is off. Transistor Q 1 conducts, and the tank inductor and tank capacitor ring sinusoidally. The circuit reduces to: The circuit equations are The solution is The dc components of these waveforms are the dc solution of the circuit, while the sinusoidal components have magnitudes that depend on the initial conditions and on the characteristic impedance R 0.

12. Fundamentals of Power Electronics 12 Chapter 20: Quasi-Resonant Converters Subinterval 2 continued Peak inductor current: This subinterval ends at the first zero crossing of i 1 (t). Define  = angular length of subinterval 2. Then Must use care to select the correct branch of the arcsine function. Note (from the i 1 (t) waveform) that . Hence

13. Fundamentals of Power Electronics 13 Chapter 20: Quasi-Resonant Converters Boundary of zero current switching If the requirement is violated, then the inductor current never reaches zero. In consequence, the transistor cannot switch off at zero current. The resonant switch operates with zero current switching only for load currents less than the above value. The characteristic impedance must be sufficiently small, so that the ringing component of the current is greater than the dc load current. Capacitor voltage at the end of subinterval 2 is

14. Fundamentals of Power Electronics 14 Chapter 20: Quasi-Resonant Converters Subinterval 3 All semiconductor devices are off. The circuit reduces to: The circuit equations are The solution is Subinterval 3 ends when the tank capacitor voltage reaches zero, and diode D 2 becomes forward-biased. Define  = angular length of subinterval 3. Then

15. Fundamentals of Power Electronics 15 Chapter 20: Quasi-Resonant Converters Subinterval 4 Subinterval 4, of angular length , is identical to the diode conduction interval of the conventional PWM switch network. Diode D 2 conducts the filter inductor current I 2 The tank capacitor voltage v 2 (t) is equal to zero. Transistor Q 1 is off, and the input current i 1 (t) is equal to zero. The length of subinterval 4 can be used as a control variable. Increasing the length of this interval reduces the average output voltage.

16. Fundamentals of Power Electronics 16 Chapter 20: Quasi-Resonant Converters Maximum switching frequency The length of the fourth subinterval cannot be negative, and the switching period must be at least long enough for the tank current and voltage to return to zero by the end of the switching period. The angular length of the switching period is where the normalized switching frequency F is defined as So the minimum switching period is Substitute previous solutions for subinterval lengths:

17. Fundamentals of Power Electronics 17 Chapter 20: Quasi-Resonant Converters 20.1.2 The average terminal waveforms Averaged switch modeling: we need to determine the average values of i 1 (t) and v 2 (t). The average switch input current is given by q 1 and q 2 are the areas under the current waveform during subintervals 1 and 2. q 1 is given by the triangle area formula:

18. Fundamentals of Power Electronics 18 Chapter 20: Quasi-Resonant Converters Charge arguments: computation of q 2 Circuit during subinterval 2 Node equation for subinterval 2: Substitute: Second term is integral of constant I 2 :

19. Fundamentals of Power Electronics 19 Chapter 20: Quasi-Resonant Converters Charge arguments continued First term: integral of the capacitor current over subinterval 2. This can be related to the change in capacitor voltage : Substitute results for the two integrals: Substitute into expression for average switch input current:

20. Fundamentals of Power Electronics 20 Chapter 20: Quasi-Resonant Converters Switch conversion ratio µ Eliminate , , V c1 using previous results: where

21. Fundamentals of Power Electronics 21 Chapter 20: Quasi-Resonant Converters Analysis result: switch conversion ratio µ Switch conversion ratio: with This is of the form

22. Fundamentals of Power Electronics 22 Chapter 20: Quasi-Resonant Converters Characteristics of the half-wave ZCS resonant switch J s ≤ 1 Switch characteristics: Mode boundary:

23. Fundamentals of Power Electronics 23 Chapter 20: Quasi-Resonant Converters Buck converter containing half-wave ZCS quasi-resonant switch Conversion ratio of the buck converter is (from inductor volt-second balance): For the buck converter, ZCS occurs when Output voltage varies over the range