1. Zero-current Switching Quasi-resonant Converters

2. Problems of classical DC/DC
Conventional switching mode power supplies operate in hard switching
Every time when the transistor is switched on or off, the overlapping of the voltage and current waveforms indicates the switching loss during the switching

3. Switching loss Switching trajectory Area indicate the losses
Low loss-> Zero current during turn-on and turn-off

4. Resonant switching Add resonant component to the switch
Force the switch to turn on and off under either zero-current or zero-voltage based on resonance
(a) General
(b) Half-wave
(c) Full-wave

5. Classification of resonant converters
Name
Quasi-resonant converter
Load-resonant converter
Resonant Transition
Comment
Not complete resonance cycle
Load becomes part of the resonant circuit
High frequency on the switching transition and back to normal condition
Type
Zero current switching
Series resonant
Phase-shifted converter
Zero voltage switching
Parallel resonant
Extended-period quasi-resonant
Multi-resonant
Series-parallel resonant

6. Zero current switching Quasi-resonant (ZCS QR) Buck converter
Similar to the classical version
Add resonant inductor Lr in series with switch
Add resonant capacitor Cr in a node of the circuit

7. Equivalent circuit Four states of operations
The equivalent circuit according to SW and D

8. Waveforms of Buck ZCS (half-wave)
Transistor have only forward current

9. Waveforms of Buck ZCS (Full-wave)
Transistor have both forward current and reverse current
Reverse current is conducted by antiparallel diode

10. Stages of operation Linear state (Fig. 5a) Resonant state (Fig. 5b)
Recovering state (Fig 5c)
Freewheeling State (Fig 5d)

11. Linear stage [t0-t1] (Fig. 5a)
When Switch SW is turned on at t0, freewheeling diode DF is still conducting the load current Io through LF in the previous stage
The voltage across Lr is therefore equal to Vin. Input current iLr rises linearly and is governed by the state equations:
Solution: iLr = Vin (t-to) /Lr

12. Linear stage (Cont’)
The way that the current rises linearly from zero makes the turn-on loss small and is considered as zero-current switching.
The sum of iDF and iLr is equal to Io
The duration of this state Td1 is: Lr Io / Vin
Boundary condition: iLr= Io
After t1, DF is not required conduction any more. Io can then be supported by iLr

13. Resonant state [t1-t2] (Fig. 5b)
Lr and Cr resonate and DF is off. The state equations are:
The solution is:
where

14. Resonant state (Cont’)
The duration of this state Td2 is:
Above equations give the conduction angle  for the half-wave and full-wave respectively. Simply look at the resonant current waveform iLr, and it can be seen that  lies within [, 3/2] and [3/2, 2].

15. Finish of the Resonant Stage
For the half-wave mode, because there is a diode in series with the transistor, the current cannot be reversed.
Therefore when the resonant current starts to enter the negative value, the diode stops conduction as shown in Fig 6a. The resonant state then finishes
For the full-wave mode, a diode is connected in parallel with the transistor. When the resonant current iLr changes to negative, the diode conducts.
During this time, the transistor can be turned off so that when the resonant current cannot be conducted again when iLr returns from negative back to positive as shown in Fig. 6b

16. Resonant stage - Boundary
Boundary condition: iLr =0
At T2,
After t2, the resonance stops and the capacitor voltage decreases

17. Recovering stage [t2, t3] (Fig. 5c
Resonant stops, Cr begins to be discharged through LF with a discharging current equal to Io.
Cr is discharged until its voltage reaches zero and DF then becomes forward bias.
The duration of this state can be solved by equating above equation to zero.
Solution:

18. Boundary condition Duration: Td3= Cr Vin (1-cos )/Io
Boundary condition: vCr=0
After t3, Capacitor reaches zero, the stop discharging
This stage finishes

19. Free-wheeling stage [t3, t4] (Fig. 5d):
Output current freewheels through the diode DF
Duration: Td4= Ts-Td1-Td2-Td3
Ts is the duration of the switching cycle.
At t4, the converter will be turned on again and the same cycle repeats again, i.e. t4 is the same as t0 in the next cycle.

20. Condition for zero-current switching (ZCS)
The condition for ZCS is that the resonant current must reach zero so that the switch can be turned off during this time.
Therefore the condition for this is:
This condition is the same as solving equation (7) in order to obtain  using the arcsin

21. Condition for zero-current switching (ZCS)
Right after t2, the diode D inside the switch is in reverse bias and the reverse voltage appears across D. During this interval, the transistor T can be turned off under ZCS. After vsw becomes positive, the reverse voltage of the SW appears across T because D is in forward bias. Therefore T must be turned off before vsw is positive.

22. ZCS condition for full wave
For full-wave mode, T must be turned off when iLr is negative so that its anti-parallel diode is conducting all the current through SW, T can be turned off under zero-current switching.

23. DC Voltage conversion ratio
The output voltage Vo can be solved by equating the input energy Ein and output energy Eo.
Because the input current is the same as the iLr,
the resonant inductor Lr only conducts between t0 and t2.
fo=o/(2)

24. Analysis of the conversion ratio
It is a recursive equation and numerical method is needed to calculate the characteristics
The ratio depends on the load resistance R for half-wave mode and
Half-wave

25. DC conversion ratio
It is relatively independent of R for full-wave mode
Full-wave

26. Analysis of the conversion ratio
The above function in the parentheses, say F()
This function is very close to 2 for the range 0<<1. However, the function for half-wave is not.

27. Output voltage
The output voltage can be alternatively calculated by the average value of the resonant capacitor voltage vcr.
It can be seen that for full-wave mode, the the area A1 is about the same as A2, and A3 is about the same as A4
Therefore the average output voltage is approximately equal to Vin(Td2+Td3)/Ts.

28. Conclusion + Discussion
The Buck ZCS-QR converter is one of the famous resonant converters for many power conversion applications.
It also has a forward converter counterpart which is the transformer isolated version.
The converter is easy to use and usually very stable in operation.

29. Boost ZCS-QR converters
The difference is the addition of resonant components Lr and Cr around the switch
This converter is also useful in many circuit designs as it can be used for power factor correction

30. Principle of operation
Four states of operations
The equivalent circuit according to SW and D

31. Half-wave waveforms When T is turned on, iLr increases from zero
The current resonates back to zero at t2 and stops because of the diode’s reverse bias

32. Full-wave waveforms Similar to half-wave
The current iLr resonates to negative.
When iLr resonates back to zero at t2, it stops because Mosfet has been turned off.

33. Linear stage [t0-t1] (Fig. 11a):
When switch SW is turned on at t0, freewheeling diode DF is still conducting the source current Iin through LF.
The current iDF is also equal to Iin at t0. The voltage across vCr is therefore equal to Vo.
When t>t0, iDF decreases such that it is equal to Iin-iLr.
iLr = Vo (t-t0) /Lr

34. Linear stage (Boundary)
This state finishes when iLr increases until iLr is greater than Iin. iDF decreases to zero.
DF is not required for conduction any more. Iin can then be supported by iLr which is shown in next state.
The duration of this state Td1 is: Lr Iin / Vo
Boundary condition: iLr=Iin

35. Resonant state [t1-t2] (Fig. 11b):
Lr and Cr resonate and DF is off. The state equations are:
Solution:

36. Resonant stage (Duration)
Boundary condition: iLr =0
At the end of stage, t2:

37. Recovering stage [t2, t3] (Fig. 10c):
Resonant stops, Cr begins to be charged by the input current Iin through LF.
Solution:

38. Recovering stage (how to end)
Cr is discharged until its voltage reaches zero and DF then becomes forward bias
The duration of this state can be solved by equating equation (42) to zero.
Duration: Td3= Cr Vo (1-cos )/Iin
Boundary condition: vCr=Vo

39. Freewheeling stage [t3, t4] (Fig. 10d):
Output current freewheels through DF.
This stage finishes when the control gate voltage of SW is turned on again at t4.
Duration: Td4= Ts-Td1-Td2-Td3

40. Condition for zero-current switching (ZCS)
The condition for ZCS is that the resonant current must reach zero so that the switch can be turned off during this time.
Therefore the condition for this is:
This condition is the same as solving equation (36) in order to obtain  using the arcsin

41. DC Voltage conversion ratio
The output voltage Vo can be solved by equating the input energy Ein and the output energy Eo.
The input current is the same as the iLF which is a constant.
Based on Fig. 11, the output current is the current of the diode DF, iDF. iDF only conducts in the linear state and freewheeling state. Hence, output energy Eo:

42. Voltage conversion ratio M is
Where
Half-wave

43. Voltage conversion ratio
It is independent of the load
Similar to the classical Boost converter
Full-wave

44. Comment + Discussion
The function in the parentheses, is the same format as F()
The transistor’s source pin shares a common ground
Similar to the other advantage and disadvantage of classical Boost convetrer

45. Buck-boost converters
Using similar method
Add Lr in series with SW
Add Cr in parallel with Lm

46. Equivalent circuit

47. Voltage conversion ratio -Buck/Boost
Half-wave Full-wave

48. Flyback converter
A transformer isolated version of Buck-Boost converter
Simple in structure
Popular in use
Only one transformer
No filter inductor
Coupled inductor

49. Flyback converter Basic circuit
Equivalent circuit for analysis (replace transformer by T-model)
Simplified equivalent circuit

50. Practical implementation
The Mosfet is modified by:
Add one diode in series
Add one diode in parallel

51. Comparison and discussion of different topologies
Stage
Duration
Td1
Td2
Td3
Td4
Ts-Td1-Td2-Td3

52. Practical implementation of Quasi-resonant ZCS converters
(a) Buck
(b) Boost
(c)Buck-Boost
(d) Cuk

53. Tutorial
A full-wave zero-current switching quasi-resonant buck converter is operated at the following specification:
Input voltage VS=50V, Output voltage Vo=20V
Switching frequency fs=500kHz, Output current Io = 10A
Calculate the requirement of the resonant component Lr and Cr.
Estimate the power loss in the Lr if its series equivalent resistance is 0.1.
(answ: Lr=0.637H, Cr=0.127F, loss=6W)

54. Answer
Assume the converter is working under the boundary of zero-current switching. Therefore,
During the boundary of zero current switching:
The voltage conversion ratio can be approximated to be:

55. Answer (cont’) The Lr and Cr can be given by the impedance equations:
The current waveforms of the resonant inductor can be approximated by
For the whole 4 states.
The rms value is therefore:
The loss is

56. Tutorial
Why does the curve of Rn=0.5 stop in the middle of drawing of the characteristics?
Answer: eqn (26)
show that 1. There Rn Vo/Vin in order to maintain ZCS. Therefore the curve of Rn =0.5 stops its drawing beyond Vo/Vin>0.5 in order to maintain the characteristics for ZCS