Download - Chapter 20 Quasi-Resonant Converters
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Fundamentals of Power Electronics 1 Chapter 20: Quasi-Resonant Converters
Chapter 20
Quasi-Resonant Converters
Introduction
20.1 The zero-current-switching quasi-resonant switch cell20.1.1 Waveforms of the half-wave ZCS quasi-resonant switch cell
20.1.2 The average terminal waveforms
20.1.3 The full-wave ZCS quasi-resonant switch cell
20.2 Resonant switch topologies20.2.1 The zero-voltage-switching quasi-resonant switch
20.2.2 The zero-voltage-switching multiresonant switch
20.2.3 Quasi-square-wave resonant switches
20.3 Ac modeling of quasi-resonant converters
20.4 Summary of key points
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Fundamentals of Power Electronics 4 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
+–
L
C R
+
v(t)
–
vg(t)
i(t)
+
v2(t)
–
i1(t) i2(t)
Switchcell
+
v1(t)
–
+
v2(t)
–
i1(t) i2(t)
+
v1(t)
–
PWM switch cell
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Fundamentals of Power Electronics 5 Chapter 20: Quasi-Resonant Converters
20.1 The zero-current-switchingquasi-resonant switch cell
+
v2(t)
–
i1(t) i2(t)
+
v1(t)
–
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
+
v2(t)
–
i1(t) i2(t)
+
v1(t)
–
Lr
Cr
Full-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)
D1
D2
Q1
Tank inductor Lr in series with transistor: transistor switches at zero crossings of inductor current waveform
Tank capacitor Cr in parallel with diode D2 : diode switches at zero crossings of capacitor voltage waveform
Two-quadrant switch is required:
Half-wave: Q1 and D1 in series, transistor turns off at first zero crossing of current waveform
Full-wave: Q1 and D1 in parallel, transistor turns off at second zero crossing of current waveform
Performances of half-wave and full-wave cells differ significantly.
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Fundamentals of Power Electronics 6 Chapter 20: Quasi-Resonant Converters
The switch conversion ratio µ
+–
+
v2(t)
–
i1(t)
v1(t)Ts
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
i2(t)Ts
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/Vg = M(d) for a PWM CCM converter, then V/Vg = 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.
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Fundamentals of Power Electronics 7 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
v2(t) Ts and i1(t) Ts
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Fundamentals of Power Electronics 8 Chapter 20: Quasi-Resonant Converters
20.1.1 Waveforms of the half-wave ZCSquasi-resonant switch cell
+–
+
v2(t)
–
i1(t)
v1(t)Ts
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
i2(t)Ts
The half-wave ZCS quasi-resonant switch cell, driven by the terminal quantities v1(t)Ts and i2(t)Ts.
= 0t
i1(t)
I2
v2(t)
0Ts
Vc1
Subinterval: 1 2 3 4
Conductingdevices:
Q1
D2
D1
Q1
D1
D2X
Waveforms:
Each switching period contains four subintervals
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+–
+
v2(t)
–
i1(t)
v1(t)Ts
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
i2(t)Ts
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+–
+
v2(t)
–
i1(t)
v1(t)Ts
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
i2(t)Ts
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+–
+
v2(t)
–
i1(t)
v1(t)Ts
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
i2(t)Ts
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+–
+
v2(t)
–
i1(t)
v1(t)Ts
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
i2(t)Ts
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+–
+
v2(t)
–
i1(t)
v1(t)Ts
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
i2(t)Ts
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Fundamentals of Power Electronics 16 Chapter 20: Quasi-Resonant Converters
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Fundamentals of Power Electronics 17 Chapter 20: Quasi-Resonant Converters
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Fundamentals of Power Electronics 18 Chapter 20: Quasi-Resonant Converters
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Fundamentals of Power Electronics 19 Chapter 20: Quasi-Resonant Converters
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Fundamentals of Power Electronics 20 Chapter 20: Quasi-Resonant Converters
Analysis result: switch conversion ratio µ
Switch conversion ratio:
with
This is of the form
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
Js
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Fundamentals of Power Electronics 21 Chapter 20: Quasi-Resonant Converters
Characteristics of the half-wave ZCS resonant switch
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
Js
ZCS boundary
F = 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Js ≤ 1
Switch characteristics:
Mode boundary:
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Fundamentals of Power Electronics 22 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
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
Js
ZCS boundary
F = 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
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Fundamentals of Power Electronics 23 Chapter 20: Quasi-Resonant Converters
Boost converter example
+–
Q1
L
C R
+
V
–
D1Vg
i2(t)
D2
Lr
CrIg
+
v1(t)
–
i1(t)
– v2(t) +For the boost converter,
Half-wave ZCS equations:
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Fundamentals of Power Electronics 24 Chapter 20: Quasi-Resonant Converters
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Fundamentals of Power Electronics 25 Chapter 20: Quasi-Resonant Converters
20.1.3 The full-wave ZCS quasi-resonant switch cell
= 0t
i1(t)
I2
v2(t)
0Ts
Vc1
Subinterval: 1 2 3 4
Conductingdevices:
Q1
D2
Q1 D1 D2X
= 0t
i1(t)
I2
v2(t)
0Ts
Vc1
Subinterval: 1 2 3 4
Conductingdevices:
Q1
D2
D1
Q1
D1
D2X
+
v2(t)
–
i1(t) i2(t)
+
v1(t)
–
Lr
Cr
Half-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)D1
D2
Q1
+
v2(t)
–
i1(t) i2(t)
+
v1(t)
–
Lr
Cr
Full-wave ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)
D1
D2
Q1
Half wave
Full wave
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Fundamentals of Power Electronics 26 Chapter 20: Quasi-Resonant Converters
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Fundamentals of Power Electronics 27 Chapter 20: Quasi-Resonant Converters
Analysis: full-wave ZCS
Analysis in the full-wave case is nearly the same as in the half-wave case. The second subinterval ends at the second zero crossing of the tank inductor current waveform. The following quantities differ:
In either case, µ is given by
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Fundamentals of Power Electronics 28 Chapter 20: Quasi-Resonant Converters
Full-wave cell: switch conversion ratio µ
Full-wave case: P1 can be approximated as
so
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
Js
ZCS boundary
F = 0.2 0.4 0.6 0.8
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Fundamentals of Power Electronics 29 Chapter 20: Quasi-Resonant Converters
20.2 Resonant switch topologies
Basic ZCS switch cell:
+
v2(t)
–
i1(t) i2(t)
+
v1(t)
–
Lr
Cr
ZCS quasi-resonant switch cell
Switch network
+
v1r(t)
–
i2r(t)
D2
SW
SPST switch SW:
• Voltage-bidirectional two-quadrant switch for half-wave cell
• Current-bidirectional two-quadrant switch for full-wave cell
Connection of resonant elements:
Can be connected in other ways that preserve high-frequency components of tank waveforms
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Fundamentals of Power Electronics 30 Chapter 20: Quasi-Resonant Converters
Connection of tank capacitor
+
v2(t)
–
i1(t) i2(t)
Vg
Lr
Cr
ZCS quasi-resonant switch
D2
SW
+–
L
C R
+
V
–
+
v2(t)
–
i1(t) i2(t)
Vg
Lr
Cr
ZCS quasi-resonant switch
D2
SW
+–
L
C R
+
V
–
Connection of tank capacitor to two other points at ac ground.
This simply changes the dc component of tank capacitor voltage.
The ac high-frequency components of the tank waveforms are unchanged.
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Fundamentals of Power Electronics 31 Chapter 20: Quasi-Resonant Converters
A test to determine the topologyof a resonant switch network
+
v2(t)
–
i1(t)
Lr
CrD2
SW
Replace converter elements by their high-frequency equivalents:
• Independent voltage source Vg: short circuit
• Filter capacitors: short circuits
• Filter inductors: open circuits
The resonant switch network remains.
If the converter contains a ZCS quasi-resonant switch, then the result of these operations is