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Chapter 20
Quasi‐Resonant Converters
• Introduction
• 20.1 The zero‐current‐switching quasi‐resonant switch cell
20.1.1
20.1.2
20.1.3
Waveforms of the half‐wave ZCS quasi‐resonant switch cell
The average terminal waveforms
The full‐wave ZCS quasi‐resonant switch cell
• 20.2 Resonant switch topologies
20.2.1
20.2.2
20.2.3
The zero‐voltage‐switching quasi‐resonant switch
The zero‐voltage‐switching multiresonant switch
Quasi‐square‐wave resonant switches
• 20.3 Ac modeling of quasi‐resonant converters
• 20.4 Summary of key points
A quasi‐square‐wave ZVS buck
Lr
D1
i1(t)
i2(t)
+
Vg
+
–
i2(t)
I
+
–
V1
Lr
+
L
V2
Lr
Q1
v1(t)
–
D2
Cr
v2(t)
C
–
R
V
v2(t)
V1
–
0
Conducting
devices:
ω0t
ω0Ts
D1 Q1
X
D2
X
• Peak transistor voltage is equal to peak transistor voltage of PWM
cell
• Peak transistor current is increased
• Zero-voltage switching in all semiconductor devices
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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
i1(t)
vg(t) +
–
L
i2(t)
+
+
v1(t)
Switch
cell
i1(t)
+
C
v2(t)
–
PWM switch cell
i(t)
R
+
v1(t)
v2(t)
–
–
–
–
Example:
v(t)
i2(t)
+
realization of the switch cell in the buck converter
Two quasi‐resonant switch cells
i1(t)
+
D1
Lr
Q1
i2(t)
+
i2r(t)
+
i1(t)
+
D1
Lr
i2(t)
+
i2r(t)
+
Q1
v1(t)
v1r(t)
–
–
D2
Cr
v2(t)
v1(t)
v1r(t)
–
–
–
v2(t)
Cr
–
Switch network
Switch network
Full-wave ZCS quasi-resonant switch cell
Half-wave ZCS quasi-resonant switch cell
Insert either of the above switch cells into the buck converter, to obtain a ZCS quasi‐resonant version of the buck converter. Lr and Cr are small in value, and their resonant frequency f0 is greater than the switching frequency fs.
D2
i1(t)
i2(t)
+
vg(t) +
–
v1(t)
–
L
i(t)
+
+
Switch
cell
v2(t)
–
C
R
v(t)
–
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20.1 The zero‐current‐switching quasi‐
resonant switch cell
Lr
i1(t)
+
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
Q1
D1
i2r(t)
+
v1(t)
v1r(t)
–
–
D2
Cr
i2(t)
+
v2(t)
–
Switch network
Half-wave ZCS quasi-resonant switch cell
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.
D1
Lr
i1(t)
+
i2r(t)
+
i2(t)
+
Q1
v1(t)
v1r(t)
–
–
D2
Cr
v2(t)
–
Switch network
Full-wave ZCS quasi-resonant switch cell
The switch conversion ratio µ
Lr
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.
⟨ v1(t)⟩Ts
+
–
i1(t)
+
v1r(t)
D1
Q1
i2r(t)
+
D2
–
v2(t) Cr
⟨ i2(t)⟩Ts
–
Switch network
Half-wave ZCS quasi-resonant switch cell
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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20.1.1 Waveforms of the half‐wave ZCS quasi‐resonant switch cell
Waveforms:
The half‐wave ZCS quasi‐resonant switch cell, driven by the terminal quantities v1(t)Ts and
i2(t)Ts.
i1(t)
I2
Lr
i1(t)
D1
Q1
+
⟨ v1(t)⟩T
s
+
–
v1r(t)
V1
Lr
i2r(t)
+
D2
–
v2(t) Cr
Subinterval:
⟨ i2(t)⟩T
s
1
2
3
θ = ω0t
4
v2(t)
Vc1
–
–
Switch network
α
Half-wave ZCS quasi-resonant switch cell
β
I2
Cr
δ
ξ
X
D2
ω0Ts
Each switching period contains four subintervals
Conducting
devices:
Q1
D1
D2
Q1
D1
Boundary of zero current switching
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20.1.2 The average terminal Waveforms
Averaged switch modeling: we need to determine the average values of i1(t) and v2(t). Lr
i1(t)
D1
Q1
i2r(t)
+
+
⟨ v1(t)⟩T
s
+
–
v1r(t)
⟨ i2(t)⟩T
v2(t) Cr
D2
–
s
–
Switch network
Half-wave ZCS quasi-resonant switch cell
i1(t)
q1
q2
⟨ i1(t)⟩Ts
I2
α
ω0
α+β
ω0
t
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Charge arguments: computation of q2
i1(t)
q1
q2
⟨ i1(t)⟩Ts
I2
α+β
ω0
α
ω0
Lr
t
i1(t)
+
V1
+
–
v2(t)
ic(t)
Cr
I2
–
Circuit during subinterval 2
Switch conversion ratio µ
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Analysis result: switch conversion ratio µ
10
P1 J s
2
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
Js
7