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Fundamentals of Power Electronics 1 Chapter 20: Quasi-Resonant Converters
Chapter 20
Quasi-Resonant Converters
Introduction20.1 The zero-current-switching quasi-resonant switch cell
20.1.1 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 topologies
20.2.1 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 2 Chapter 20: Quasi-Resonant Converters
The resonant switch concept
A quite general idea:
1. PWM switch network is replaced by a resonant switch network2. 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) i
2(t)
+
v1(t)
PWM switch cell
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Fundamentals of Power Electronics 3 Chapter 20: Quasi-Resonant Converters
Two quasi-resonant switch cells
+
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
+
L
C R
+
v(t)
vg(t)
i(t)
+
v2(t)
i1(t) i2(t)
Switchcell
+
v1(t)
Insert either of the above switchcells into the buck converter, to
obtain a ZCS quasi-resonant
version of the buck converter.Lrand Cr are small in value, and
their resonant frequencyf0 is
greater than the switchingfrequencyfs.
f0 =1
2 L rCr=
0
2
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Fundamentals of Power Electronics 4 Chapter 20: Quasi-Resonant Converters
20.1 The zero-current-switching
quasi-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 inductorLr in series with transistor:
transistor switches at zero crossings of inductor
current waveform
Tank capacitor Cr in parallel with diodeD2 : diode
switches at zero crossings of capacitor voltagewaveform
Two-quadrant switch is required:
Half-wave: Q1 andD1 in series, transistor
turns off at first zero crossing of currentwaveform
Full-wave: Q1 andD1 in parallel, transistorturns off at second zero crossing of currentwaveform
Performances of half-wave and full-wave cells
differ significantly.
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Fundamentals of Power Electronics 5 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 rippleapproximation as usual, for these elements:
i2(t) i2(t) Tsv1(t) v1(t) Ts
In steady state, we can further approximate these quantities by their dcvalues:
i2(t) I2v1(t) V1
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 6 Chapter 20: Quasi-Resonant Converters
The switch conversion ratio
+
+
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
i2(t) i2(t) Tsv1(t) v1(t) Ts
i2(t) I2v1(t) V1
=v2(t) Ts
v1r(t) Ts
=i1(t) Ts
i2r(t) Ts
= 2V1
= 1I2
In steady state:
A generalization of the duty cycle
d(t)
The switch conversion ratio isthe ratio of the average terminalvoltages of the switch network. It
can be applied to non-PWM switch
networks. For the CCM PWMcase, = d.
If V/Vg =M(d) for a PWM CCMconverter, then V/Vg =M() for the
same converter with a switch
network having conversion ratio .
Generalized switch averaging, and, are defined and discussed inSection 10.3.
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Fundamentals of Power Electronics 7 Chapter 20: Quasi-Resonant Converters
20.1.1 Waveforms of the half-wave ZCS
quasi-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-waveZCS quasi-resonant switch
cell, driven by the terminal quantities v1(t) Ts and i2(t) Ts.
V1L
r
I2Cr
= 0t
i1(t)
I2
v2(t)
0T
s
Vc1
Subinterval: 1 2 3 4
Conductingdevices:
Q1
D2
D1
Q1
D1
D2
X
Waveforms:
Each switching period contains foursubintervals
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Fundamentals of Power Electronics 8 Chapter 20: Quasi-Resonant Converters
Subinterval 1
+
+
v2(t)
i1(t)
V1
Lr
I2
DiodeD2 is initially conducting the filterinductor currentI
2
. Transistor Q1
turns on,
and the tank inductor current i1 starts to
increase. So all semiconductor devicesconduct during this subinterval, and thecircuit reduces to:
Circuit equations:
d i1
(t)
d t =V
1L r
i1(t) =V1L r
t= 0tV1R0
with i1(0) = 0
Solution:
where R0 =L
rCr
This subinterval ends when diodeD2becomes reverse-biased. This occurs
at time 0t= , when i1(t) =I2.
=I2R0V1
i1() = 1
R0= I2
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Fundamentals of Power Electronics 9 Chapter 20: Quasi-Resonant Converters
Subinterval 2
DiodeD2 is off. Transistor Q1 conducts, and
the tank inductor and tank capacitor ring
sinusoidally. The circuit reduces to:
+
+
v2(t)
i1(t)
V1
Lr
I2Cr
ic(t)
The circuit equations are
L rdi1(0t)
dt= V1 v2(0t)
Crdv2(0t)
dt= i1(0t) I2
v2() = 0
i1() = I2
The solution is
i1(0t) = I2 + V1
R0sin 0t
v2(0t) = V1 1 cos 0t
The dc components of thesewaveforms are the dc
solution of the circuit, whilethe sinusoidal components
have magnitudes that dependon the initial conditions andon the characteristicimpedanceR0.
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Fundamentals of Power Electronics 10 Chapter 20: Quasi-Resonant Converters
Subinterval 2continued
i1(0t) = I2 +V1R0
sin 0t
v2(0t) = V1 1 cos 0t
Peak inductor current:
I1pk = I2 + 1R0
This subinterval ends at the first zerocrossing of i1(t). Define = angular length of
subinterval 2. Theni1( + ) = I2 +
V1R0
sin = 0
sin = 2 0V
1
V1L r
= 0t
i1(t)
I2
Subinterval: 1 2 3 4
0T
s
Must use care to select the correctbranch of the arcsine function. Note(from the i1(t) waveform) that > .
Hence
= + sin 1I2R0V1
2 < sin 1 x 2
I2
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