Analysis of quasi-square-wave ZVS converters
i2(t)
ZVS-QSW buck: single-transistor case
Lr
D1
i1(t)
i2(t)
+
+
–
Vg
+
v1(t)
Q1
D2
Cr
–
V1
Lr
I
V2
Lr
+
L
v2(t)
C
v2(t)
R
V
V1
0
–
–
–
Resonant transitions but transistor
and diode conduction intervals are
similar to PWM
Conducting
devices:
 0t
 0T s
D1 Q1
X
D2
X
Peak voltages
g applied
pp
to
semiconductors are same as PWM
Tank capacitor is in parallel with all
semiconductor devices, hence all
semiconductors operate with ZVS
Magnetics are small, and are similar to
DCM
Peak currents are increased, and
are similar to DCM
ECEN 5817
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Single-transistor ZVS-QSW
waveforms and state-plane analysis
i1
iL
D1
Q1
+
V1
D2
C
_
1
2
3
L
+
+
vc
V
_
_
4
5
jl
mc
oTs
ot
mc
jl
ot
Devices conducting





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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
A way to solve and plot the characteristics
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ECEN 5817
Solving, p 2
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
Results: Switch conversion ratio µ vs. F
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ECEN 5817
Switch conversion ratio µ vs. 
Course website contains Excel spreadsheet (with function macros) that
evaluates the above equations and can plot the above characteristics.
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
Summary of 1-transistor ZVS-QSW characteristics
µ vs. F
ECEN 5817
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ZVS-QSW switch cell
Converter examples
High-frequency view of the switch network
Q
D
Q
D
D
Q
Q
Basic switch implementation options
D
Q: current-bidirectional (e.g. MOSFET)
D: single-quadrant (diode)
Q: current-bidirectional (e.g. MOSFET)
D: current-bidirectional synchronous rectifier
(e.g. MOSFET)
Q
D
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
Two-transistor (synchronous-rectifier) ZVS-QSW
Lr
D1
i1(t)
i2(t)
+
Vg
+
–
v1(t)
I
+
Q1
D2
Cr
–
v2(t)
+
L
C
–
R
V
–
• Resonant transitions but transistor and conduction intervals are similar
to PWM; peak voltages are the same as in hard-switched PWM
• Tank capacitor is in parallel with all semiconductor devices, hence all
semiconductors operate with ZVS
• Peak currents are increased, and are similar to DCM
• Constant-frequency duty-cycle control, similar to standard PWM, is
possible
• ZVS-QSW (resonant-transition) concept extends to a number of other
important practical soft-switching converters
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ECEN 5817
2-transistor ZVS-QSW: state plane
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
Waveforms and definition
of duty cycle, 2 transistors
• Here,, the controller dutyy
cycle Dc is defined as the
duty cycle that would be
chosen by a conventional
PWM chip
• The resonant transitions are
“dead times” that occur at
the beginning
g
g of the DTs and
D’Ts intervals
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ECEN 5817
Constant-frequency control characteristics
of the 2-switch ZVS-QSW
Constant frequency, duty cycle control:
Low output impedance, µ doesn’t depend much on J
Very similar to conventional PWM CCM switch, but exhibits ZVS over a range
of operating points
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
2-switch ZVS-QSW: ZVS boundary
Reducing F = fs/f0 leads
to ZVS over a wider
id
range of µ and J
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ECEN 5817
AC (small-signal dynamic)
modeling of quasi-resonant converters
Quasi-resonant converters inherit properties of PWM parents, with switch
conversion ratio  playing the role of the PWM switch duty cycle d
AC modeling approach:
• Start from (v,i,fs) found for the resonant switch
• Perturb and linearize
•
Replace d with  in the small-signal AC dynamic model of the PWM parent
converter (from ECEN5797 Intro to PE)
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
Example 1: Full-wave ZCS-QR Buck
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ECEN 5817
Small-signal AC model of the PWM buck converter
Textbook, Fig.7.17(a)
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
Small-signal AC model of the full-wave ZCS-QR buck
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ECEN 5817
Example 2: Half-wave ZCS-QR buck
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
Perturb and linearize 
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ECEN 5817
Small-signal AC model of the half-wave ZCS-QR buck
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
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ECEN 5817
Summary of the linearization/perturbation results
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817
How about 2-switch ZVS-QSW?
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ECEN5817, ECEE Department, University of Colorado at Boulder
ECEN 5817