ECEN5817, ECEE Department, University of Colorado at Boulder
Analysis of quasi-square-wave ZVS converters
D1
i1(t) i2(t)
Lr
IV1
Lr
–V2
Lr
i2(t)ZVS-QSW buck: single-transistor case
+– CrVg D2
Q1
+
v2(t)
–
+
v1(t)
–
L
C R
+
V
– 0Ts
v2(t) V1
0t
0
Conductingdevices: D2X XQ1D1
Resonant transitions but transistor and diode conduction intervals are similar to PWM Peak voltages applied to
ECEN 58171
similar to 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
g ppsemiconductors are same as PWM
Magnetics are small, and are similar to DCM
Single-transistor ZVS-QSW waveforms and state-plane analysis
mc+
V1
_
+
V
_
L
C
+
vc
i1iLD1
D2
Q1
jl
mc
ot
oTs1 2 3 4 5
_
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jlot
Devices conducting
ECEN5817, ECEE Department, University of Colorado at Boulder
A way to solve and plot the characteristics
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Solving, p 2
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ECEN5817, ECEE Department, University of Colorado at Boulder
Results: Switch conversion ratio µ vs. F
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Switch conversion ratio µ vs.
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Course website contains Excel spreadsheet (with function macros) that evaluates the above equations and can plot the above characteristics.
ECEN5817, ECEE Department, University of Colorado at Boulder
Summary of 1-transistor ZVS-QSW characteristics
µ vs. F
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ZVS-QSW switch cell
Q
D
Converter examples High-frequency view of the switch network
D
Q
DQ
Q D
Basic switch implementation options
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Q 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)
ECEN5817, ECEE Department, University of Colorado at Boulder
Two-transistor (synchronous-rectifier) ZVS-QSW
D1
Q1
+
i1(t) i2(t)
+
Lr
L+
I
+– CrVg D2
Q1v2(t)
–
v1(t)
–
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
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• 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
2-transistor ZVS-QSW: state plane
ECEN 581710
ECEN5817, ECEE Department, University of Colorado at Boulder
Waveforms and definition of duty cycle, 2 transistors
• Here, the controller duty , ycycle 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 of the DTs and
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g g s
D’Ts intervals
Constant-frequency control characteristicsof the 2-switch ZVS-QSW
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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
ECEN5817, ECEE Department, University of Colorado at Boulder
2-switch ZVS-QSW: ZVS boundary
Reducing F = fs/f0 leads ZVS id to ZVS over a wider
range of µ and J
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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
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• Replace d with in the small-signal AC dynamic model of the PWM parent converter (from ECEN5797 Intro to PE)
ECEN5817, ECEE Department, University of Colorado at Boulder
Example 1: Full-wave ZCS-QR Buck
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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
Small-signal AC model of the full-wave ZCS-QR buck
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Example 2: Half-wave ZCS-QR buck
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ECEN5817, ECEE Department, University of Colorado at Boulder
Perturb and linearize
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Small-signal AC model of the half-wave ZCS-QR buck
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ECEN5817, ECEE Department, University of Colorado at Boulder
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Summary of the linearization/perturbation results
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ECEN5817, ECEE Department, University of Colorado at Boulder
How about 2-switch ZVS-QSW?
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