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

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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

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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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