Parameters for various resonant switch networks

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Parameters for various resonant switch networks

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Salient features of small-signal transfer functions, for basic converters

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Half-wave ZCS quasi-resonant buckLow frequency model: set tank elements to zero

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5

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Half-wave ZCS quasi-resonant boostLow frequency model: set tank elements to zero

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8

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Quasi-square-wave ZVS converters

+– CrVg

D1

D2

Q1

+

v2(t)

–

i1(t) i2(t)

+

v1(t)

–

Lr

L

C R

+

V

–

I

0Ts

i2(t)

v2(t)V1

0t

0

Conductingdevices: D2X XQ1D1

A quasi-square-wave ZVS buck

Resonant transitions but transistor and diode conduction intervals are 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

Peak voltages applied to semiconductors are same as PWM

Magnetics are small, and are similar to DCM

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Goal: Find steady-state solution for this resonant switch cellApproach: State plane analysis followed by averaging of

terminal waveforms

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Interval 1Q1 conduction

Begins when Q1 starts to conductFor ZVS operation, this occurs when D1 had been previously conducting

CircuitInitial conditions

DynamicsWhat ends interval

EndpointsLength of interval

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State plane

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Interval 2Dead time




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Interval 3D2 conduction




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Interval 4Dead time




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Interval 5 (1)D1 conduction




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Waveforms

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Average switch input current

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Average output current

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Average output current, p. 2

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Control input: transistor/diode conduction angle

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A way to solve and plot the characteristics

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Solving, p 2

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Results: Switch conversion ratio µ vs. F

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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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Soft-switching converters with constant switching frequency

With two or more active switches, we can obtain zero-voltage switching in converters operating at constant switching frequency

Often, the converter characteristics are nearly the same as their hard-switched PWM parent converters

The second switch may be one that is already in the PWM parent converter (synchronous rectifier, or part of a half or full bridge). Sometimes, it is not, and is a (hopefully small) auxiliary switch

Examples:• Two-switch quasi-square wave (with synchronous

rectifier)• Two-switch multiresonant (with synchronous rectifier)• Phase-shifted bridge with zero voltage transitions• Forward or other converter with active clamp circuit

These converters can exhibit stresses and characteristics that approach those of the parent hard-switched PWM converter (especially the last two), but with zero-voltage switching over a range of operating points

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Quasi-square wave buck with two switches

• Q2 can be viewed as a synchronous rectifier

• Additional degree of control is possible: let Q2 conduct longer than D2 would otherwise conduct

• Constant switching frequency control is possible, with behavior similar to conventional PWM

• Can obtain µ < 0.5

• See Maksimovic PhD thesis, 1989

Original one-switch version

Add synchronous rectifier

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State plane

• Remaining details of analysis left as homework problem

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Characteristics: 1 transistor version

µ vs. F

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Waveforms and definition of duty cycle, 2 transistors

• Here, the controller duty 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 of the DTs and D’Ts intervals.

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Constant-frequency control characteristicstwo switch quasi-resonant buck converter

Constant frequency, duty cycle control:

Low output impedance, µ doesn’t depend much on J

Very similar to conventional PWM CCM buck converter, but exhibits ZVS over a range of operating points

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ZVS boundary

Reducing F = fs/f0 leads to ZVS over a wider range of µ and J

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Parameters for various resonant switch networks