Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion I plan on indicating for each...

Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion

• I plan on indicating for each lecture(s) of this year the equivalent lecture(s) from Spr. 06. This will make it easy if you choose to watch those lectures to stay in synch with this years class if we should run at a slightly different pace. I will also indicate if there is any new material for this year not covered in Spr. 06 so you will know to watch / attend that particular lecture this year. Similarly, any material covered in Spr. 06 but not covered this year will not show up as an equivalent lecture so you will know you can skip it.

• Today (lecture 4) we will cover material covered in lecture 7 of the Spr. 06 class. You may wish to watch some of Spring 06 lectures 1 to 3 for some valuable insight and historical perspective on resonant power conversion techniques.

ECEN 5817Housekeeping


2 different ways to construct transfer function H


Dc conversion ratio of the PRC

At resonance, this becomes

• PRC can step up the voltage, provided R > R0

• PRC can produce M approaching infinity, provided output current is limited to value less than Vg / R0


Model: series resonant converter


Comparison of approximate and exact characteristics

0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.2

0.4

0.6

0.8

1.0

exact M, Q=2approx M, Q=2exact M, Q=10approx M, Q=10exact M, Q=0.5approx M, Q=0.5

F

M =

V/V

g

1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

exact M, Q=0.5approx M, Q=0.5exact M, Q=10approx M, Q=10exact M, Q=2approx M, Q=2

F

M=

V/V

g

Series resonant converter

Below resonance:

0.5 < F < 1

Above resonance:

1 < F


Comparison of approximate and exact characteristics

Parallel resonant converterExact equation:

solid lines

Sinusoidal approximation: shaded lines


Chapter 19

Resonant Conversion

Introduction

19.1 Sinusoidal analysis of resonant converters

19.2 ExamplesSeries resonant converterParallel resonant converter

19.3 Soft switchingZero current switchingZero voltage switching

19.4 Load-dependent properties of resonant converters

19.5 Exact characteristics of the series and parallel resonant converters


19.3 Soft switching

Soft switching can mitigate some of the mechanisms of switching loss and possibly reduce the generation of EMI

Losses due to high voltage and high current present in switch during transitions, Losses due to shorting device capacitances

Semiconductor devices are switched on or off at the zero crossing of their voltage or current waveforms:

Zero-current switching: transistor turn-off transition occurs at zero current. Zero-current switching eliminates the switching loss caused by IGBT current tailing and by stray inductances. It can also be used to commutate SCR’s.

Zero-voltage switching: transistor turn-on transition occurs at zero voltage. Diodes may also operate with zero-voltage switching. Zero-voltage switching eliminates the switching loss induced by diode stored charge and device output capacitances.

Zero-voltage switching is usually preferred in modern converters, including soft-switching PWM converters.


19.3.1 Operation of the full bridge below resonance: Zero-current switching

Series resonant converter example

L

+–Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Current bi-directional switches

ZCS vs. ZVS depends on tank current zero crossings with respect to transistor switching times = tank voltage zero crossings

Operation below resonance: input tank current leads voltage

Zero-current switching (ZCS) occurs


Tank input impedance

Re

|| Zi ||

f0

L

R0

Qe = R0 /Re

Operation below resonance: tank input impedance Zi is dominated by tank capacitor.

Zi is negative, and tank input current leads tank input voltage.

Zero crossing of the tank input current waveform is(t) occurs before the zero crossing of the voltage vs(t) – before switch transitions


Switch network waveforms, below resonanceZero-current switching

t

vs(t)

Vg

– Vg

vs1(t)

t

is(t)

t

Q1

Q4

D1

D4

Q2

Q3

D2

D3

Conductingdevices:

“Hard”turn-on of

Q1, Q4

“Soft”turn-off of

Q1, Q4


Q2, Q3


Q2, Q3

L

+–Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Conduction sequence: Q1–D1–Q2–D2

Tank current is negative at the end of each half interval – antiparallel diodes conduct after their respective switches

Q1 is turned off during D1 conduction interval, without loss


Classical but misleading example: Transistor switchingwith clamped inductive load (4.3.1)

Buck converter example

transistor turn-off transition

Loss:


Switch network waveforms, below resonanceZero-current switching

t

vs(t)

Vg

– Vg

vs1(t)

t

is(t)

t

Q1

Q4

D1

D4

Q2

Q3

D2

D3

Conductingdevices:


Q1, Q4


Q1, Q4


Q2, Q3


Q2, Q3

L

+–Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Conduction sequence: Q1–D1–Q2–D2

Q1 is turned off during D1 conduction interval, without loss

Note on terminology:


ZCS turn-on transition: hard switching

L

+–Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Q1 turns on while D2 is conducting. Stored charge of D2 and of semiconductor output capacitances must be removed. Transistor turn-on transition is identical to hard-switched PWM, and switching loss occurs.

t

ids(t)

tQ1

Q4

D1

D4

Q2

Q3

D2

D3

Conductingdevices:


Q1, Q4


Q1, Q4

t

Vgvds1(t)


More on diode reverse recovery

Circuits with diode and switch in loop – when turn on switch diode turns off (unless ZVS)


More on diode reverse recovery

In steady-state:

Diode equations:

•

•

Stored minority charge profile underforward-biased conditions


Induced losses

•Stored charge is exponential function of voltage - require large change in q to get small change in vD

•vD remains > 0 until all stored charge removed – holding voltage across MOSFET = Vg while MOSFET is providing not only iL, but diode reverse current as well.

•Induces losses in MOSFET

•This energy loss is MUCH greater than the energy stored in diode in the form of stored charge as well as across depletion capacitance

rgrLgloss QVtIVW


19.3.2 Operation of the full bridge above resonance: Zero-voltage switching

Series resonant converter example

L

+–Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Operation above resonance: input tank current lags voltage

Zero-voltage switching (ZVS) occurs


Tank input impedance

Re

|| Zi ||

f0

L

R0

Qe = R0 /Re

Operation above resonance: tank input impedance Zi is dominated by tank inductor.

Zi is positive, and tank input current lags tank input voltage.

Zero crossing of the tank input current waveform is(t) occurs after the zero crossing of the voltage vs(t) – after switch transitions


Switch network waveforms, above resonanceZero-voltage switching

L

+–Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Conduction sequence: D1–Q1–D2–Q2

Tank current is negative at the beginning of each half-interval – antiparallel diodes conduct before their respective switches

Q1 is turned on during D1 conduction interval, without loss – D2 already off!

t

vs(t)

Vg

– Vg

vs1(t)

t

is(t)

t

Q1

Q4

D1

D4

Q2

Q3

D2

D3

Conductingdevices:

“Soft”turn-on of

Q1, Q4

“Hard”turn-off of

Q1, Q4


Q2, Q3


Q2, Q3


ZVS turn-off transition: hard switching?

L

+–Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

When Q1 turns off, D2 must begin conducting. Voltage across Q1 must increase to Vg. Transistor turn-off transition is identical to hard-switched PWM. Switching loss may occur… but….

t

ids(t)

Conductingdevices:

t

Vgvds1(t)

t

Q1

Q4

D1

D4

Q2

Q3

D2

D3


Q1, Q4


Q1, Q4


Classical but misleading example: Transistor switchingwith clamped inductive load (4.3.1)

Buck converter example

transistor turn-off transition

Loss:


Soft switching at the ZVS turn-off transition

L

+–Vg

Q1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

–

is(t)

+

vds1(t)

–to remainderof converter

Cleg

Cleg Cleg

Cleg

Conductingdevices:

t

Vgvds1(t)

Q1

Q4

D2

D3

Turn offQ1, Q4

Commutationinterval

X

• Introduce small capacitors Cleg across each device (or use device output capacitances).

• Introduce delay between turn-off of Q1 and turn-on of Q2.

Tank current is(t) charges and discharges Cleg. Turn-off transition becomes lossless. During commutation interval, no devices conduct.

So zero-voltage switching exhibits low switching loss: losses due to diode stored charge and device output capacitances are eliminated.


19.4 Load-dependent propertiesof resonant converters

Resonant inverter design objectives:

1. Operate with a specified load characteristic and range of operating points• With a nonlinear load, must properly match inverter output

characteristic to load characteristic

2. Obtain zero-voltage switching or zero-current switching• Preferably, obtain these properties at all loads• Could allow ZVS property to be lost at light load, if necessary

3. Minimize transistor currents and conduction losses• To obtain good efficiency at light load, the transistor current should

scale proportionally to load current (in resonant converters, it often doesn’t!)

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