fundamentals of power electronics 1 chapter 19: resonant conversion 19.3.1 operation of the full...

Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion

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:


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)


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.

Also get reduction in EMI.


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


19.4 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!)


Topics of DiscussionSection 19.4

Inverter output i-v characteristics

Two theorems• Dependence of transistor current on load current• Dependence of zero-voltage/zero-current switching on load

resistance• Simple, intuitive frequency-domain approach to design of resonant

converter

Example

Analysis valid for resonant inverters with resistive loads as well as resonant converters operating in CCM


CCM PWM vs. resonant inverter output characteristics

CCM PWM• Low output impedance – neglecting

losses, output voltage function of duty cycle only, not of load

• Steady-state IV curve looks like voltage source

Resonant inverter (or converter operating in CCM)

• Higher output impedance – output voltage strong function of both control input and load current (load resistance)

• What does steady-state IV curve look like? (i.e. how does || v || depend on || i ||?)


Analysis of inverter output characteristics – simplifying assumptions

• Load is resistive

– Load does not change resonant frequency

– Can include any reactive components in tank

• Resonant network is purely reactive (neglect losses)


Thevenin equivalent of tank network output port

Voltage divider

Sinusoidal steady-state


Output magnitude


Inverter output characteristics



Let H be the open-circuit (R→) transfer function:

and let Zo0 be the output impedance (with vi →short-circuit). Then,

The output voltage magnitude is:

with

This result can be rearranged to obtain

Hence, at a given frequency, the output characteristic (i.e., the relation between ||vo|| and ||io||) of any resonant inverter of this class is elliptical.



General resonant inverter output characteristics are elliptical, of the form

This result is valid provided that (i) the resonant network is purely reactive, and (ii) the load is purely resistive.

with


Matching ellipseto application requirements

Electronic ballast Electrosurgical generator


Example of gas discharge lamp ignition and steady-state operation from CoPEC research

LCC resonant inverter

Vg = 300 VIref = 5 A


Example of repeated lamp ignition attempts with overvoltage protection

LCC resonant inverter

Vg = 300 VIref = 5 AOvervoltage protection at 3500 V


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!)


Input impedance of the resonant tank network

vs1(t)

EffectiveresistiveloadR

is(t) i(t)

v(t)

+

–

Zi Zo

Transfer functionH(s)

+–

Effectivesinusoidal

sourceResonantnetwork

Purely reactive

where


ZN and ZD

ZD is equal to the tank output impedance under the condition that the tank input source vs1 is open-circuited. ZD = Zo

ZN is equal to the tank output impedance under the condition that the tank input source vs1 is short-circuited. ZN = Zo


Magnitude of the tank input impedance

If the tank network is purely reactive, then each of its impedances and transfer functions have zero real parts, and the tank input and output impedances are imaginary quantities. Hence, we can express the input impedance magnitude as follows:


A Theorem relating transistor current variations to load resistance R

Theorem 1: If the tank network is purely reactive, then its input impedance || Zi || is a monotonic function of the load resistance R.

So as the load resistance R varies from 0 to , the resonant network input impedance || Zi || varies monotonically from the short-circuit value|| Zi0 || to the open-circuit value || Zi ||.

The impedances || Zi || and || Zi0 || are easy to construct. If you want to minimize the circulating tank currents at light load,

maximize || Zi ||. Note: for many inverters, || Zi || < || Zi0 || ! The no-load transistor current

is therefore greater than the short-circuit transistor current.


Proof of Theorem 1

Derivative has roots at:

Previously shown: Differentiate:

So the resonant network input impedance is a monotonic function of R, over the range 0 < R < .

In the special case || Zi0 || = || Zi||,|| Zi || is independent of R.


Zi0 and Zi for 3 common inverters

fundamentals of power electronics 1 chapter 19: resonant conversion 19.3.1 operation of the full...

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