Resonant converstion

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Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion

Chapter 19

Resonant Conversion

Introduction

19.1 Sinusoidal analysis of resonant converters

19.2 Examples

Series resonant converter

Parallel resonant converter

19.3 Exact characteristics of the series and parallel resonantconverters

19.4 Soft switching

Zero current switchingZero voltage switching

The zero voltage transition converter

19.5 Load-dependent properties of resonant converters


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Introduction to Resonant Conversion

Resonant power converters contain resonant L-C networks whosevoltage and current waveforms vary sinusoidally during one or moresubintervals of each switching period. These sinusoidal variations arelarge in magnitude, and the small ripple approximation does not apply.

Some types of resonant converters:

Dc-to-high-frequency-ac inverters

Resonant dc-dc converters

Resonant inverters or rectifiers producing line-frequency ac


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A basic class of resonant inverters

Resonant tank network

ResistiveloadR

is(t) i(t)

v(t)

+

+

dcsource

vg(t)vs(t)

+

Switch network

L Cs

Cp

NS NT

Series tank network

L Cs

Basic circuit

Several resonant tank networks

Parallel tank network

L

Cp

LCC tank ne twork

L Cs

Cp


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Tank network responds only to fundamental

component of switched waveforms

f

Switch

output

voltage

spectrum

Resonant

tank

response

Tank

current

spectrum

ffs 3fs 5fs

ffs 3fs 5fs

fs 3fs 5fs

Tank current and outputvoltage are essentiallysinusoids at the switching

frequencyfs.Output can be controlledby variation of switchingfrequency, closer to oraway from the tankresonant frequency


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An electronic ballast

Half-bridge, driving LCC tank circuit and gasdischarge lamp

Must producecontrollable high-frequency (50 kHz)ac to drive gas

discharge lamp

DC input istypically producedby a low-harmonicrectifier

Similar to resonantdc-dc converter,but output-siderectifier is omitted


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Derivation of a resonant dc-dc converter

Rectify and filter the output of a dc-high-frequency-ac inverter

The series resonant dc-dc converter


7/27Fundamentals of Power Electronics 7 Chapter 19: Resonant Conversion

A series resonant link inverter

+

R

+

v(t)

Resonant tank network

dcsource

vg(t)

Switch network

L Cs

i(t)

Low-passfilter

network

acload

Switch network

Same as dc-dc series resonant converter, except output rectifiers arereplaced with four-quadrant switches:



Resonant conversion: advantages

The chief advantage of resonant converters: reduced switching loss

Zero-current switching

Zero-voltage switching

Turn-on or turn-off transitions of semiconductor devices can occur atzero crossings of tank voltage or current waveforms, thereby reducingor eliminating some of the switching loss mechanisms. Henceresonant converters can operate at higher switching frequencies thancomparable PWM converters

Zero-voltage switching also reduces converter-generated EMI

Zero-current switching can be used to commutate SCRs

In specialized applications, resonant networks may be unavoidable

High voltage converters: significant transformer leakageinductance and winding capacitance leads to resonant network



Resonant conversion: disadvantages

Can optimize performance at one operating point, but not with widerange of input voltage and load power variations

Significant currents may circulate through the tank elements, evenwhen the load is disconnected, leading to poor efficiency at light load

Quasi-sinusoidal waveforms exhibit higher peak values thanequivalent rectangular waveforms

These considerations lead to increased conduction losses, which canoffset the reduction in switching loss

Resonant converters are usually controlled by variation of switchingfrequency. In some schemes, the range of switching frequencies canbe very large

Complexity of analysis



Resonant conversion: Outline of discussion

Simple steady-state analysis via sinusoidal approximation

Simple and exact results for the series and parallel resonantconverters

Mechanisms of soft switching

Resonant inverter design techniques. Circulating currents, and thedependence (or lack thereof) of conduction loss on load power

Following this chapter: extension of sinusoidal analysis techniques to

model control system dynamics and small-signal transfer functions



19.1 Sinusoidal analysis of resonant converters

A resonant dc-dc converter:

If tank responds primarily to fundamental component of switchnetwork output voltage waveform, then harmonics can be neglected.

Let us model all ac waveforms by their fundamental components.



The sinusoidal approximation

f

Switch

output

voltage

spectrum

Resonant

tank

response

Tank

current

spectrum

ffs 3fs 5fs

ffs 3fs 5fs

fs 3fs 5fs

Tank current and outputvoltage are essentiallysinusoids at the switching

frequencyfs.Neglect harmonics ofswitch output voltagewaveform, and model onlythe fundamentalcomponent.

Remaining ac waveformscan be found via phasoranalysis.



19.1.1 Controlled switch network model

is(t)

+

vg vs(t)

+

Switch network

NS

1

2

1

2

If the switch network produces asquare wave, then its outputvoltage has the following Fourierseries:

The fundamental component is

So model switch network output portwith voltage source of value vs1(t)


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Model of switch network input port

is(t)

+

vg vs(t)

+

Switch network

NS

1

2

1

2

Assume that switch network

output current is

It is desired to model the dccomponent (average value)of the switch network inputcurrent.


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Switch network: equivalent circuit

Switch network converts dc to ac

Dc components of input port waveforms are modeled Fundamental ac components of output port waveforms are modeled

Model is power conservative: predicted average input and outputpowers are equal


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19.1.2 Modeling the rectifier and capacitive

filter networks

Assume large output filter

capacitor, having small ripple.

vR(t) is a square wave, havingzero crossings in phase with tankoutput current iR(t).

If iR(t) is a sinusoid:

Then vR(t) has the followingFourier series:


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Sinusoidal approximation: rectifier

Again, since tank responds only to fundamental components of appliedwaveforms, harmonics in vR(t) can be neglected. vR(t) becomes

Actual waveforms with harmonics ignored


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Rectifier dc output port model

Output capacitor charge balance: dcload current is equal to averagerectified tank output current

Hence


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Equivalent circuit of rectifier

Rectifier input port:

Fundamental components ofcurrent and voltage aresinusoids that are in phase

Hence rectifier presents aresistive load to tank network

Effective resistanceRe is

With a resistive loadR, this becomes

Rectifier equivalent circuit


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19.1.3 Resonant tank network

Model of ac waveforms is now reduced to a linear circuit. Tanknetwork is excited by effective sinusoidal voltage (switch networkoutput port), and is load by effective resistive load (rectifier input port).

Can solve for transfer function via conventional linear circuit analysis.


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Solution of tank network waveforms

Transfer function:

Ratio of peak values of input and

output voltages:

Solution for tank output current:

which has peak magnitude


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19.1.4 Solution of converter

voltage conversion ratio M= V/Vg

EliminateRe:


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Conversion ratio M

So we have shown that the conversion ratio of a resonant converter,

having switch and rectifier networks as in previous slides, is equal tothe magnitude of the tank network transfer function. This transferfunction is evaluated with the tank loaded by the effective rectifierinput resistanceRe.


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19.2 Examples

19.2.1 Series resonant converter


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Model: series resonant converter


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Construction ofZi


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Construction ofH

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