chapter 19 resonant conversionecee.colorado.edu/~ecen5817/lectures/l3_ecen5817_notes.pdf19.2.3...

ECEN5817, ECEE Department, University of Colorado at Boulder

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

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19.4 Load-dependent properties of resonant converters

19.5 Exact characteristics of the series and parallel resonant converters

A class of resonant DC-to-AC inverters

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A resonant DC-DC converter

Transfer functionH(s)

A resonant dc-dc converter:

iR(t)

vR(t)

+

–

+– R

+

v(t)

–

Resonant tank network

is(t)

dcsource

vg(t)vs(t)

+

–

Switch network

L Cs

NS NT

i(t)

Rectifier network

NR NF

Low-passfilter

network

dcload

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network

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

Section 19.1: modeling based on sinusoidal approximation

The sinusoidal approximation

Switchoutput

Tank current and output

f

voltagespectrum

Resonanttank

response

ffs 3fs 5fs

f 3f 5f

Tank current and output voltage are essentially sinusoids at the switching frequency fs

Neglect harmonics of switch output voltage waveform, and model only the fundamental

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f

Tankcurrent

spectrum

ffs 3fs 5fs

fs 3fs 5fs component

Remaining ac waveforms can be found via standard phasor analysis


19.1.1 Controlled switch network model

is(t)NS

1

+–vg vs(t)

+

–

Switch network

1

2

1

2

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Fourier series expansion of square-wave switch network output voltage vs(t):

The fundamental component is

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

Model of switch network input port

is(t)

+

NS

1

Find dc (average) component of the switch network input current

+–vg vs(t)

–

Switch network

2

1

2

Fundamental component of the

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output current:


Switch network: equivalent circuit

• Switch network converts dc to ac

• Dc components of input port waveforms are modeled

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• Fundamental ac components of output port waveforms are modeled

• Model is power conservative: predicted average input and output powers are equal

19.1.2 Modeling the rectifier and capacitive filter networks

iR(t)

R

+

(t)

i(t)

+

(t)

| iR(t) |

Rv(t)

–

Rectifier network

NR NF

Low-passfilter

network

dcload

vR(t)

–

Assume large output filter it h i ll i l

If iR(t) is a sinusoid:

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capacitor, having small ripple.

vR(t) is a square wave, having zero crossings in phase with tank output current iR(t).

Then vR(t) has the following Fourier series:


Sinusoidal approximation: rectifier

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

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Rectifier dc output port model

iR(t)

R

+

v(t)

i(t)

+

vR(t)

| iR(t) | Output capacitor charge balance: dc load current is equal to average rectified tank output current

Rv(t)

–

Rectifier network

NR NF

Low-passfilter

network

dcload

vR(t)

–

Hence

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Equivalent circuit of rectifier

Rectifier input port:

Fundamental components of current and voltage are i id h i hsinusoids that are in phase

Hence rectifier presents a resistive load to tank network

Effective resistance Re is

Rectifier equivalent circuit

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With a resistive load R, this becomes

Loss free resistor: all power absorbed by Re is transferred to the output port

19.1.3 Resonant tank network

Model of ac waveforms is now reduced to a linear circuit. Tank k i i d b ff i i id l l ( i h k

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network is excited by effective sinusoidal voltage (switch network output port), and is load by effective resistive load (rectifier input port)

Can solve for transfer function via conventional linear circuit analysis


Solution of tank network waveforms

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19.1.4 Solution of convertervoltage conversion ratio M = V/Vg

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19.2 Examples19.2.1 Series resonant converter

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Model: series resonant converter

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Construction of Zi – resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 10 Ω

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Construction of H = V / Vg – resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 10 Ω

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Model: series resonant converter

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19.2.2 Subharmonic modes of the SRC

Example: excitation of tank by third harmonic of switching frequency

Can now approximate vs(t) by its third harmonic:

Result of analysis:

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SRC DC conversion ratio M

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Subharmonic modes

19.2.3 Parallel resonant dc-dc converter

Differs from series resonant converter as follows:

Different tank network

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Rectifier is driven by sinusoidal voltage, and is connected to inductive-input low-pass filter

Need a new model for rectifier and filter networks


Model of uncontrolled rectifierwith inductive filter network – input port

Fundamental component of iR(t):

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Model of uncontrolled rectifierwith inductive filter network – output port

Output inductor volt second balance: dc voltage is equal to average rectified tank output voltage

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Effective resistance Re

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Equivalent circuit model of uncontrolled rectifierwith inductive filter network

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Output port modeled as a dependent voltage source based on rectified tank voltage, in contrast to SRC where output port is modeled as dependent current source based on rectified tank current


Equivalent circuit modelParallel resonant dc-dc converter

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Ways to construct transfer function H in terms of impedances

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Construction of Zo – resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ

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Construction of H = V / Vg – resonant (high Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ

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Construction of H

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Dc conversion ratio of the PRC

At resonance, this becomes

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• 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


Comparison of approximate and exact PRC characteristics

Parallel resonant converterExact equation:

solid linessolid lines

Sinusoidal approximation: shaded lines

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chapter 19 resonant conversionecee.colorado.edu/~ecen5817/lectures/l3_ecen5817_notes.pdf19.2.3...

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