ECEN 5817 Housekeeping update

Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion

• For both on-campus and CAETE students: A DVD of recorded lectures from Professor Erickson’s Spring ’06 class will be mailed to you sometime next week. These will not be available on the CAETE website CUAnywhere.colorado.edu

• For on-campus students: You will not have access to this semesters recorded lectures on the CAETE website

• For CAETE students: By popular request, scanned and e-mailed homework will be accepted provided the submissions meet the following requirements:• Black and white (no color, no grayscale)• 200 – 300 dpi• All problems scanned into ONE PDF file for the whole assignment• PDF file is easy to read, easy to open, and easy to print

ECEN 5817Housekeeping update


Chapter 19Resonant 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


Equivalent circuit of rectifier

Rectifier input port:

Fundamental components of current and voltage are sinusoids that are in phase

Hence rectifier presents a resistive load to tank network

Effective resistance Re is

With a resistive load R, this becomes

Rectifier equivalent circuit

Loss free resistor


19.1.4 Solution of convertervoltage conversion ratio M = V/Vg

Eliminate Re:


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 to the magnitude of the tank network transfer function. This transfer function is evaluated with the tank loaded by the effective rectifier input resistance Re.


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:


Subharmonic modes of SRC

•Not often used - reduced switch utilization and decreased voltage conversion ratio

•Still need to be aware their existence


19.2 Examples19.2.1 Series resonant converter

iR(t)

vR(t)

+

–

+–

transfer functionH(s)

R

+

v(t)

–

resonant tank network

is(t)

dcsource

vg(t)vs(t)

+

–

switch network

L Cs

NS NT

i(t)

rectifier networkNR NF

low-passfilter

network

dcload


Model: series resonant converter


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


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

Buck characteristic


Construction of Zi


Construction of H

ee RRQ /0


Model: series resonant converter


Construction of Zi – Non-resonant (low Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ


Construction of H – Non-resonant (low Q) caseC = 0.1 μF, L = 1 mH, Re = 1 kΩ


19.2.3 Parallel resonant dc-dc converter

Differs from series resonant converter as follows:

Different tank network

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):


Model of uncontrolled rectifierwith inductive filter network – output port

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


Effective resistance Re

Again define

In steady state, the dc output voltage V is equal to the average value of | vR |:

For a resistive load, V = IR. The effective resistance Re can then be expressed


Equivalent circuit model of uncontrolled rectifierwith inductive filter network

Dependent voltage source based on rectified tank voltage. Vs. SRC, dependent current source based on rectified tank current.


Equivalent circuit modelParallel resonant dc-dc converter


2 different ways to construct transfer function H


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


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

Buck-boost characteristic


Construction of Zo


Construction of 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


Comparison of approximate and exact characteristics

0.5 0.6 0.7 0.8 0.9 1.00.0

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 50.0

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

/Vg

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

ECEN 5817 Housekeeping update

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