Power Electronics Group - PEL 1 CCFL Inverters based on Piezoelectric Transformers: Analysis and Design Considerations Prof. Giorgio Spiazzi Dept. Of Information

11Power Electronics Group - PELPower Electronics Group - PEL

CCFL Inverters based on Piezoelectric

Transformers: Analysis and Design

Considerations

CCFL Inverters based on Piezoelectric

Transformers: Analysis and Design

ConsiderationsProf. Giorgio SpiazziProf. Giorgio Spiazzi

• Dept. Of Information Engineering – DEI• University of Padova


Outline

• Characteristics of Cold Cathode Fluorescent Lamps (CCFL)

• Review of piezoelectric effect• CCFL inverters based on

piezoelectric transformers• Design considerations• Modeling


Cold Cathode Fluorescent Lamp (CCFL)

• CCFL is a mercury vapor discharge light source which produces its output from a stimulated phosphor coating inside glass lamp envelope.

• Closely related to “neon” sign lamps first introduced in 1910 by Georges Claude in Paris

• Cold cathode refers to the type of electrodes used: they do not rely on additional means of thermoionic emission besides that created by electrical discharge through the tube





• The phosphors coating the lamp tube inner surface are composed of Red-Green-Blue fluorescent compounds mixed in the appropriate ratio in order to obtain a good color rendering when used as an LCD display backlight

Energy conversion efficiency:Energy conversion efficiency:

Ultraviolet lightUltraviolet light

Visible lightVisible light


Cold Cathode Fluorescent Lamp

Lamp v-i characteristic:Lamp v-i characteristic:

Lamp Lamp lengthlength

Lamp voltage primarily depends on length and is fairly constant Lamp voltage primarily depends on length and is fairly constant with current, giving a non-linear characteristic. Lamp current is with current, giving a non-linear characteristic. Lamp current is roughly proportional to brightness or intensity and is the roughly proportional to brightness or intensity and is the controlled variable of the backlight supply.controlled variable of the backlight supply.



• These lamps require a high ac voltage for ignition and operation.

• A sinusoidal voltage provides the best electrical-to-optical conversion.

• There are four important parameters in driving the CCFL: – strike voltage – maintaining voltage– frequency– lamp current



• Operating a CCFL over time results in degradation of light output. Typical life rating is 20000 hours to 50% of the lamp initial output

• The light output of a CCFL has a strong dependency on temperature

Percentage of light output as a function Percentage of light output as a function of lamp temperatureof lamp temperature



• Stray capacitances to ground cause a considerable loading effect that can easily degrade efficiency by 25%

Lamp display housing:Lamp display housing:


Current-fed Self-

Resonant Royer

Converter


High voltage High voltage transformertransformer


Ballast Ballast capacitorcapacitor


Self resonant Self resonant inverterinverter


Control of Control of supply currentsupply current


Lamp current Lamp current measurementmeasurement


DimmingDimming


Magnetic and Piezoelectric Transformer Comparison

• Low cost• Multiple sources• Single-ended or balanced output• Wide range of load conditions (output power

easily scaled)• Secondary side ballasting capacitor required• Reliability affected by the high-voltage

secondary winding• EMI generation (stray high-frequency

magnetic field)

Magnetic transformer characteristicsMagnetic transformer characteristics



• Inherent sinusoidal operation• High strike voltage (no need of ballasting

capacitor)• No magnetic noise• Small size• High cost (but decreasing)• Must be matched with lamp characteristics• Reduced power capability• Single-ended output (balanced output are possible) • Few sources• Unsafe operation at no load (can be damaged)

Piezoelectric transformer characteristicsPiezoelectric transformer characteristics



Size comparisonSize comparison


Piezoelectric Effect

• The piezoelectric effect was discovered in 1880 by Jacques and Pierre Curie:– Tension and compression applied to

certain crystalline materials generate voltages (piezoelectric effect)

– Application to the same crystals of an electric field produces lengthening or shortening of the crystals according to the polarity of the field (inverse piezoelectric effect)



• In the 20th century metal oxide-based piezoelectric ceramics have been developed.

• Piezoelectric ceramics are prepared using fine powders of metal oxides in specific proportion mixed with an organic binder. Heating at specific temperature and time allows to attain a dense crystalline structure

• Below the Curie point they exhibit a tetragonal or rhombohedral symmetry and a dipole moment

• Adjoining dipoles form regions of local alignment called domains

• The direction of polarization among neighboring domains is random, producing no overall polarization

• A strong DC electric field gives a net permanent polarization (poling)



Po

lari

zati

on

axi

sP

ola

riza

tio

n a

xis

Random orientation Random orientation of polar domainsof polar domains

Polarization using Polarization using a DC electric fielda DC electric field

Residual Residual polarizationpolarization

PolarizationPolarization



Effect of electric field E Effect of electric field E on polarization P and on polarization P and

corresponding corresponding elongation/contraction of elongation/contraction of

the ceramic materialthe ceramic material

Relative increase/decrease in dimension (strain S) in direction of polarization



EE

EE

SS

PP


Disk after polarization

(poling)

Disk compressed

Disk stretched

Applied voltage of

same polarity as poling voltage

Applied voltage of opposite

polarity as poling voltage

Po

lin

g v

olt

age


Generator and motor actions Generator and motor actions of a piezoelectric elementof a piezoelectric element


Actuator Actuator behaviorbehavior

Transducer Transducer behaviorbehavior

S=sE.T+d.E

D=d.T+T.EWhere:S: Strain [ ]T: Stress [N/m2]E: Electric Field [V/m]s: elastic compliance [m2/N]D: Electric Displacement [C/m2]d: Piezoelectric constant [m/V]

Piezoelectric EffectPolarization



Based on the poling orientation, the piezoelectric ceramics can be design to

function in:

longitudinal mode: P is parallel to THas a larger d33, along the thickness direction when compared to the planar direction

transverse mode: P is perpendicular to THas a larger d31, along the planar direction when compared to the thickness direction


Piezoelectric Transformers (PT)

• In Piezoelectric Transformers, energy is transformed from electrical form to electrical form via mechanical vibration.



•Longitudinal vibration mode– Transverse actuator and Longitudinal

transducer Rosen-type or High-Voltage PT

Three main categoriesThree main categories



• Thickness vibration mode– Longitudinal actuator and Longitudinal

transducer Low-Voltage PT




•Radial vibration mode– Transverse actuator and Transverse

transducer (radial shape preferred)



Equivalent Electric Model

Rosen-type Thick. Vibr. mode Radial Vibr. modeR 0.756199 1.44 6.89991 L 2.464173mH 27H 7.93842mHC 3.57nF 254pF 269.171pFN 35.89 0.47 0.908Ci 81.6216nF 2.305nF 4.60799nF

Co 23.85pF 8.911nF 1.62414nF

length=30mm length=20mm radius=10.5mmwidth=8mm width=20mm thickness1=0.76mmthickness=2mm thickness=2.2mm thickness2=2.28mm

L C+

Ui Uo

+

-

Io

iL

R

CoRL

Ci-1:N


Voltage Gain

Load resistance: 1M, 100k, 10k, 5k, 1k, 500

Rosen-type Piezoelectric Transformer sample

Resonance frequencies


Load resistance: 1M, 100k, 10k, 5k, 1k, 500

Rosen-type Piezoelectric Transformer sample

Input Impedance


Half-Bridge Inverter for PT

Lam

p

PT+UDC

iinv

C1

S1

S2C2

iL

Half-Bridge inverter

ui

+

-


Soft-Switching Condition

T/2

tr

t

ui

UDC

t

/

iinv

U1 Fundamental components

Half-bridge inverter


Coupling Networks

PT Rosen-type Model

L C

+

uiUo

+

-

iL

R

CoCi

-

UA

+

+UA

io

S1

S2

C1

C2

LampHalf-Bridge

inverter

1:n21

+

uinv

-

Cou

plin

g n

etw

ork

Zg


Coupling Networks

• It is not always possible to find a value for input inductor that guarantees both power transfer and soft switching requirements

• Less circulating energy as compared to parallel inductor

• Non linear control characteristics can lead to large signal instabilities

Series inductor

Ls

CN1


Effect of Coupling Inductor Ls on Voltage Conversion Ratio

MPT = UoRMS/UiRMS, Mi = UiRMS/UinvRMS, Mg = Mi MPT

f270

[dB]

|MPT|{|Mg|{

|Mi|{

-1045 50 55 60 65 70 75 80

f1

Io=1mA

Io=6mA

|Mgd|Io=1mA

|Mgd|Io=6mA

fsw [kHz]

Udc=13V, Ls=42H

Udc=13V, Ls=42H


Effect of Coupling Inductor Ls on Input Impedance

Positive input phasePositive input phase

f160

[dB]

|Zg|

045 50 55 60 65 70 75 80

fsw [kHz]

f2

Io=1mA

Io=6mA

Zg

2

2

0


Effect of Coupling Inductor Ls on Voltage Conversion Ratio

• It introduces an additional voltage gain (frequency dependent) between the RMS value of the inverter voltage fundamental component and the RMS value of the PT input voltage

• It introduces more resonant peaks in the overall voltage gain Mg (limitation in switching frequency variation)


Control Characteristics: Variable Frequency

1

4

3

5

Io

[mARMS]

2

60 61 62 63 65

fsw [kHz]64

Udc = 13V


Control Characteristics: Variable dc Link Voltage

1

4

3

5

Io

[mARMS]

Ls = 42H2

11 12 13 14 15

Udc [V]16

fsw = 65kHz

CNCN11CNCN11

Ls = 38H

Increasing LIncreasing LSS value causes the gain curve value causes the gain curve

IIoo = f(U = f(UAA) to become non monotonic) to become non monotonic


Large-Signal Instability

ILS = [5A/div]

ui = [50V/div]

Io = [10mA/div]

ILS = [5A/div]

ui = [50V/div]

Io = [10mA/div]

Main converter waveforms when Udc is slowly approaching 21V (fsw = 65kHz, Ls = 42H).


Coupling Networks

• It is always possible to find a value for input inductor that guarantees both power transfer and soft switching requirements

• Higher circulating energy as compared to series inductor

Parallel inductor

Lp

CB

CN2


Effect of Coupling Network on Voltage Conversion Ratio

f150

[dB]

045 50 55 60 65 70 75 80

fsw [kHz]

f2

}Io=1mA}Io=6mA|MPT|{

|Mg|{

|Mi|{

|Mgd|Io=1mA

|Mgd|Io=6mA

Io=1mAIo=6mA

CNCN22: L: Lpp=20=20H, CH, CBB=1=1F, UF, Udcdc=30V=30VCNCN22: L: Lpp=20=20H, CH, CBB=1=1F, UF, Udcdc=30V=30V


Effect of Coupling Network on Input Impedance

f160

[dB]

|Zg|

045 50 55 60 65 70 75 80

fsw [kHz]

f2

Io=1mA Io=6mA

Zg2

2

0


Effect of Coupling Network on Switch Commutations

• Differently from the series inductor coupling network, now the inductor current iLp has to charge and discharge also the PZT input capacitance, that is much higher than the switch output capacitances, so that the positive impedance phase is a necessary but not sufficient condition to achieve soft commutations


Experimental Measurements

iLp io

uinv

Trapezoidal PT input voltageTrapezoidal PT input voltageTrapezoidal PT input voltageTrapezoidal PT input voltage

Charge of input

capacitance

Charge of input

capacitance


Control Characteristics: Variable Frequency

1

4

3

5

Io

[mARMS]

2

64 66 68 70 72

fsw [kHz]

Lp = 20H, CB = 1F

Udc = 30V

CNCN22CNCN22


Control Characteristics: variable dc link voltage

1

4

3

5

Io

[mARMS]

Lp = 20H, CB = 1F

2

10 15 20 25 30

Udc [V]35

fsw = 65kHz

CNCN22CNCN22



• Square-wave output voltage• Switching frequency changes in order

to control lamp current• Attention must be paid to the

resonance frequency change with load• Dedicated IC available

Frequency Control



Frequency Control



• Constant switching frequency• Asymmetrical output pulses• Amplitude of fundamental input voltage

component is controlled by the duty-cycle• Many control ICs for DC/DC converters can be

used

Duty-cycle Control

tont

ui

UDC

TS

U1S

on

Tt

cycleduty


Full-Bridge Inverter for PT

Lam

p

PT+

iinv

S1

S2iL

S3

S4

Full-Bridge inverter

UDC ui

+

-

• Switching frequency control• Duty-cycle control• Phase-shift control


Full-Bridge Inverter for PT

• Constant switching frequency• Amplitude of fundamental input

voltage component is controlled by phase shifting the inverter legs

• No DC voltage applied to PT• Dedicated control IC

Phase-Shift Control


Resonant Push-Pull Topology


Resonant Push-Pull Topology

• Variable switching frequency• Voltage gain at PT input• Sinusoidal driving voltage


Analysis of Small-Signal Instabilities and Modeling

ApproachesExample of high-frequency V –I Example of high-frequency V –I

characteristics characteristics OSRAM L 18W/10OSRAM L 18W/10


Steady-state VRMS-IRMS Characteristic

MATSUSHITA MATSUSHITA FHF32 T-8 32WFHF32 T-8 32W

Negative incremental Negative incremental impedanceimpedance

Positive incremental Positive incremental impedanceimpedance


Modulated Lamp Voltage and Current

Upper trace: iUpper trace: iLampLamp [0.5A/div] Lower trace: u [0.5A/div] Lower trace: uLampLamp [74V/div] [74V/div]

tsinuU2tu sooo tsinUtu moo

mmoo tsinIti

OSRAMOSRAM

L 18W/10L 18W/10

ffmm=200Hz=200Hz ffmm=2kHz=2kHz

ffmm=5kHz=5kHz

tsiniI2ti sooo

Incremental Incremental impedance:impedance:

mo

oL

I

UZ


Lamp Incremental Impedance

Re(ZRe(ZLL))

Im(ZIm(ZLL))

mm= 0= 0 mm= =

p

zLL s

1

s1

KZApproximation:Approximation: KKLL< 0, < 0, zz< 0< 0

Right-half plane zeroRight-half plane zero


Lamp Model (Ben Yaakov)

IIo1o1IIo2o2

UUo2o2

UUo1o1

SRslope

So

maxoL R

I

UR 1oL1oS1o1oSmaxo IRIRUIRU

LRslope



2o

3L K

I

KR KK22, K, K33 = lamp constants = lamp constants

o2od

3oLo IK

I

KIRU

The lamp resistance is considered to be dependent The lamp resistance is considered to be dependent on a delayed version of RMS lamp currenton a delayed version of RMS lamp current

ododq

3oLqod

odq

3o2

odq

3od

IIod

oo

IIo

oo i

I

KiRi

I

KiK

I

Ki

I

Ui

I

Uu

odqooqo

Small-signal perturbation:Small-signal perturbation:

Subscript q means quiescent pointSubscript q means quiescent point



sIGKRs

sIGI

KR

s1sIG

I

KsIRsU

oL2LqL

oLodq

3Lq

LoL

odq

3oLqo

sIsGsIs

1

1sI oLo

L

od

p

z2

o

oL s

1

s1

KsI

sUsZ

Lq

2Lz R

K

0K0Z 2L Lp

Delay:Delay:


Lamp Pspice Model (Ben Yaakov)

uuoo

Lamp time constantLamp time constant

++

--

iioo22 IIoRMSoRMS

22

iioo=u=uoo/R/RLL

2o

3L K

I

KR


Accounts also for Accounts also for the positive slopethe positive slope

Lamp Model (Do Prado)

LPbL eaR PPLL = Lamp power = Lamp power

a, b positive constantsa, b positive constants

0.2

0.4

0.6

0.8

1.0

1.2

21 3 4 5 6

Io [mARMS]

RL [M]

600

700

800

900

1000

1100

1200

Uo [VRMS]

21 3 4 5 6

Io [mARMS]



LooqLqpbPb

ooqpPb

ooqooq pb1iIReeaiIeaiIuU LLLL

LPbL eaR



LoqLqoLqo pIbRiRu

sPIbRsIRsU LoqLqoLqo

sGsUIsIUGsIIsUUsP LooqooqLooqooqL Delay:Delay:



LqL

LqL

Lq

LqLq

LLq

LLqLq

o

oL

bP1

s1

bP1

s1

bP1

bP1R

sGbP1

sGbP1R

sI

sUsZ

p

z

p

zLq

o

oL s

1

s1

RsI

sUZ

LqLz Pb1

LqLp Pb1

If bPIf bPLqLq>1: >1: zz<0, Z<0, ZLL(0)<0(0)<0

Negative incremental impedance and Negative incremental impedance and RHP zeroRHP zero


Lamp Pspice Model (Do Prado)

PPLL

RRLL

uuoo

uuoo-R-R44iioo

iioo



Lamp Model (Onishi)

AA00-A-A44 positive constants positive constantso

IA3

IA1o

L I

eAeAAR

o4o2



Delay:Delay:

ood

IA3

IA1o

oLo II

eAeAAIRU

od4od2

odLpIA

43IA

21oLqodIIod

oo

IIo

oo iReAAeAAiRi

I

Ui

I

Uu oq4oq2

odqooqo

sIsGsI oLod

sIsGReAAeAAs

1RsU oLLpIA

43IA

21L

Lqooq4oq2


Lamp Model (Onishi)

p

zs

o

oL s

1

s1

RsI

sUsZ

Lq

sLz R

R Lp oq4oq2 IA

43IA

21s eAAeAAR

Negative incremental impedance and Negative incremental impedance and RHP zeroRHP zero

If RIf RSS>0: >0: zz<0, Z<0, ZLL(0)<0(0)<0


Lamp Pspice Model (Onishi)

IIoRMSoRMS

RRLL

UUoo=R=RLLiioo



Control Problem

0,s

s

I

U

sI

sUsZ z

p

z

o

o

o

oL

An Impedance with a RHP zero cannot be driven An Impedance with a RHP zero cannot be driven directly by a voltage source, since its current directly by a voltage source, since its current

transfer function will contain a RHP poletransfer function will contain a RHP pole


Series Impedance Lamp Ballast

++UUSS(s)(s)

ZZBB

ZZLL

--UUoo(s)(s)

FB

B

LBS

o

T1

1

Z

1

ZZ

1

1

Z

1

sU

sI

IIoo(s)(s)

TTFF must satisfy Nyquist stability criterion must satisfy Nyquist stability criterion

B

LF Z

ZT


Example of Instability

Series inductor coupling networkSeries inductor coupling network

LSLSInverterInverter

PTPTLampLamp

uiui

isis

+-

ffoscosc 6kHz 6kHz


Example of Instability

ILp = [1A/div]

Io = [2mA/div]

fosc=6.45kHzfosc=6.45kHz

Parallel inductor + dc blocking capacitor Parallel inductor + dc blocking capacitor coupling networkcoupling network


Phasor Transformation [11]

tj SetXetx

A sinusoidal signal x(t) can be represented by a time A sinusoidal signal x(t) can be represented by a time varying complex phasor , i.e.: varying complex phasor , i.e.: tX

Example: AM signalExample: AM signal tcosxX2tx sM

sinjcosxX2tX M


Phasor Transformation

Example: FM signalExample: FM signal xtcosX2tx sM

xsinjxcosX2tX M

Inductor phasor transformation:Inductor phasor transformation: tudt

tdiL L

L

tjL

tjL

SS etUeetIedt

dL

tj

Ltj

LStjL SSS etUeetIje

dt

tIdeL



Inductor phasor transformation:Inductor phasor transformation: tudt

tdiL L

L

tUtILj

dt

tIdL LLS

L

++

LL iiLL

--uuLL ++

LL--

tIL

tUL

jjSSLL



Capacitor phasor transformation:Capacitor phasor transformation: ti

dt

tduC C

C

tItUCj

dt

tUdC CCS

C

++

CC iiCC

--uuCC ++CC

--

tIC

tUC

1/j1/jSSCC


Generalized Averaging Method [13]

A waveform x(A waveform x(••) can be approximated on the interval ) can be approximated on the interval [ t-T, t ] to arbitrary accuracy with a Fourier series [ t-T, t ] to arbitrary accuracy with a Fourier series

representation of the form:representation of the form:

k

sTtjkk

setxsTtx s s (0, T], (0, T], T

2s

txk = time-dependent complex Fourier series coefficients = time-dependent complex Fourier series coefficients

calculated on a sliding window of amplitude Tcalculated on a sliding window of amplitude T

dexT

1

dsesTtxT

1tx

s

s

jkt

Tt

sTtjkT

0k


Generalized Averaging Method

The analysis computes the time evolution of these The analysis computes the time evolution of these Fourier series coefficients as the window of length T Fourier series coefficients as the window of length T

slides over the waveform x(slides over the waveform x(••). The goal is to ). The goal is to determine an appropriate state-space model in determine an appropriate state-space model in which these coefficients are the state variableswhich these coefficients are the state variables

txdxT

1tx

0

t

Tt

Classical state-space averaging theory:Classical state-space averaging theory:

The average value coincides with the The average value coincides with the Fourier coefficient of index 0!Fourier coefficient of index 0!


Application to Power Electronics

tu,txfdt

txd

u(t) = periodic function of time with period Tu(t) = periodic function of time with period T

Let’s apply the generalized averaging method to a Let’s apply the generalized averaging method to a generic state-space model that has some periodic generic state-space model that has some periodic

time-dependence: time-dependence:

k

k

tu,txfdt

txd

Let’s compute the Let’s compute the relevantrelevant Fourier Fourier coefficients of both sides: coefficients of both sides:


Differentiation Property

tjkdt

tdx

dt

tdks

k

k xx

This relation is valid for constant frequency This relation is valid for constant frequency ss, ,

but still represents a good approximation for but still represents a good approximation for slowly varying slowly varying ss(t) (t)

k

k

tu,txfdt

td

x

kks

k tu,txftjkdt

td x

x


Transform of Functions of Variables

?tu,txfk

A general answer does not exist unless function f A general answer does not exist unless function f is a polynomial. In this case, the following is a polynomial. In this case, the following

convolutional relationship can be used:convolutional relationship can be used:

i

iikkyxyx

where the sum is taken of all integers i.where the sum is taken of all integers i.


Lamp dynamic Model

tytitidt

tdy

tuyGtueAA

tyti

ooL

oLotyA30

o4

o

IA3o

L I

eAAR

o4 Only the negative slope in

the UoRMS-IoRMS curve is modeled

Only the negative slope in the UoRMS-IoRMS curve is modeled

y(t) is lamp RMS current squaredy(t) is lamp RMS current squared


Generalized averaged lamp model

Considering that lamp voltage uo(t) and current io(t) are, with a good approximation, sinusoidal waveforms, we can take into account only the complex Fourier coefficients corresponding to indexes +1 and –1 (actually only one of the two coefficients is necessary), while for the variable y(t), only the index‑0 coefficient is considered, since we are concerned with its dc value.

Considering that lamp voltage uo(t) and current io(t) are, with a good approximation, sinusoidal waveforms, we can take into account only the complex Fourier coefficients corresponding to indexes +1 and –1 (actually only one of the two coefficients is necessary), while for the variable y(t), only the index‑0 coefficient is considered, since we are concerned with its dc value.

00ooL0

1o0L1o0L1o

1o0L1o0L1o

yiidt

yduyGuyGi

uyGuyGi

2

1o1o1o1o1o1o1o0oo i2ii2iiiiii


Non-linear large-signal lamp model

o2o

2oL

o

,oL,oyA3o

o,o

yii2dt

dy

uGueAA

yi

o4

uo = uo+juo io = io+jio

uo = uo+juo io = io+jio

o0yy

The fundamental component amplitude of the lamp current is: The fundamental component amplitude of the lamp current is:

2o

2o1o ii2i2

Each complex variable is decomposed into real and imaginary part:

Each complex variable is decomposed into real and imaginary part:


Comparison between complete model and fundamental

component model

0 0.2 0.4

4

5

6

Time [ms]

Lam

p cu

rren

t I o [

mA

RM

S]

7Fundamental component

model

Completemodel

Step change of the lamp RMS current from 4 to 6mARMS Step change of the lamp RMS current from 4 to 6mARMS


Small-signal lamp modelConsidering small-signal perturbations around an

operating point:Considering small-signal perturbations around an

operating point:

2o

2o4 II2A

43Sq eAAR

2o

2o4o4 II2A

3o

2o

2o

YA3o

oLq

eAA

II2

eAA

YG

where

:where:

o2o

2oL

o

,oL,oyA3o

o,o

yii2dt

dy

uGueAA

yi

o4

oooooLqLo

oo

oSqLqLqoLqo

oo

oSqLqLqoLqo

yiUiUG4dt

yd

yY2

URG1GuGi

yY2

URG1GuGi

ooooo

oooo2o

2o

o iIiII

4iIiI

II

2i2

o2o1o ii2i2

Lamp current fundamental component amplitudeLamp current fundamental component amplitude


Ballast dynamic model

tin

ti

C

1

dt

tduC

ti

dt

tdu

titiC

1

dt

tdu

tun

tututRi

L

1

dt

tdi

tutsinsignUL

1

dt

tdi

o21

L

o

o

LC

Lsi

i

C21

oiL

L

isss

s

1o21

1L

o1os

1o

1L

1Cs1C

1L1si

1is1i

1C21

1o

1i1L1Ls1L

1iss

1ss1s

in

i

C

1uj

dt

udC

iuj

dt

ud

iiC

1uj

dt

ud

un

uuiR

L

1ij

dt

id

u2

jUL

1ij

dt

id

only the complex Fourier coefficients of indexes +1 are considered

only the complex Fourier coefficients of indexes +1 are considered

2

jtsinsign1s


Ballast small-signal model

o21

L

osoos

o

o21

L

osoos

o

LsCCs

C

LsCCs

C

Lsi

siisi

Lsi

siisi

C21

oiLsLLs

L

C21

oiLsLLs

L

iss

sssss

s

issss

s

in

i

C

1Ûu

dt

ud

in

i

C

1Ûu

dt

udC

iÛu

dt

udC

iÛu

dt

ud

iiC

1Ûu

dt

ud

iiC

1Ûu

dt

ud

un

uuiR

L

1Îi

dt

id

un

uuiR

L

1Îi

dt

id

uU2

L

1Îi

dt

idL

uÎi

dt

id

Complete ballast Complete ballast model:model:

Complete ballast Complete ballast model:model:

xCz

uBxAx

Tss Uû

TooCiLs yuuuiiz


Large-signal and small-signal model comparison

UUss amplitude step variation (-5%) amplitude step variation (-5%)

0 100 200 300 400 500 600 700 800 900 1000

uip

k [

V]

Time [s]

Large-signalnon linear model

Small-signallinear model

-3

-2

-1

0

0 100 200 300 400 500 600 700 800 900 1000

uop

k [

V]

Time [s]

Large-signalnon linear model

Small-signallinear model

-60

-40

-20

0

20

40

60


Instability analysis

1 2 3 4 5 6 7 8

-4000

-2000

0

2000

Lamp current Io [mARMS]

Unstable

max

(R

e[]

)

L=120krad/s

L=100krad/s

L=80krad/s

L=60krad/s

Plot of the highest real part of the system eigenvalues as a function of the RMS lamp current for different values of the lamp time constant L=1/L

Plot of the highest real part of the system eigenvalues as a function of the RMS lamp current for different values of the lamp time constant L=1/L

49.6 49.7 49.8 49.9 50-8

-4

0

4

8

50.1

Time [ms]

Lam

p cu

rren

t I o [

mA

RM

S]


Instability analysis

1 2 3 4 5 6 7 8

-4000

-2000

0

2000

Lamp current Io [mARMS]

Unstable

max

(R

e[]

)

Ls=10HLs=15H

Ls=20H

Ls=28H

Plot of the highest real part of the system eigenvalues as a function of the RMS lamp current for different values of the coupling inductor Ls

(L = 100krad/s)

Plot of the highest real part of the system eigenvalues as a function of the RMS lamp current for different values of the coupling inductor Ls

(L = 100krad/s)


Conclusions

• Piezoelectric transformers represent good alternative to magnetic transformers in inverters for CCFL

• Different inverter topologies and control techniques must be compared in order to find the best solution for a given application

• Large-signal as well as small-signal instabilities can arise due to the dynamic lamp behavior


References1.Ray L. Lin, Fred C. Lee, Eric M. Baker and Dan Y. Chen, “Inductor-less

Piezoelectric Transformer Electronic Ballast for Linear Fluorescent Lamp” IEEE Applied Power Electronic Conference (APEC), 2001, pp.664-669.

2.Chin S. Moo, Wei M. Chen, Hsien K. Hsieh, “An Electronic Ballast with Piezoelectric transformer for Cold Cathode Fluorescent Lamps” Proceedings of IEEE International Symposium on Industrial Electronics (ISIE), 2001, pp. 36-41.

3.H. Kakehashi, T. Hidaka, T. Ninomiya, M. Shoyama, H. Ogasawara, Y. Ohta, “Electronic Ballast using Piezoelectric transformer for Fluorescent Lamps” ”IEEE Power Electronics Specialists Conference Proc. (PESC), 1998, pp.29-35.

4.Sung-Jim, Kyu-Chan Lee and Bo H. Cho, “Design of Fluorescent Lamp Ballast with PFC using Power Piezoelectric Transformer” IEEE Applied Power Electronic Conference Proc. (APEC), 1998, pp.1135-1141.

5.Ray L. Lin, Eric Baker and Fred C. Lee, “Characterization of Piezoelectric Transformers”, Proceedings of Power Electronics Seminars at Virginia Tech, Sept. 19-21, 1999, pp. 219-225.

6.E. Deng, S. Cuk, “ Negative Incremental Impedance and Stability of Fluorescent Lamps,” IEEE Applied Power Electronics Conf. Proc. (APEC), 1997. pp.1050-1056.

7.S. Ben-Yaakov, M. Shvartsas, S. Glozman, “Statics and Dynamics of Fluorescent lamps Operating at High Frequency: Modeling and Simulation,” IEEE Trans. On Industry Applications, vol.38, No.6, Nov./Dec. 2002, pp.1486-1492.


References8.S. Ben-Yaakov, S. Glozman, and R. Rabinovici, “Envelope simulation by SPICE compatible

models of electric circuits driven by modulated signals,” IEEE Trans. Ind. Electron., vol. 47, pp. 222–225, Feb. 2000.

9.S. Glozman, S. Ben-Yaakov, “Dynamic interaction analysis of HF ballasts and fluorescent lamps based on envelope simulation,” IEEE Trans. Industry Application, vol. 37, Sept./Oct. 2001, pp. 1531‑1536.

10.Y. Yin, R. Zane, J. Glaser, R. W. Erickson, “Small-Signal Analysis of Frequency-Controlled Electronic Ballast“, IEEE Trans. On Circuits and Systems, - I: Fund. Theory and Applications, vol.50, No.8, August 2003, pp.1103-1110.

11.C. T. Rim, G. H. Cho, “Phasor Transformation and its Application to the DC/DC Analyses of Frequency Phase-Controlled Series Resonant Converters (SRC),” Trans. On Power Electronics, Vol.5. No.2, April 1990, pp.201-211.

12.J.Ribas, J.M. Alonso, E.L. Corominas, J. Cardesin, F. Rodriguez, J. Garcia-Garcia, M. Rico-Secades, A.J. Calleja, “Analysis of Lamp-Ballast Interaction Using the Multi-Frequency-Averaging Technique,” IEEE Power Electronics Specialists Conference CDRom. (PESC), 2001.

13.R. Sanders, J. M. Noworolski, X. Z. Liu, G. Verghese, “Generalized Averaging Method for Power Conversion Circuits,” IEEE Trans. On Power Electronics, Vol.6, No.2, April 1991, pp.251-258.

14.M. Cervi, A. R. Seidel, F. E. Bisogno, R. N. do Prado, “Fluorescent Lamp Model Based on the Equivalent Resistance Variation,” IEEE Industry of Application Society (IAS) CDROM, 2002.

15.Onishi N., Shiomi T., Okude A., Yamauchi T., "A Fluorescent Lamp Model for High Frequency Wide Range Dimming Electronic Ballast Simulation" IEEE Applied Power Electronic Conference (APEC), 1999, pp.1001-1005.

Documents

Power Electronics Group - PEL 1 CCFL Inverters based on Piezoelectric Transformers: Analysis and Design Considerations Prof. Giorgio Spiazzi Dept. Of Information