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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 lightVisible 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)


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)



Pola

rizat

ion

axis

Pola

rizat

ion

axis

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

Polin

g vo

ltage


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 4.60799nFCo 23.85pF 8.911nF 1.62414nFlength=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 GainLoad 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

C1S1

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 ne

twor

k

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=1mAIo=6mA

|Mgd|Io=1mA

|Mgd|Io=6mA

fsw [kHz]

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

Zg2

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 65fsw [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

CNCN11

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=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 voltage

Charge of input

capacitance


Control Characteristics: Variable Frequency

1

4

3

5

Io

[mARMS]

2

64 66 68 70 72fsw [kHz]

Lp = 20H, CB = 1F

Udc = 30V

CNCN22


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

CNCN22



• 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

onTtcycleduty


Full-Bridge Inverter for PT

Lam

pPT+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 s1

s1KZApproximation:Approximation: KKLL< 0, < 0, zz< 0< 0

Right-half plane zeroRight-half plane zero


Lamp Model (Ben Yaakov)

IIo1o1 IIo2o2

UUo2o2

UUo1o1

SRslope

So

maxoL R

IUR 1oL1oS1o1oSmaxo IRIRUIRU

LRslope


Lamp Model (Ben Yaakov)2

o

3L K

IKR KK22, K, K33 = lamp constants = lamp constants

o2od

3oLo IK

IKIRU

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

IKiRi

IKiK

IKi

IUi

IUu

odqooqo

Small-signal perturbation:Small-signal perturbation:

Subscript q means quiescent pointSubscript q means quiescent point


Lamp Model (Ben Yaakov)

sIGKRs

sIGIKRs1sIG

IKsIRsU

oL2LqL

oLodq

3Lq

LoL

odq

3oLqo

sIsGsIs1

1sI oLo

L

od

p

z2

o

oL s1

s1K

sIsUsZ

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

IKR


Accounts also for Accounts also for the positive slopethe positive slope

Lamp Model (Do Prado)LPb

L eaR PPLL = Lamp power = Lamp powera, b positive constantsa, b positive constants

0.2

0.4

0.6

0.8

1.0

1.2

21 3 4 5 6Io [mARMS]

RL [M]

600

700

800

900

1000

1100

1200Uo [VRMS]

21 3 4 5 6Io [mARMS]


Lamp Model (Do Prado)

LooqLqpbPb

ooqpPb

ooqooq pb1iIReeaiIeaiIuU LLLL

LPbL eaR



LoqLqoLqo pIbRiRu

sPIbRsIRsU LoqLqoLqo

sGsUIsIUGsIIsUUsP LooqooqLooqooqL Delay:Delay:


Lamp Model (Do Prado)

LqL

LqL

Lq

LqLq

LLq

LLqLq

o

oL

bP1s1

bP1s1

bP1bP1

RsGbP1sGbP1

RsIsUsZ

p

z

p

zLq

o

oL s1

s1R

sIsUZ

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 IeAeAAR

o4o2



Delay:Delay:

ood

IA3

IA1o

oLo II

eAeAAIRUod4od2

odLpIA

43IA

21oLqodIIod

oo

IIo

oo iReAAeAAiRi

IUi

IUu oq4oq2

odqooqo

sIsGsI oLod

sIsGReAAeAAs1RsU oLLpIA

43IA

21L

Lqooq4oq2


Lamp Model (Onishi)

p

zs

o

oL s1

s1R

sIsUsZ

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,ss

IU

sIsUsZ 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

T11

Z1

ZZ1

1Z1

sUsI

IIoo(s)(s)

TTFF must satisfy Nyquist stability criterion must satisfy Nyquist stability criterion

B

LF Z

ZT


Example of Instability

Series inductor coupling network

LSInverter

PT Lamp

ui

is

+-

ffoscosc 6kHz 6kHz


Example of Instability

ILp = [1A/div]

Io = [2mA/div]

fosc=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 LL

tjL

tjL

SS etUeetIedtdL

tj

Ltj

LStjL SSS etUeetIje

dttId

eL



Inductor phasor transformation:Inductor phasor transformation: tudt

tdiL LL

tUtILj

dttId

L LLSL

++LL iiLL

--uuLL ++LL

-- tIL

tUL

jjSSLL



Capacitor phasor transformation:Capacitor phasor transformation: tidt

tduC CC

tItUCj

dttUd

C CCSC

++

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], T2

s

tx k = 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

dexT1

dsesTtxT1tx

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

txdxT1tx 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:

kk

tu,txfdt

txd

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


Differentiation Property tjk

dttdx

dttd

ksk

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

ktu,txf

dttd

x

kksk tu,txftjk

dttd

xx


Transform of Functions of Variables

?tu,txf k

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

iikk yxyx

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


Lamp dynamic Model

tytitidt

tdy

tuyGtueAAtyti

ooL

oLotyA30

o4

o

IA3o

L IeAAR

o4

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

y(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.

00ooL0

1o0L1o0L1o

1o0L1o0L1o

yiidtyd

uyGuyGiuyGuyGi

21o1o1o1o1o1o1o0oo i2ii2iiiiii


Non-linear large-signal lamp model

o2o

2oL

o

,oL,oyA3o

o,o

yii2dt

dy

uGueAA

yio4

uo = uo+juo io = io+jio

o0 yy

The fundamental component amplitude of the lamp current is:

2o

2o1o ii2i2

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 Io [

mA

RM

S]

7Fundamental component

model

Completemodel

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


Small-signal lamp modelConsidering small-signal perturbations around an

operating point:

2o

2o4 II2A

43Sq eAAR

2o

2o4o4 II2A

3o

2o

2o

YA3o

oLq

eAA

II2eAA

YG

where

:

o2o

2oL

o

,oL,oyA3o

o,o

yii2dt

dy

uGueAA

yio4

oooooLqLo

oo

oSqLqLqoLqo

oo

oSqLqLqoLqo

yiUiUG4dtyd

yY2

URG1GuGi

yY2

URG1GuGi

ooooo

oooo2o

2o

o iIiII4iIiI

II2i2

o2o1o ii2i2

Lamp current fundamental component amplitude


Ballast dynamic model

tin

tiC1

dttdu

Cti

dttdu

titiC1

dttdu

tun

tututRiL1

dttdi

tutsinsignUL1

dttdi

o21

L

o

o

LC

Lsi

i

C21

oiL

L

isss

s

1o21

1L

o1os

1o

1L1Cs

1C

1L1si

1is1i

1C21

1o1i1L1Ls

1L

1iss

1ss1s

ini

C1uj

dtud

Ci

ujdtud

iiC1uj

dtud

unu

uiRL1ij

dtid

u2jUL1ij

dtid

only the complex Fourier coefficients of indexes +1 are considered

2jtsinsign 1s


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

ini

C1Ûu

dtud

ini

C1Ûu

dtud

Ci

Ûudtud

CiÛu

dtud

iiC1Ûu

dtud

iiC1Ûu

dtud

unu

uiRL1Îi

dtid

unuuiR

L1Îi

dtid

uU2L1Îi

dtid

LuÎi

dtid

Complete ballast Complete ballast model:model:

xCzuBxAx

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

(Re[

])

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

49.6 49.7 49.8 49.9 50-8

-4

0

4

8

50.1

Time [ms]

Lam

p cu

rren

t Io [

mA

RM

S]


Instability analysis

1 2 3 4 5 6 7 8

-4000

-2000

0

2000

Lamp current Io [mARMS]

Unstable

max

(Re[

]) Ls=10H

Ls=15HLs=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)


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


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