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**CCFL Inverters based on Piezoelectric Transformers: Analysis and Design Considerations**

Prof. Giorgio Spiazzi Dept. Of Information Engineering – DEI University of Padova

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**Outline Characteristics of Cold Cathode Fluorescent Lamps (CCFL)**

Review of piezoelectric effect CCFL inverters based on piezoelectric transformers Design considerations Modeling

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**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

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**Cold Cathode Fluorescent Lamp (CCFL)**

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**Cold Cathode Fluorescent Lamp (CCFL)**

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: Ultraviolet light Visible light

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**Cold Cathode Fluorescent Lamp**

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

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**Cold Cathode Fluorescent Lamp**

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

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**Cold Cathode Fluorescent Lamp**

Operating a CCFL over time results in degradation of light output. Typical life rating is 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 of lamp temperature

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**Cold Cathode Fluorescent Lamp**

Lamp display housing: Stray capacitances to ground cause a considerable loading effect that can easily degrade efficiency by 25%

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**Current-fed Self-Resonant Royer Converter**

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**High voltage transformer**

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Ballast capacitor

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**Self resonant inverter**

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**Control of supply current**

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**Lamp current measurement**

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Dimming

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**Magnetic and Piezoelectric Transformer Comparison**

Magnetic transformer characteristics 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)

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**Magnetic and Piezoelectric Transformer Comparison**

Piezoelectric 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)

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**Magnetic and Piezoelectric Transformer Comparison**

Size comparison

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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)

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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)

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**Piezoelectric Effect Polarization Random orientation of polar domains**

Polarization using a DC electric field Residual polarization Polarization axis

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**Residual polarization Residual polarization**

Piezoelectric Effect P Residual polarization Effect of electric field E on polarization P and corresponding elongation/contraction of the ceramic material E Residual polarization S Relative increase/decrease in dimension (strain S) in direction of polarization E

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

Piezoelectric Effect Generator and motor actions of a piezoelectric element Poling voltage Disk after polarization (poling) Disk compressed Disk stretched Applied voltage of same polarity as poling voltage Applied voltage of opposite polarity as poling voltage

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**Piezoelectric Effect S=sE.T+d.E D=d.T+T.E Actuator behavior**

Polarization Actuator behavior S=sE.T+d.E D=d.T+T.E Transducer behavior Where: 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]

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Piezoelectric Effect Based on the poling orientation, the piezoelectric ceramics can be design to function in: longitudinal mode: P is parallel to T Has a larger d33, along the thickness direction when compared to the planar direction transverse mode: P is perpendicular to T Has a larger d31, along the planar direction when compared to the thickness direction

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**Piezoelectric Transformers (PT)**

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

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**Piezoelectric Transformers (PT)**

Three main categories Longitudinal vibration mode Transverse actuator and Longitudinal transducer Rosen-type or High-Voltage PT

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**Piezoelectric Transformers (PT)**

Three main categories Thickness vibration mode Longitudinal actuator and Longitudinal transducer Low-Voltage PT

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**Piezoelectric Transformers (PT)**

Three main categories Radial vibration mode Transverse actuator and Transverse transducer (radial shape preferred)

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**Equivalent Electric Model**

Rosen-type Thick. Vibr. mode Radial Vibr. mode R 1.44 L mH 27H mH C 3.57nF 254pF pF N Ci nF 2.305nF nF Co 23.85pF 8.911nF nF length=30mm length=20mm radius=10.5mm width=8mm width=20mm thickness1=0.76mm thickness=2mm thickness=2.2mm thickness2=2.28mm

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**Resonance frequencies Rosen-type Piezoelectric Transformer sample**

Voltage Gain Load resistance: 1M, 100k, 10k, 5k, 1k, 500 Resonance frequencies Rosen-type Piezoelectric Transformer sample

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**Rosen-type Piezoelectric Transformer sample**

Input Impedance Load resistance: 1M, 100k, 10k, 5k, 1k, 500 Rosen-type Piezoelectric Transformer sample

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**Half-Bridge Inverter for PT**

C2 S2 iinv iL + PT UDC + S1 ui Lamp C1 - Half-Bridge inverter

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**Soft-Switching Condition**

Half-bridge inverter ui tr UDC t T/2 j/ w U1 Fundamental components iinv t

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**Coupling Networks - Zg PT Rosen-type Model L C + ui Uo iL R Co Ci UA**

io S1 S2 C1 C2 Lamp Half-Bridge inverter 1:n21 uinv Coupling network Zg

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**Coupling Networks Series inductor Ls CN1**

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 Ls CN1

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**Effect of Coupling Inductor Ls on Voltage Conversion Ratio**

MPT = UoRMS/UiRMS, Mi = UiRMS/UinvRMS, Mg = Mi MPT f1 f2 70 [dB] |Mgd|Io=1mA Udc=13V, Ls=42mH |Mgd|Io=6mA |Mg|{ Io=1mA |MPT|{ Io=6mA |Mi|{ -10 45 50 55 60 65 70 75 80 fsw [kHz]

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**Effect of Coupling Inductor Ls on Input Impedance**

Positive input phase f1 f2 60 [dBW] Zg Io=6mA |Zg| Io=1mA 45 50 55 60 65 70 75 80 fsw [kHz]

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**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)

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**Control Characteristics: Variable Frequency**

1 4 3 5 Io [mARMS] 2 60 61 62 63 65 fsw [kHz] 64 Udc = 13V

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**Control Characteristics: Variable dc Link Voltage**

Increasing LS value causes the gain curve Io = f(UA) to become non monotonic 1 4 3 5 Io [mARMS] Ls = 42mH 2 11 12 13 14 15 Udc [V] 16 fsw = 65kHz CN1 Ls = 38mH

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**Large-Signal Instability**

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

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**Coupling Networks Parallel inductor CB Lp CN2**

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 Lp CB CN2

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**Effect of Coupling Network on Voltage Conversion Ratio**

CN2: Lp=20mH, CB=1mF, Udc=30V f1 f2 50 |Mgd|Io=1mA [dB] |Mgd|Io=6mA |Mg|{ }Io=1mA |MPT|{ }Io=6mA Io=6mA Io=1mA |Mi|{ 45 50 55 60 65 70 75 80 fsw [kHz]

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**Effect of Coupling Network on Input Impedance**

60 Zg [dBW] Io=6mA Io=1mA |Zg| 45 50 55 60 65 70 75 80 fsw [kHz]

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**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

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**Experimental Measurements**

Trapezoidal PT input voltage Charge of input capacitance

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**Control Characteristics: Variable Frequency**

Lp = 20mH, CB = 1mF Io [mARMS] CN2 5 4 3 2 Udc = 30V 1 64 66 68 70 72 fsw [kHz]

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**Control Characteristics: variable dc link voltage**

Lp = 20mH, CB = 1mF Io [mARMS] CN2 5 4 3 2 fsw = 65kHz 1 10 15 20 25 30 35 Udc [V]

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**Half-Bridge Inverter for PT**

Frequency Control 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

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**Half-Bridge Inverter for PT**

Frequency Control

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**Half-Bridge Inverter for PT**

Duty-cycle 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 ton t ui UDC TS U1

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**Full-Bridge Inverter for PT**

Switching frequency control Duty-cycle control Phase-shift control Lamp PT + iinv S1 S2 iL S3 S4 Full-Bridge inverter UDC ui -

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**Full-Bridge Inverter for PT**

Phase-Shift Control 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

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**Resonant Push-Pull Topology**

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**Resonant Push-Pull Topology**

Variable switching frequency Voltage gain at PT input Sinusoidal driving voltage

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**Analysis of Small-Signal Instabilities and Modeling Approaches**

Example of high-frequency V –I characteristics OSRAM L 18W/10

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**Steady-state VRMS-IRMS Characteristic**

MATSUSHITA FHF32 T-8 32W Negative incremental impedance Positive incremental impedance

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**Modulated Lamp Voltage and Current**

Incremental impedance: fm=200Hz fm=2kHz OSRAM L 18W/10 fm=5kHz Upper trace: iLamp [0.5A/div] Lower trace: uLamp [74V/div]

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**Lamp Incremental Impedance**

Im(ZL) wm= 0 wm= Re(ZL) Approximation: KL< 0, wz< 0 Right-half plane zero

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Physical Explanation Original first-order differential equation describing the gas discharge behavior proposed by Francis [1] : PL = Lamp power yL= 1/zL = lamp conductance A, B positive constants Steady-state:

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**Small-signal perturbation: Substituting into the Francis equation:**

Physical Explanation Small-signal perturbation: Substituting into the Francis equation:

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**Small-signal incremental impedance:**

Physical Explanation Small-signal incremental impedance: No negative incremental impedance nor RHP zero

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**Modified first-order differential equation:**

Physical Explanation Modified first-order differential equation: f(io) = monotonically decreasing function of io yL= 1/zL = lamp conductance A, B positive constants Steady-state:

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**Physical Explanation Small-signal perturbation:**

Substituting into the modified Francis equation:

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**Small-signal incremental impedance:**

Physical Explanation Small-signal incremental impedance: Negative incremental impedance and RHP zero

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**Lamp Model (Ben Yaakov)**

Uo1 Uo2 Io1 Io2

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**Lamp Model (Ben Yaakov)**

K2, K3 = lamp constants The lamp resistance is considered to be dependent on a delayed version of RMS lamp current Small-signal perturbation: Subscript q means quiescent point

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**Lamp Model (Ben Yaakov)**

Delay:

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**Lamp Pspice Model (Ben Yaakov)**

io2 IoRMS2 io=uo/RL + Lamp time constant uo -

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**Lamp Model (Do Prado) PL = Lamp power a, b positive constants**

Accounts also for the positive slope 600 700 800 900 1000 1100 1200 Uo [VRMS] 2 1 3 4 5 6 Io [mARMS] 0.2 0.4 0.6 0.8 1.0 1.2 2 1 3 4 5 6 Io [mARMS] RL [MW]

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**Small-signal perturbation: Subscript q means quiescent point**

Lamp Model (Do Prado) Small-signal perturbation: Subscript q means quiescent point Delay:

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**Negative incremental impedance and RHP zero**

Lamp Model (Do Prado) If bPLq>1: wz<0, ZL(0)<0 Negative incremental impedance and RHP zero

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**Lamp Pspice Model (Do Prado)**

io uo-R4io RL uo Lamp time constant PL

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**Small-signal perturbation: Subscript q means quiescent point**

Lamp Model (Onishi) A0-A4 positive constants Small-signal perturbation: Subscript q means quiescent point Delay:

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**Negative incremental impedance and RHP zero**

Lamp Model (Onishi) If RS>0: wz<0, ZL(0)<0 Negative incremental impedance and RHP zero

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**Lamp Pspice Model (Onishi)**

Lamp time constant IoRMS Uo=RLio RL

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Control Problem An Impedance with a RHP zero cannot be driven directly by a voltage source, since its current transfer function will contain a RHP pole

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**Series Impedance Lamp Ballast**

ZB Io(s) + US(s) Uo(s) ZL - TF must satisfy Nyquist stability criterion

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**Example of Instability**

Series inductor coupling network ui is + - fosc 6kHz Inverter LS PT Lamp

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**Example of Instability**

Parallel inductor + dc blocking capacitor coupling network ILp = [1A/div] Io = [2mA/div] fosc=6.45kHz

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**Phasor Transformation [11]**

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

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**Phasor Transformation**

Example: FM signal Inductor phasor transformation:

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**Phasor Transformation**

Inductor phasor transformation: + L - jwSL + L iL - uL

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**Phasor Transformation**

Capacitor phasor transformation: + C - 1/jwSC + C iC - uC

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**Generalized Averaging Method [13]**

A waveform x(•) can be approximated on the interval [ t-T, t ] to arbitrary accuracy with a Fourier series representation of the form: s (0, T], = time-dependent complex Fourier series coefficients calculated on a sliding window of amplitude T

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**Generalized Averaging Method**

The analysis computes the time evolution of these Fourier series coefficients as the window of length T slides over the waveform x(•). The goal is to determine an appropriate state-space model in which these coefficients are the state variables Classical state-space averaging theory: The average value coincides with the Fourier coefficient of index 0!

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**Application to Power Electronics**

Let’s apply the generalized averaging method to a generic state-space model that has some periodic time-dependence: u(t) = periodic function of time with period T Let’s compute the relevant Fourier coefficients of both sides:

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**Differentiation Property**

This relation is valid for constant frequency ws, but still represents a good approximation for slowly varying ws(t)

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**Transform of Functions of Variables**

A general answer does not exist unless function f is a polynomial. In this case, the following convolutional relationship can be used: where the sum is taken of all integers i.

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

Lamp dynamic Model Only the negative slope in the UoRMS-IoRMS curve is modeled y(t) is lamp RMS current squared

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**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.

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**Non-linear large-signal lamp model**

Each complex variable is decomposed into real and imaginary part: uo = uoa+juob io = ioa+jiob The fundamental component amplitude of the lamp current is:

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**Comparison between complete model and fundamental component model**

Step change of the lamp RMS current from 4 to 6mARMS 7 Fundamental component model 6 Lamp current Io [mARMS] 5 Complete model 4 0.2 0.4 Time [ms]

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**Small-signal lamp model**

Considering small-signal perturbations around an operating point: where: Lamp current fundamental component amplitude

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Ballast dynamic model only the complex Fourier coefficients of indexes +1 are considered

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**Ballast small-signal model**

Complete ballast model:

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**Large-signal and small-signal model comparison**

Us amplitude step variation (-5%) Small-signal linear model 60 Large-signal non linear model 40 -1 20 Duipk [V] Duopk [V] Small-signal linear model -2 -20 Large-signal non linear model -40 -3 -60 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 Time [ms] Time [ms]

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Instability analysis Plot of the highest real part of the system eigenvalues l as a function of the RMS lamp current for different values of the lamp time constant tL=1/wL 49.6 49.7 49.8 49.9 50 -8 -4 4 8 50.1 Time [ms] Lamp current Io [mARMS] Unstable 2000 wL=120krad/s max (Re[l]) wL=80krad/s -2000 wL=100krad/s -4000 wL=60krad/s 1 2 3 4 5 6 7 8 Lamp current Io [mARMS]

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Instability analysis Plot of the highest real part of the system eigenvalues l as a function of the RMS lamp current for different values of the coupling inductor Ls (wL = 100krad/s) 2000 Unstable Ls=10mH Ls=15mH max (Re[l]) Ls=20mH -2000 -4000 Ls=28mH 1 2 3 4 5 6 7 8 Lamp current Io [mARMS]

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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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References 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 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 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 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 Ray L. Lin, Eric Baker and Fred C. Lee, “Characterization of Piezoelectric Transformers”, Proceedings of Power Electronics Seminars at Virginia Tech, Sept , 1999, pp E. Deng, S. Cuk, “ Negative Incremental Impedance and Stability of Fluorescent Lamps,” IEEE Applied Power Electronics Conf. Proc. (APEC), pp 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

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References 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 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. 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 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 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. 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 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. 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

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