Multilayer Modal Actuator-Based Piezoelectric...

ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 54, no. 2, february 2007 359

Multilayer Modal Actuator-Based PiezoelectricTransformers

Yao-Tien Huang, Wen-Jong Wu, Yen-Chieh Wang, and Chih-Kung Lee

Abstract—An innovative, multilayer piezoelectric trans-former equipped with a full modal filtering input electrodeis reported herein. This modal-shaped electrode, based onthe orthogonal property of structural vibration modes, ischaracterized by full modal filtering to ensure that only thedesired vibration mode is excited during operation. Thenewly developed piezoelectric transformer is comprised ofthree layers: a multilayered input layer, an insulation layer,and a single output layer. The electrode shape of the inputlayer is derived from its structural vibration modal shape,which takes advantage of the orthogonal property of the vi-bration modes to achieve a full modal filtering effect. Theinsulation layer possesses two functions: first, to couple themechanical vibration energy between the input and output,and second, to provide electrical insulation between the twolayers. To meet the two functions, a low temperature, co-fired ceramic (LTCC) was used to provide the high mechan-ical rigidity and high electrical insulation. It can be shownthat this newly developed piezoelectric transformer has theadvantage of possessing a more efficient energy transfer anda wider optimal working frequency range when compared totraditional piezoelectric transformers. A multilayer piezo-electric, transformer-based inverter applicable for use inLCD monitors or portable displays is presented as well.

I. Introduction

The advantages of using piezoelectric transformers tolight LCD monitor backlights include its thin thick-

ness, a small temperature rise, and a low electromag-netic interference (EMI) noise. In addition, a piezoelec-tric transformer is more suitable for mass production thantraditional, coil-based transformers. If piezoelectric trans-formers are used to light cold cathode fluorescent lamps(CCFLs) in today’s large-size LCD monitors, an extra highstepup ratio capability is required. To achieve such a highstepup ratio, a multilayer, piezoelectric transformer [1]–[3]is typically adopted.

Adopting a modal actuator and a modal sensor de-sign, the input electrode of a piezoelectric transformerwas first reported by Lee in 1987 [4]–[6]. In these works,a quasimodal-shaped input electrode was incorporated ina Rosen-type piezoelectric transformer. Although the in-put distributed electrode did not represent the full modalstrain due to the fact that the input electrode covered only

Manuscript received June 20, 2006; accepted September 14, 2006.The present study was financially supported from the National Sci-ence Council of Taiwan, through Grant NSC 95-2622-E-002-003.

Y.-T. Huang and C.-K. Lee are with the Institute of AppliedMechanics, National Taiwan University, Taipei, Taiwan (e-mail:[email protected]).

W.-J. Wu, Y.-C. Wang, and also C.-K. Lee are with the Depart-ment of Engineering Science and Ocean Engineering, National Tai-wan University, Taipei, Taiwan.

Digital Object Identifier 10.1109/TUFFC.2007.249

half of the full piezoelectric transformer, the effect of themodal filtering with its roots based on the orthogonalitycondition of different modes was significant. The previ-ously reported experimental results indicated that quasi-modal, Rosen-type piezoelectric transformers can possessan output waveform of a lower, high-order harmonics whencompared to traditional Rosen-type piezoelectric trans-formers, and that translate into a possible higher totalenergy transfer efficiency [7], [8]. Although modal sen-sor and actuator concepts can be adopted, some defi-ciencies still remain as the geometry constraint of a half-length actuator (input side of the transformer) prevents amodal actuator from completely eliminating the influencesof the unwanted modes. In order to remove the above-mentioned deficiencies and to further reduce the influenceof the load impedance connected to the sensor part (out-put side) of piezoelectric transformers, a newly developed,full-modal piezoelectric transformer that incorporates aninsulation layer to separate the sensor and the actuatorlayer is presented herein. The main idea behind develop-ing such a modal electrode was to design the shape of adistributed electrode to match the surface stress distri-bution of the piezoelectric transformer. Our full-modal,piezoelectric transformer is different from the previouslydeveloped quasimodal piezoelectric transformer as, theo-retically, our new, full-modal type can provide full modalfiltering so as to prevent high-frequency noise from feed-ing into the piezoelectric transformer. It can be shown thatour new, full-modal, piezoelectric transformer possesses ahigher energy transfer efficiency and a larger optimal work-ing frequency range when compared to previous piezoelec-tric transformers.

In order to provide the extra high stepup ratio forlarge-size LCD monitors, our newly developed piezoelec-tric transformer consists of a multilayer structure at the in-put layer [9], [10]. An innovative piezoelectric transformer-based inverter—which switches from a frequency-swept toa constant, current feedback control when the CCFL isturned on—was developed to further expand the advan-tages of this line of piezoelectric technology. In fact, a full-modal, piezoelectric transformer that possesses higher en-ergy transfer efficiency makes it not only easier for control,but it also ensures the presence of a higher stepup ratioand a lower temperature rise.

II. Structure of Full-Modal Piezoelectric

Transformer

Our 26 mm × 5 mm × 5 mm piezoelectric trans-former was manufactured by Eleceram Technology Co.

0885–3010/$25.00 c© 2007 IEEE

Authorized licensed use limited to: National Taiwan University. Downloaded on December 24, 2008 at 22:13 from IEEE Xplore. Restrictions apply.

360 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 54, no. 2, february 2007

(a)

(b)

(c)

Fig. 1. (a) Schematic of a multilayer, full-modal, actuator-basedpiezoelectric transformer. (b) Input electrode of a full-modal, piezo-electric transformer. (c) Input electrode of an uniform electrodepiezoelectric transformer. (Note: shaded area represents the surfaceelectrode.)

Ltd., Taoyuan, Taiwan. We glued the middle insulationlayer to the input and output terminals (Fig. 1). The mul-tilayered input section with each layer poled and electri-cally connected in a parallel configuration created a surfaceelectrode that was proportional to the modal strain of thedesired operating mode. In Figs. 1(b) and (c), we can seethe shape of the input electrode at which the odd-layer,piezoelectric lamina was connected to the left side of thepiezoelectric transformer, and the even-layer connected tothe right side of the piezoelectric transformer.

We knew that, in choosing a suitable insulation layer,we needed to consider the requirement for a high dielectricconstant to insulate the output high voltage, and that itmust be of high rigidity in order to transfer the vibrationenergy between the input and output. Thus, we chose alow-temperature, co-fired ceramic (LTCC) as the middleinsulation layer. The single layer output section was poledopposite along the horizontal direction (the 1-direction),the central electrode was used as the output ground ter-

minal, and the terminals at the two ends were connectedtogether to drive the loads. Following traditional piezoelec-tric sign convention, the poling direction of each laminawithin a piezoelectric laminate was denoted as a 3′ axis.That is, the electric output of the piezoelectric transformerwas extracted from this axis, e.g., using Dout

3′ as the outputelectric displacement.

The modal actuator layer had its poling direction inthe 3-direction, and the externally applied electric fieldalong the 3-direction drove the entire piezoelectric trans-former. The governing equation of a full-modal, piezoelec-tric transformer derived from the dynamics equation alongthe x-direction, thus can be represented by (1) [7], [8]:

c∂2u(x, t)

∂x2 − e31mEin3

∂S(x)∂x

= ρ∂2u(x, t)

∂t2. (1)

The second term represents the external forcing term,which is the coupling between the input electrical fieldalong the 3-direction Ein

3 and the piezoelectricity of theinput section. In addition, e31 is the piezoelectric constant;S(x) represents the shape function of the input electrodealong the 1-direction, m is the number of the piezoelectriclayers in the input section, c is the effective elastic stiffnessof the full-modal, piezoelectric transformer along the 1-direction, and u(x, t) represents the displacement alongthe 1-direction. In (1), the boundary conditions of this full-modal, piezoelectric transformer can be represented by (2)and (3):

0 = HW

[c∂u

∂x− h3′3′Dout

3′ (x, t)] ∣∣∣∣∣

x=0

⇒ ∂u

∂x

∣∣∣∣∣x=0

=h3′3′Dout

3′ (0, t)c

,(2)

and

0 = HW

[c∂u

∂x− h3′3′Dout

3′ (x, t)] ∣∣∣∣∣

x=l

⇒ ∂u

∂x

∣∣∣∣∣x=l

=h3′3′Dout

3′ (l, t)c

,(3)

where l is the length of the piezoelectric transformer, Dout3′

represents the output electric displacement at the two dif-ferent ends (x = 0 and x = l) of the piezoelectric trans-former. In (2) and (3), h3′3′ represents the stress/electricdisplacement constant of the output section, and H andW represent the thickness and width of the full-modal,piezoelectric transformer, respectively. The displacementfield u(x, t) along the 1-direction can be assumed to be:

u(x, t) =∞∑

i=1

Ai(t)ϕi(x), (4)

where ϕi(x) represents the modal coordinates, and Ai(t)represents the magnitude along the modal coordinate. Themodal coordinates can be shown as:

ϕi =

√2l

cos√

λix λi =(

iπ

l

)2

, (5)


huang et al.: multilayer modal actuator-based piezoelectric transformers 361

where i represents the i-th resonance mode. Substitutingthe displacement field into the governing equation, thenperforming an eigen-function expansion to the governingequation reduces the partial differential equation (Fig. 1)into an infinite set of ordinary differential equations:

d2Ai(t)dt2

+cλi

ρAi(t) =

qi(t) +

√2l

[(−1)i+1 h3′3′Dout

3′ (l, t)c

+h3′3′Dout

3′ (0, t)c

],

qi(t) = −e31mEin3

ρ

∫ l

0

(∂S(x)

∂x

)φi(x)dx. (6)

The right side of (6) represents the external forcing termof the governing equation and the input electric field canbe shown as Ein

3 . In this paper, the electrode shape of theinput section S(x) possesses two forms: one takes a con-stant form of traditional piezoelectric transformers, andthe other is proportional to ∂ϕi(x)/∂x, i.e., the modalstrain that corresponds to the mode of interest, to arriveat a full-modal actuator design. In (6), the last two forc-ing terms are contributed by the boundary conditions andrepresent electric displacement at the structural ends ofthe piezoelectric transformer. In our paper, we use a full-modal, piezoelectric transformer to light a single CCFL,which was driven by connecting the two output electrodestogether. With the symmetry of the two terminal ends andthe opposite poling, the two terminals will have the sameload impedance. Furthermore, if the piezoelectric trans-former works in an open condition or is connected to aload of equal impedance at the two ends, the influences ofthe boundary conditions will cancel each other out for thecase in which there is an odd mode resonance. Thus, theinput electric field can be shown to be periodic, i.e.:

Ein3 (t) =

∣∣∣Ein3

∣∣∣ cosωt. (7)

By combining the above, the governing equation can berewritten as:

d2Ai(t)dt2

+cλi

ρAi(t) = ri cosωt,

ri = −e31

∣∣∣Ein3

∣∣∣ρ

√2l

[∫ l

0

∂S(x)∂x

cos(

iπx

l

)dx

], (8)

where ri is defined as the driving factor and is independentof time. The solution of (8) thus becomes:

Ai(t) =ri cosωt

(ω2i − ω2)

, ωi =

√cλi

ρ. (9)

From (4) and (9), the displacement of the full-modal,piezoelectric transformer along the 1-direction can be rep-resented as:

u(x, t) =∞∑

i=1

ri cosωt

(ω2i − ω2)

ϕi(x)

=r1 cosωt

(ω21 − ω2)

ϕ1(x) +r2 cosωt

(ω22 − ω2)

ϕ2(x)

+r3 cosωt

(ω23 − ω2)

ϕ3(x) + · · · + rn cosωt

(ω2n − ω2)

ϕn(x),

n = ∞.

(10)

The symbol ω represents the angular frequency of theinput electric field, and ωi is the resonant frequency of thei-th piezoelectric transformer vibration mode. From (10)we know that, when an input electric field possessing asingle frequency is near the first resonant frequency, someenergy will leak to other resonant modes if the drivingfactor ri is not equal to zero at other resonant frequencies.From this theoretical standpoint, we can see that the shapeof the input electrode S(x) may influence the distributionof the input energy, even if the input voltage is a singlefrequency. In order to verify the effect of the full modalelectrode, a normalized driving factor rib can be defined as:

rib = − 1i2

ri

e31|Ein3 |

ρ

√2l

, (11)

In (11), the normalized driving factor was divided by i2

and was used to represent displacement that is inverselyproportional to ω2 in (10). The normalized driving factorin the paper then can be used to display the distributionof input energy when the shape of the input electrode ischanged. In our paper, the multilayer piezoelectric trans-former consists of two different kinds of input electrodes,one of which is a full-modal electrode, and the other isa traditional distributed type [see (12) and (13)]. Morespecifically,

Sm(x) = sin(πx

l

), (12)

Sd(x) = H

[x − (1 − a)

l

2

]− H

[x − (1 + a)

l

2

],

(13)

where Sm(x) represents a full-modal electrode and Sd(x)represents a traditional, uniform electrode. Substituting(12) and (13) into (11) yields the relationship between theresonant mode and the normalized driving factor (Fig. 2).In Fig. 2, rib(modal) and rib(uniform) represent the nor-malized driving factors for a piezoelectric transformer ofa full-modal electrode and a piezoelectric transformer of adistributed electrode, respectively.

It is clear from Fig. 2 that the normalized driving factorfor a full-modal piezoelectric transformer is zero, except atthe first resonant frequency. More specifically, a full-modalelectrode can provide the absolute band-pass filtering forthe piezoelectric transformer. From Fig. 2, we see that,even if a single-frequency input voltage has its driving fre-quency located very close to the first resonant frequency,there still will be some energy that will be discharged to



Fig. 2. Normalized driving factors for piezoelectric transformers withfull-modal electrodes and with distributed/uniform electrodes.

affect other resonant frequencies for a piezoelectric trans-former possessing a uniform electrode. This discharged en-ergy affects the piezoelectric transformer by lowering itsenergy transfer efficiency. However, a piezoelectric trans-former with a full-modal electrode will possess full-modalfiltering ability such that the input energy will not leakto other resonant modes. Thus, with no energy leakage,higher energy transfer efficiency can be obtained.

With an attempt to understand the input energy dis-tribution more clearly, an impedance analyzer (4294, Ag-ilent Technologies, Santa Clara, CA) was used to mea-sure the input impedance of two piezoelectric transform-ers, one with full-modal electrodes and one with uniformdistributed electrodes, when the output electrodes wereshorted to the ground. Fig. 3 shows the input impedanceof a piezoelectric transformer of a traditional uniform elec-trode. It is clear that, if the piezoelectric transformer isnot operated near a structural resonant frequency, it pos-sesses characteristics of a static capacitance such as thatof a typical piezoelectric actuator. If the driving frequencyis placed near a structural resonant frequency, the inputimpedance of a piezoelectric transformer has both an an-tiresonant peak and a resonant peak.

It can be seen from the experimental results that thefirst resonant frequency was about 68.8 kHz, which wasset as the designed working frequency for the full-modal,piezoelectric transformer. At this first resonant frequency,the input impedance of the full-modal, piezoelectric trans-former showed an antiresonant peak and a resonant peaksimilar to that of the uniform electrode piezoelectric trans-former. The electric energy was delivered in full by thepiezoelectric transformer at near the resonant peak. How-ever, the input impedance of a full-modal, piezoelectrictransformer is vastly different from that of a uniform dis-tributed type. The input impedance of the full-modal,piezoelectric transformer at the third and the fifth res-onant frequencies are similar to a static capacitance. Inaddition, the phase difference of the input impedance atthose conditions is near minus 90 degrees, which meansthat the full-modal, piezoelectric transformer does not de-liver any electric energy through the third and the fifth res-onant modes. This experimental result matches well withthe theoretical prediction.

(a)

(b)

Fig. 3. Comparison of modal and uniform piezoelectric transformers.(a) Input impedance. (b) Phase.

In addition to the input impedance, the stepup ratiosof the two different kinds of piezoelectric transformers alsowere measured using a network analyzer (4395A, AgilentTechnologies) when the output electrode was connectedto a 1 MΩ probe impedance. The measured stepup ratioand the phase angle are shown in Fig. 4. It can be seenfrom Fig. 4(a) that the gain of the full-modal, piezoelectrictransformer at the first resonant frequency was 63.4, and65.6 for a traditional uniform, electrode-based type. Atthe third resonant frequency, the stepup ratio of the tradi-tional and the modal-based, piezoelectric transformer was21.2 and 1.78, respectively. In other words, the gain wasminimal at the third resonant frequency for the modal-based, piezoelectric transformer. The experimental resultverifies the modal filtering effect and matches the theo-retical prediction. In summary, the experimental resultsshown in Figs. 3 and 4 demonstrate the excellent modalfiltering effect on the input voltage when a modal-basedinput electrode is adopted.

Traditionally, piezoelectric, transformer-based invertersuse a MOSFET (metal-oxide semiconductor field effecttransistors) to switch on an LC (inductor-capacitor) res-onant tank. If the switching frequency coincides with theresonant frequency of the LC resonant tank, the drivingvoltage delivered to the piezoelectric transformer will beclose to sinusoidal with the same frequency as the switch-ing frequency. When an inductor is absent, and thus theresonant condition cannot be met, the switch of the MOS-FET on the piezoelectric transformer delivers a square



(a)

(b)

Fig. 4. Comparison of modal and uniform piezoelectric transformers.(a) Gain/stepup ratio. (b) Phase.

waveform to the piezoelectric transformer. The higher har-monics of the square waveform then will excite unwantedvibration modes such that the energy transfer efficiencywill be degraded. Even though an inductor eliminates someof the higher harmonics of the driving waveform, the re-maining higher harmonic noise cannot be further reducedto a lower desired level. A full modal piezoelectric trans-former as presented above can provide the modal filter-ing effect by taking advantage of the orthogonality of thepiezoelectric transformer structural mode. In other words,the newly developed, full-modal, piezoelectric transformercan prevent the input voltage noise from inducing undesir-able, high-order vibration. In other words, an input elec-

trode based on a modal actuator concept can be regardedas a band-pass filter that can clean up the noise embeddedwithin an input voltage waveform.

III. Operating a Full-Modal, Piezoelectric

Transformer Under a High-Power Condition

To determine an optimal working condition, factorssuch as driving frequency, stepup ratio, and efficiency mustbe examined. As the stepup ratio and driving frequency al-ready have been evaluated above, we need to next considerefficiency, especially when operating under a high-powercondition. A function generator (3314, Hewlett Packard,Palo Alto, CA) and a power amplifier (4052, NF Instru-ments, Yokohama, Japan) were used to provide the dif-ferent frequency input voltages. 10X and 100X voltageprobes (P6139A and P5100, Tektronix Inc., Beaverton,OR) were used to measure the input and output volt-age waveforms. A current probe and a current amplifier(A6302 and AM503B, Tektronix Inc.) were used to mea-sure the input current. The output current was obtainedby measuring the voltage across a 100 Ω resistor that wasconnected between the load and ground. The input volt-age was found to be 6 Vrms, and the driving frequencywas found to vary from 63 kHz to 70 kHz [11].

From Fig. 5(a), we can see that the stepup ratio fordifferent load impedances lies between the ranges of 30to 80. The energy transfer efficiency was found to behigher than 90% when the load impedance was betweenthe ranges of 80 kΩ to 200 kΩ. In addition, the optimalworking frequency range was determined to be between66 kHz and 67.5 kHz. To simulate the load impedance ef-fect of a 300-mm CCFL, a 100 kΩ load was used and con-nected to the output electrode. A sinusoidal input voltagethen was used to drive the full-modal, piezoelectric trans-former, and the driving frequency was found to vary from66 kHz to 68.5 kHz. The input power was set at about3.5 W, and the energy transfer efficiencies of the two differ-ent types of piezoelectric transformers were measured (seeFig. 6). The experimental results clearly indicate that apiezoelectric transformer with a full-modal input electrodepossesses higher total energy efficiency. The efficiency ofthe full-modal, piezoelectric transformer at 68.5 kHz was13.5% higher than that obtained from a traditional, uni-form, input electrode piezoelectric transformer. Also, wecan see that the optimal working frequency range of afull-modal, piezoelectric transformer, which possesses highenergy transfer efficiency, is wider in range than that of apiezoelectric transformer with a uniform input electrode.

From previous experimental results, we know that theoptimal operating region of a piezoelectric transformeris located somewhere between the resonant frequencyand antiresonant frequency [12], [13]. In order to fur-ther verify the optimal working frequency range, the in-put impedances of the two piezoelectric transformers weremeasured. The load impedances at 100 kΩ and 200 kΩwere connected to the output section of the piezoelectric



(a)

(b)

(c)

Fig. 5. Modal piezoelectric transfer under a high-power operatingcondition at different load impedances. (a) Stepup ratio. (b) Effi-ciency. (c) Maximum efficiency.

Fig. 6. Efficiency comparison for full-modal and uniform piezoelectrictransformers.

transformer to simulate a CCFL load condition. The ex-perimental results are shown in Fig. 7. Fig. 7(a) representsthe magnitude of the input impedance of the two piezoelec-tric transformers, and Fig. 7(b) represents the phase angleof the input impedance. With an attempt to compare theoptimal operating range between the resonant frequencyand the antiresonant frequency, Fig. 8 was redrawn bynormalizing Fig. 7. The minimum input impedances of thetwo different piezoelectric transformers in Fig. 7(a) werenormalized to equal one, and the frequency at minimumimpedance also was assumed to be equal to one. The max-imum phase angle of the two different piezoelectric trans-formers shown in Fig. 7(b) were normalized to be equalto one, and the frequency for possessing maximum phaseangle was normalized to be equal to one as well (Fig. 8).From Fig. 8, we can observe the corresponding phase anglechange between the resonant and the antiresonant frequen-cies within the optimal operating range. It is quite clearfrom the data shown that a full-modal, piezoelectric trans-former has more of a wider optimal frequency range whencompared to a piezoelectric transformer with uniform elec-trodes. In summary, a full modal electrode possesses bettertotal energy transfer efficiency.

IV. Properties of a 300 mm CCFL and Driving

Circuit

A piezoelectric, transformer-based inverter was devel-oped to demonstrate the merits of the newly developedpiezoelectric transformer. A 300-mm long, CCFL used intoday’s 14-inch notebook displays was used as the elec-tric load. The properties of the 300-mm CCFL were mea-sured (Fig. 9), and steps were taken to ensure that the loadimpedance matched well with the optimal load impedancefor the piezoelectric transformer.

From Fig. 9, we can see that the CCFL impedancechanged from 80 kΩ to 200 kΩ when power changed from2 W to 4 W. Comparing this result with the data shownin Fig. 5(c), we can see that the maximum energy trans-fer efficiency achieved was higher than 90%. The drivingcircuit of the piezoelectric-based inverter can be seen in



(a)

(b)

Fig. 7. Input impedance of modal and uniform piezoelectric trans-formers at 100 kΩ and 200 kΩ load. (a) Magnitude. (b) Phase.

Fig. 10. An UCC3976 IC (Texas Instruments, Dallas, TX)was used to sweep the frequency from high to low in orderto light the CCFL. In addition, a PMOS IRF9Z24NS andNMOS IRF540S (International Rectifier Corporation, ElSegundo, CA) were used to form a half-bridge driver topower the full-modal, piezoelectric transformer.

V. Experimental Results of a

Piezoelectric-Based Inverter

In order to verify the full-modal filtering effect, a driv-ing circuit was used to drive the two different kinds ofthe piezoelectric transformer. The first type was a full-modal, piezoelectric transformer, and the second type wasa piezoelectric transformer with uniform electrodes. An in-ductor was placed in front of the piezoelectric transformerto produce the LC resonance in order to filter out thehigh-frequency noise embedded within the input voltage(Fig. 9). The static input capacitances of the two piezo-electric transformers will be different due to the shape dif-ferences of the input electrodes. In our experiments, theinput capacitance of the full-modal, piezoelectric trans-former was measured to be 90 nF, and 170 nF was themeasured input capacitance for the piezoelectric trans-former with uniform electrodes. As it was not possibleto locate a single inductor to perfectly match both piezo-

(a)

(b)

Fig. 8. Normalized driving frequency results of full-modal and uni-form piezoelectric transformers. (a) Magnitude. (b) Phase.

electric transformers, a 0.1 uF capacitance was connectedin parallel to the full-modal, piezoelectric transformer inorder to compensate for the capacitance difference. Withthis compensating component in place, a 26 uH induc-tor was then used to produce the desired LC resonance.Taking the above-mentioned inductance and capacitanceinto account, the LC resonant frequency of the modaland uniform piezoelectric transformer was calculated tobe 75.6 kHz and 71.6 kHz, respectively. The two resonantfrequencies were found to be very close to each other, andboth are slightly higher than the resonant frequency ofthe piezoelectric transformer. The experimental results areshown in Fig. 11. The data were recorded by using an os-cilloscope (LT364, LeCroy Corporation, Chestnut Ridge,NY). The input and output voltage was measured by using10x and 100x voltage probes (P6109A and P5100, Tek-tronix Inc.) with an oscilloscope. The input current wasmeasured by using a current probe and a current amplifier(A6302 and AM503B, Tektronix Inc.) together. The out-put current was measured using a Tektronix AC currentprobe (CT2, Tektronix Inc.). The input/output power ofthe piezoelectric transformer then was calculated by mul-tiplying these waveforms together. After the lamp was ig-nited, the driving frequency was close-looped controlledby using the tube current. The constant current feedbackcontrol algorithm served two purposes: to keep the lamp



Fig. 9. Properties of a 300-mm long CCFL.

Fig. 10. Driving circuit of a piezoelectric-based inverter.

brightness constant, and to make sure the piezoelectrictransformer worked within the optimal working frequencyrange. It should be noted that this LC resonant tank couldfilter out some high-order harmonics on the switched fre-quency, which is typically used for traditional piezoelec-tric transformers. Nevertheless, some spillover noise stillcan escape the LC resonance filtering and be discharged.However, this discharged noise can be effectively elimi-nated by using our newly developed, full-modal electrode.In Fig. 11(a), the working frequency was 65.6 kHz, and theinput power was 3.32 W and output power 2.96 W. Theenergy transfer efficiency was determined to be 89.1%. InFig. 11(b), the working frequency was 65.8 kHz, the inputpower 3.27 W and output power 3.05 W. The energy trans-fer efficiency was determined to be 93.3%. In summary, afull-modal, piezoelectric transformer possesses higher en-ergy efficiency than that of a traditional type due to theeffective modal filtering provided by the input electrode.Traditionally, the driving circuit of the piezoelectric trans-former uses an inductance to adjust the shape of the inputvoltage. Nevertheless, it is difficult to choose a perfectlymatched inductance for all the operating conditions that apiezoelectric transformer may encounter. By using a full-modal input electrode, our results show that the piezo-

(a)

(b)

Fig. 11. Experimental voltage and current waveforms for piezoelectrictransformers. (a) Uniform electrode. (b) Full-modal electrode whenconnected to light a 30-cm CCFL.

electric transformer can achieve higher energy transfer ef-ficiency. In addition, its wider optimal working frequencyrange makes the driving circuit easier to control.

The full-modal, piezoelectric transformer was used toraise the direct current (DC) voltage to the desired alter-nating current (AC) voltage. The DC voltage was derivedfrom the DC power supply, and the voltage was lower than13.5 V. A 300-mm CCFL was used, and the tube currentwas sensed by using a control IC (UCC3976, Texas Instru-ments). The frequency of the input voltage was varied tokeep the tube current constant, which in turn allowed thepiezoelectric transformer to remain operating in the opti-mal working frequency range. The maximum energy trans-fer efficiency of the piezoelectric transformer was found tobe about 94%, and the temperature rise was lower than 5degrees; the CCFL tube current was about 5 mA.

VI. Conclusions

An innovative, multilayered, piezoelectric transformer,which adopts a full-modal concept in the design of the in-put electrode shape, was developed. The normalized driv-ing factor rib was used to theoretically examine the full-modal filtering effect. The characteristics of a voltage gaintransfer function and input impedance were experimen-



tally measured to demonstrate the modal-filtering effectof the full-modal electrode. The energy transfer efficiencyof the full-modal, piezoelectric transformer was found tobe higher than that of a distributed type. A wider opti-mal working frequency range also was found to ease thefeedback control algorithm. An inverter, developed by in-corporating the newly developed full-modal, piezoelectrictransformer, was designed and fabricated to light a 300-mm CCFL. The piezoelectric transformer was found tohave more than 3.5 W in output power while possessing94% power efficiency. The total temperature rise of theinverter was less than 5 degrees. All these characteristicsclearly demonstrate the excellent features and advantagesof the newly developed, multilayer, modal actuator-based,piezoelectric transformer that easily can be incorporatedinto the design of a broad range of potential applications.

Acknowledgments

The authors would also like to thank Eleceram Tech-nology Co. Ltd. for continuously providing us with piezo-electric transformers and for some portion of the researchfunding for this research work. They also would like tothank Texas Instruments (USA) for generously providingus with the control ICs. The continuous financial supportfrom AdvanceWave Technologies, Inc., the Materials Re-search Laboratory of the Industrial Technology ResearchInstitute (ITRI), and Taiwan National Science Councilthrough NSC 95-2622-E-002-003 is also greatly appreci-ated.

References

[1] M. Yamamoto, Y. Sasaki, A. Ochi, T. Inoue, and S. Hama-mura, “Step-down piezoelectric transformer for AC-DC convert-ers,” Jpn. J. Appl. Phys., vol. 40, pp. 3637–3642, May 2001.

[2] M. Yamamoto, Y. Shimada, Y. Sasaki, T. Inoue, K. Nakamura,and S. Ueha, “A multilayered piezoelectric transformer operat-ing in the third order longitudinal mode and its application foran inverter,” IEICE Trans. Electron., vol. E85-C, no. 10, pp.1824–1832, Oct. 2002.

[3] B. Koc, Y. Gao, and K. Uchino, “Design of a circular piezoelec-tric transformer with crescent-shape input electrodes,” Jpn. J.Appl. Phys., vol. 42, pp. 509–514, 2003.

[4] C. K. Lee, “Piezoelectric laminates for torsional and bendingmodal control: Theory and experiment,” Ph.D. dissertation,Cornell University, Ithaca, New York, 1987.

[5] C. K. Lee, “Theory of laminated piezoelectric plates for the de-sign of distributed sensors/actuators: Part I. Governing equa-tions and reciprocal relationships,” J. Acoust. Soc. Amer., vol.87, pp. 1144–1158, Mar. 1990.

[6] C. K. Lee, “Piezoelectric laminates: Theory and experimentsfor distributed sensors and actuators,” in Intelligent StructuralSystems. Norwell, MA: Kluwer, 1992, pp. 75–167.

[7] Y. S. Hsu, C. K. Lee, and W. H. Hsiao, “Optimizing piezoelec-tric transformer for maximum power transfer,” Smart Mater.Struct., vol. 12, pp. 373–383, June 2003.

[8] Y. S. Hsu, C. K. Lee, and W. H. Hsiao, “Electric and mechanicalfully coupled theory and experimental verification of Rosen-typepiezoelectric transformers,” IEEE Trans. Ultrason., Ferroelect.,Freq. Contr., vol. 52, pp. 1829–1839, Oct. 2005.

[9] Y. T. Huang, W. H. Hsiao, Y. S. Hsu, and C. K. Lee, “Experi-mental investigation of multi-layer modal actuator-based piezo-

electric transformer,” in Proc. 15th Int. Conf. Adaptive Struct.Technol. (ICAST 2004), Bar Harbor, ME, Oct. 24–27, 2004.

[10] Y. T. Huang, W. H. Hsiao, Y. S. Hsu, and C. K. Lee, “High-power backlight inverter for LCD-TV using piezoelectric trans-formers,” in Proc. 16th Int. Conf. Adaptive Struct. Technol.(ICAST 2005), 2005, pp. 376–384.

[11] C. Y. Lin, “Design and analysis of piezoelectric transformer con-verters,” Ph.D. dissertation, Department of Electrical Engineer-ing, Virginia Polytechnic Institute and State University, Peters-burg, VA, 1997.

[12] K. Sakurai, K. Ohnishi, and Y. Tomikawa, “Presentation of anew equivalent circuit of a piezoelectric transformer under high-power operation,” Jpn. J. Appl. Phys., vol. 38, pp. 5592–5597,Sep. 1999.

[13] J. Shimamura, M. Sakamoto, and K. Kamitani, “Method andapparatus for driving piezoelectric transformer,” U.S. Patent No.6,348,755, Feb. 2002.

Yao-Tien Huang received his B.S. degree inmechanical engineering in 2001, and a M.S.degree in applied mechanics in 2002, from theNational Taiwan University, Taipei, Taiwan.He is currently a Ph.D. candidate at the Insti-tute of Applied Mechanics, National TaiwanUniversity.

His major research interests include thedesign and applications of piezoelectric trans-formers.

Wen-Jong Wu received his M.S. and Ph.D.degrees from the Institute of Applied Mechan-ics, National Taiwan University, Taipei, Tai-wan, in 1998 and 2003, respectively. Since2003, he has been an assistant professor atthe Department of Engineering Science andOcean Engineering, National Taiwan Univer-sity.

His research interests include systems de-sign, integration of precision metrology, smartsensor networks, and piezoelectric power de-vices.

Yen-Chieh Wang received his B.S. degreein mechanical engineering from the NationalTaiwan University, Taipei, Taiwan, in 2005.He is currently a M.S. candidate in the De-partment of Engineering Science and OceanEngineering, National Taiwan University.

His major research interests include theapplications of piezoelectric transformers.

Chih-Kung Lee received his M.S. and Ph.D.degrees in theoretical and applied mechanicsfrom Cornell University, Ithaca, NY. He waswith IBM’s Almaden Research Center in SanJose, CA, for 7 years. In 1994, he joined thefaculty at the Institute of Applied Mechanics,National Taiwan University, Taipei, Taiwan.He is currently holding a 4-year appointmentas Director General of Engineering and Ap-plied Sciences at Taiwan’s National ScienceCouncil, Taipei, Taiwan.

His research interests include microelec-tromechanical systems, nano systems, piezoelectric systems, automa-tion, optoelectronic system design and fabrication, precision metrol-ogy, and biochip systems.


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