Multilayered Unipoled Piezoelectric Transformers

Transcription

1 Japanese Journal of Applied Physics Vol. 3, No. 6A,, pp # The Japan Society of Applied Physics Multilayered Unipoled Piezoelectric Transformers Shashank PRIYA, Seyit URAL, Hyeoung Woo KIM, Kenji UCHINO and Toru EZAKI APC International Ltd., Duck Run, Mackeyville, PA 77-8, USA International Center for Actuators and Transducers, Pennsylvania State University, University Park, PA 68, USA Taiheiyo Cement Corporation, -- Ohsaku Sakura, Chiba, Japan (Received January 6, ; accepted February 3, ; published June 9, ) This study describes a multi-layer piezoelectric voltage and power transformer which has one direction poling, operates in a wide-frequency range and delivers both step-up and step-down voltages by inverting the electrical connections. In this design, the input and output electrodes are on the same side of the disk and are isolated from each other by a fixed gap. Investigations were performed on a disk of diameter 9. mm. The electrode pattern is a ring/dot structure, where a strip connects the dots. Various ratios of input to output area were studied and it was found that area ratio in the range of or the output diameter in range of 3 mm yields and efficiency. The power density for the optimized single layer transformer was W/cm 3 while that for the 3-layer structure was W/cm 3. Though the power increased with multilayer structure, the effective power density decreased because of the interlayer constraints. [DOI:.3/JJAP.3.33] KEYWORDS: Piezoelectric Transformer, unipoled,, power supply, lead zirconate titanate, automobile lighting. Introduction The piezoelectric transformer offers several advantages compared to the electromagnetic ones such as higher electromechanical power density, no electromechanical noise, higher efficiency at resonance, easier miniaturization, nonflammable and simpler fabrication process. Due to these factors piezoelectric transformer (PT) market has grown significantly in the past decade. Technological advancements in many arenas have opened door for the PT. In addition to the conventional applications such as backlight inverters, power supplies for notebook computers, AC DC converters, power supplies for displays, car navigation system, LCDs for small screen devices, cathode ray tubes, image intensifiers, air cleaners and copying machines, various new areas have been proposed for PT s. ) These include ozone filters, negative ion generators, igniters for gas discharge element, galvanic isolation elements in IC s, high voltage generators, robotics and toys, power sensing, automobile lighting and general-purpose lighting. ) Various transformer designs have been proposed to meet the variety of specifications in both step up and step-down applications. 6 ) In step-up applications Rosen type 6) still remains the preferred design for the manufacturers. However, this design has inherent disadvantages such as, no isolation between input and output region and two direction poling. 3) Another problem with Rosen type transformer is that it cannot be used for step-down applications since the generator section is so long (low capacitance) that there is limited current flow. Other structures such as alternately poled transformers 7) and radial mode transformer 8) (laminated or co-fired with alternate poling) are not commercialized widely. In step-down applications, nd harmonic thickness mode transformer 9 ) and laminated radial mode transformer 8) are the preferred designs. One of the problems of the laminated radial-mode transformers is that they tend to exhibit sharp dependence on the output load causing large variation in the voltage gain and efficiency. For this reason laminated radial mode transformers cannot be used in the high load gradient environment such as gas lighting and cathode ray tubes. Another problem of the radial mode address: spriya@piezoworld.com 33 transformers is that they have conversion efficiency at reactive loads or not pure resistive loads. Since, they lack the capability to provide impedance matching with the lower loads; it generates heat and losses in the circuit at loads less than the matching impedance. Thickness mode transformers work in MHz frequency range. The power density of such transformers is very high, according to the relation: Powder density / " T 33 f r k eff However, the driving circuit associated with these transformers is complicated. It is also difficult to achieve clear resonance spectrum for the ceramic working in thickness mode. Other designs presented in literature have complicated poling pattern, difficult design pattern for multilayer cofiring and involve many material and design parameters for optimization. In order to remedy these problems a piezoelectric transformer should be designed such that it utilizes higher coupling vibration modes for better energy conversion, lower output capacitance for, one direction poling (henceforth referred as unipoled ) for easier electrical connections and isolation between the input and output parts for good insulation. The transformer design should be such that the power generated can be controlled by some physical parameter. Further, we prefer the transformer design such that the same structure can be used for both stepup and step-down applications. This study addresses all these issues. Berlincourt first proposed unipoled piezoelectric transformers. ) These transformer designs consisted of the input and output sections with the same direction of polarization and on the same piezoelectric ceramic. Both radial and longitudinal poled topologies were described without any results on any configuration. Recently, Laoratanakul et al. 3,) studied one of the variation of Berlincourt s design, disk shaped unipoled structure. The electrode pattern in this design simply consisted of ring dot structure. The characterization on a single layer structure with an outer diameter of 3.6 mm showed that this transformer generates power of up to 8 W. However, this design of radial-unipoled transformers has several limitations. An inherent problem is that they cannot be multi-layered using the same electrode pattern.

2 3 Jpn. J. Appl. Phys., Vol. 3, No. 6A () S. PRIYA et al. Hence, they have limited power transformation capacity. This disadvantage relates to the complete isolation of the output electrodes from the outer edges of the ceramic [see Fig. ]. The only way in which the output electrodes of the two layers can be connected is by drilling a hole through the output section. This inherently reduces the mechanical vibration absorption capacity of the device, which in turn, reduces the electrical transformation capability. Another problem with previous design of unipoled piezoelectric transformers is that the tuning capability of the power is low. Since, the only way in which power of such transformers could be increased is by increasing the area of the output region, which implies that the total transformer size has to be increased. This, of course, increases both the size and the manufacturing cost of the transformer. Since in any particular application the device has to fit in a limited amount of space, it makes these unipoled piezoelectric transformers invalid. Further, the equivalent circuit parameter cannot be adjusted to suit the particular driving circuit specifications. The only way, in which equivalent circuit parameters of the prior transformers can be changed, is by adjusting the volume of the ceramic and electrode pattern. In this paper a unipoled transformer is described which has an improved electrode pattern making it suitable for multilayer. This transformer structure is studied with common ground and floating electrode patterns. The optimization of this transformer has been done for a disk of 9. mm diameter. This size was chosen because it suits the applications such as laptop adapters and AC/DC converters. Further, the experimental results on this transformer are shown to be in agreement with those computed using the FEM simulation.. Experimental Procedure Commercial piezoelectric ceramic composition, APC 8 (American Piezo Ceramics, Inc., Mackeyville, PA), was selected to fabricate the transformer. Disks of this composition were sintered at 8 C for 3 h and than machined to the proper dimensions. Fired on silver was used as the electrode. In case of multi-layer transformer, individual layers were bonded together by using STYCAST 6 (Emerson & Cuming Inc.). Previously it was shown that out of various bonding agents such as Ecobond LV (Emerson & Cuming Inc.), STYCAST and E-Solder (Von Roll Isola Inc.), STYCAST was most effective for transformer applications. ) The STYCAST bond is thinner because of its low viscosity ( mm, as measure by optical microscopy) and has low filler content and so it spreads more uniformly. Figures and shows the electrode pattern for the unipoled transformer described in this study. The total size of the one layer disk was chosen to be 9. mm in diameter. Initially, Finite Element Analysis (by using ATILA, Magsoft Corp.), was done to visualize the stress distribution and locate the nodal point. Figure shows the stress distribution in the inner disk when outer ring is excited. The electrode gap between the inner and outer section is determined from the distance between the inner and outer section where the stress is minimum of the order of.6 MPa. From the stress distribution at the edges this distance was found to be.3 mm. Figures 3 and 3 shows the interdigital electrode connection for the multilayer structure with common and separated ground. Transformer characterization was done using the conventional equipments and a home-built software. Initially, piezoelectric equivalent circuit parameters were determined using HP 9 impedance analyzer under the short circuit condition, and matching impedance of the transformer was computed using the relation: Matching impedance ¼ ðinput short circuitedþ; f r C b ðoutputþ Where f r is the resonance frequency and C b is the damped capacitance. Figure shows the schematic diagram of the measurement system. A sinusoidal frequency sweep of required voltage was carried out by using HP 33A function generator and NF amplifier. This voltage was applied to the input section of the transformer (shown on the figure by I, G and O). The output of the transformer was connected to the matching load. The input and output voltage and current were controlled and measured by using HIOKI tester. The temperature of the sample was monitored through HIOKI 3 thermometer. Output Dia. Input Diameter Fig.. Schematic of the electrode pattern on a disk shaped ceramic. The input (outer circle) and output electrodes (inner circle) are laid on the same side and the disk is poled in one direction. Conventional design of the unipoled transformer. Proposed design in this study and cross-section of the disk. Fig.. Stress pattern computed using FEM analysis of the ring-dot structure. t

3 Jpn. J. Appl. Phys., Vol. 3, No. 6A () S. PRIYA et al. 3 Input ground Output Output Input Input Output ground Fig. 3. Multi-layering of the transformer. Cross-sectional layout of the multilayered structure with common ground and Cross-sectional layout of the multilayered structure with floating electrode pattern. HP 33A NF Ampl. HIOKI 393 HIOKI 3 I O G Matching imp. load Fig.. Schematic diagram of the transformer characterization system. The transformer is indicated by the three terminals input (I), output (O) and ground (G). Transformer is connected to the Hioki tester through function generator and high frequency amplifier. Temperature on the surface of transformer is monitored through digital thermometer. 3. Design Criterion Unipoled transformers were characterized by having the input and output electrodes on the same side of the disk, as shown in Fig.. In this design, the strip connecting the center region to the edge of the transformer is present in order to provide the electrode connection for multilayering. The bottom electrode of the disk is common ground to both input and output sections. Applying the electrical excitation to the external ring (input), the radial extensional vibration is generated which is propagated to the center dot (output). At the center electrodes, the mechanical vibrations are again converted into electrical voltage. The wires should be soldered at the nodal points of the input and output sections. For input the nodal point lies at one-fourth from the edge of the transformer and for the output nodal point lies at the center. Simplistically, the gain of the transformer is given by: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C a ðinputþ Gain ¼ C a ðoutputþ and efficiency of the transformer is given by: Efficiency ¼ C b,out þ f r,in C a,in R in C a,out where C a, C b and R are the usual equivalent circuit parameters and subscripts in and out stand for the input and output respectively. The transformer characteristics for the unipoled structure are directly related to the ratio of input/output area which essentially means the capacitance ratio of the input and output section. Figure shows the plot of efficiency, output power, matching impedance and gain for different area ratios. The maximum power is referred to the condition when the temperature rise at the highest point (i.e., the disk center) is C rise from the room temperature. Average gain in Fig. refers to the magnitude of the gain in the maximum efficiency region. All the data in this figure are for one layer transformer having size of 9:mm :6mmand the isolation gap between the input and output section was of. mm. The output section diameter was varied to get the area ratio dependence. It can be seen from this figure that gain and output power behave oppositely with area ratio. For large area ratio, high gain can be obtained but output power decreases dramatically. The efficiency also drops for the high area ratio. The matching impedance is inversely proportional to the output electrode area and hence increases with increasing area ratio. The results of this figure indicate that high gain transformer can be obtained for high area ratio while low gain transformer can be obtained for lower area ratio. For area ratio less than., again the power and efficiency start to drop. The middle region corresponding to area ratio of is the most effective region. In this region, the efficiency of the transformer is around 97%, output power between 6 W, average gain around 3 and matching impedance is the range of 9. For the output electrode diameter of 3.6 mm, a of 6 W was obtained from a single layer at a temperature rise of C giving an effective power density of W/cm 3. These numbers are very encouraging for the power supply, AC/DC converter and battery charger application. Further, for a slightly higher area ratio of 3., a step-up transformer can be designed such that a gain of 8 is obtained at the matching load along with medium power level. This kind of transformer can be used in the automobile application. The transformer is always operated between the frequency limits given by:! SC ¼ pffiffiffiffiffiffiffiffiffiffi L C and! OC ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L ðc þ C d Þ

4 36 Jpn. J. Appl. Phys., Vol. 3, No. 6A () S. PRIYA et al. Efficiency Average Gain (V/V) Matching Impedance (Ω) Area ratio Area Ratio (d) 8 6 Area ratio where! is the angular frequency, subscripts OC and SC denote open and short circuit, C and L denote the motional capacitance and inductance and C d denotes the output damped capacitance. The most favorable condition for the transformer action in unipoled case is when the impedance spectrum of the input and output section are matching. This means that the difference between the resonance frequencies of the output and input in the open circuit condition and the Area ratio Fig.. Variation of transformer parameters with area ratio (input area/ output area). All the data is for a disk of size 9:mm :6mm. Efficiency Output power Average gain (Gain of the transformer in the maximum efficiency region) and (d) Matching impedance. f r (output) - f r (input), khz Open circuit condition Short circuit condition Output diameter (mm).7 Area ratio Fig. 6. Change in resonance and antiresonance frequency under open and short-circuit condition with output electrode diameter. High power and high efficiency is obtained for the zero change. difference between the antiresonance frequencies between the output and input section in the short circuit condition are equal. In this condition, both the input and output sections resonate at the same frequency which allows the effective conversion of energy. The effective coupling factor given by k ¼ f a f r f a is maximum for this situation. Figure 6 shows the plot of resonance and antiresonance frequency difference as a function of output diameter and the area ratio. In these measurements the open or short circuit refers to the condition when one terminal is under open or short circuit condition (input or output) and the measurement is done across the other. It can be seen from this plot that the two lines intersect at the output diameter of around 3.9 mm. This diameter corresponds to the area ratio of.8, which exhibits the peak power level. Hence, it can be conjectured that for a total size of 9: :6 mm, the most effective dimension for the output diameter is 3:8. mm.. Transformer Characteristics with Common and Floating Ground Using the above result, transformer with an output diameter of mm was studied in detail. Figure 7 shows the transformer characteristics for the single layer transformer with output diameter of mm and total size of the disk 9: :6 mm with electrode pattern as described in Fig. 3. The matching impedance for this output diameter was 9. The data was taken across the load of k. The data was taken in the low and condition. Measurement in the condition (< W) gives the range of the frequency in which transformer can be used. The maximum power level corresponds to the condition when the temperature rise in the ceramic is more than C. As can be seen in Fig. 7, a gain of over with an efficiency of 97% and power level of W could be realized in the frequency range of 8 86 khz. The transformer characteristics were also done across a load of. This load was about. times lower than the matching impedance. A high power of W was realized with % efficiency. The gain in the high efficiency region lied between.8. and temperature rise of the transformer was about C. These values f a (Output) - f a (Input), khz

5 Jpn. J. Appl. Phys., Vol. 3, No. 6A () S. PRIYA et al. 37 Gain (V/V) Low power High power Low power High power Temperature Rise ( C) Low power High power Low power High power (d) Fig. 7. Transformer characteristics of a single layer disk having dimensions 9: :6 mm and common ground electrode. The diameter of the output electrode is mm and isolation between input and output electrode is of mm. The matching impedance of the transformer is 9. are a bit promising as it shows the good load tolerance capability of the transformer. The characteristics of the single layer transformer with floating electrode [as described in Fig. 3] were studied in order to evaluate the effect of isolated input and output. Further, for the cofired multilayer samples floating electrode pattern makes the fabrication process. The screen-printing of the floating electrode pattern involves just one mask while that with common ground electrode involves two masks and also double assembling. For comparison purposes with transformer having common ground, in this case too the output diameter was of mm and total size of the disk was 8:8 :6 mm. The matching impedance for the transformer was found to be 7. A maximum gain of.7 with an efficiency of % and power level of. W were realized in the frequency range of 88 9 khz. The data shows that the power level is almost the same as that of the transformer with common ground electrode but it has the advantage of better isolation and easier multilayering capability. In usual transformer applications the required magnitude of the matching impedance is in the range of. As the magnitude of the matching impedance is inversely proportional to the damped output capacitance so by increasing the capacitance the matching impedance magnitude can be lowered. For a single layer transformer once the output diameter is fixed, only decreasing the thickness of the ceramic can increase the capacitance magnitude. This would result in impractical dimensions. The single layer transformer with floating electrode pattern having size of 8:8 :6 mm and output diameter of mm had the matching impedance magnitude of 7. So for the matching impedance of, the thickness of the same transformer had to be.8 mm which cannot be fabricated using bulk processing techniques. The most suitable and widely used method for tuning the impedance magnitude is by multilayering the structure. However, for the unipoled transformers, a multilayer structure is equivalent to parallel connection of transformers. Here each layer corresponds to a transformer unit, so, for example, a 3-layer structure would represent parallel connection of 3 transformers.. Parallel Connection of Transformers Jeong et al. ) have studied the parallel connection of the piezoelectric transformers. Basically, by connecting n units in parallel, the motional resistance and inductance of the transformer are reduced by =n times and the capacitance is increased by n times. The matching load is reduced by n times and the pffiffi gain of the transformer increases approximately by n times (valid only for lower n values). Because of the lower impedance the operating frequency range is also reduced. The output power of the transformer is increased roughly by a factor of n, though at higher n the power density is considerably reduced. In this way, a compact transformer can be obtained and it can be expected that the power of the transformer for a 3-layer structure will increase by 3 times. Figure 8 shows the impedance curve of the short-circuited output terminal of 3 single layer transformers and their parallel-connection. The parallelly connected transformers are separate independent individual layers. There is a small spurious in the impedance curve around 8 khz for all the cases. The resonance and anti-resonance frequencies for the parallel-connected transformer are very close to that of single layer case. Figure 9 shows the transformer characteristics of the parallelly connected transformer. A power of 33 W with 93% efficiency was obtained. This power level provides a ratio of :9n, where n is the number of transformers. For the parallel connection of two transformers a power of 6 W was obtained with efficiency of %. This power level provides a ratio of :8n. These results provided the motivation for making a multilayer unipoled transformer. Figure shows the characteristics of the laminated 3- layer transformer with common ground electrode having the same structure as described in Fig. 7. The total dimensions of the transformer were 9:mm :8mm. The matching impedance of the transformer was 3. The maximum power of this transformer was around 3 W with C temperature rise in the frequency range of 8 86 khz. The gain of the transformer in this range changes from.8 to. Impedance (Ω) Single Transformer Parallel connected Phase (degree) Fig. 8. Short-circuited impedance spectrum of the output terminals for the 3 parallel-connected unipoled transformers with output diameter of mm and total size of 9: :6 mm.

6 38 Jpn. J. Appl. Phys., Vol. 3, No. 6A () S. PRIYA et al. Gain (V/V) Gain (V/V) Output Power ( C) Temperature rise ( C) 3 3 (d) Temperature rise ( C) 3 3 (d) Fig. 9. Transformer characteristics of a three-parallel connected transformers having floating electrode pattern. The diameter of the output electrode is mm and isolation between input and output electrode is of mm. The matching impedance of the transformer is 3. Fig.. Transformer characteristics of a three-layer structure having dimensions 8:8 :8 mm and floating electrode pattern. The diameter of the output electrode is mm and isolation between input and output electrode is of mm. The matching impedance of the transformer is. Gain (V/V) Load = 3 Ω Load = 3 Ω and the efficiency is around 97%. Comparing this data with that for a single layer structure described in Fig. 7, it can be seen that the power increases by. times and the maximum gain of the transformer decreases by 8%. The efficiency and gain is almost the same as that of the single layer and the operating frequency level is shifted to lower side. For the single layer the operating range is between 8 86 khz while for the 3-layer the operating frequency lies in the range of 8 88 khz. Figure shows the characteristics of the laminated 3-layer transformer with the floating electrode pattern. The total dimensions of the transformer were 8:8mm :8mm. The matching impedance of the transformer was. The maximum power of this transformer was around W with C temperature rise in the frequency range of 88 9 khz. The gain of the transformer in this range changes from.6 to. and the efficiency is around %. This power level is a bit low as compared to the transformer with common ground electrode. This may be due to damping of Temperature Rise ( C) Load = 3 Ω (d) Load = 3 Ω Fig.. Transformer characteristics of a three-layer structure having dimensions 9: :8 mm and common ground electrode. The diameter of the output electrode is mm and isolation between input and output electrode is of mm. The matching impedance of the transformer is. the vibration associated with the non-vibrating area and heat conduction. This argument is justified on the basis of the fact that Q m and k p are lower for the input and output terminals in the floating electrode pattern design. In case of the laminated transformer the power level is less than that for the 3 independent parallely connected transformers. This difference in the power level from the conventional parallel-connected transformers can be explained in terms of structural difference and heat dissipation. Heat dissipation from the surface seems is the primary factor for the decrement of power density, as the efficiency of the parallely connected transformers in the laminated and nonlaminated case are almost the same. Due to lamination, heat dissipation area is drastically reduced leading to heating of the bonded layers. 6) The secondary factor responsible for the power density decrement is interlayer constraint. In the laminated transformer case, 3-layers are bonded to each other and so they behave as one unit. Consequently, the vibration in one layer also affects that on another layer. This puts some restriction on the radial expansion and contraction. If the layers vibrate slightly out of phase with each other or there exists a small difference in the resonance frequency of the layers it can produce some mismatch causing decrement in the effective coupling factor and mechanical Q m. The results of Figs. and provide a novel piezoelectric transformer, which has a simple structure; one directional poling and can yield a. The power density for the three-layer structure with common ground and floating ground was found to be W/cm 3 and W/ cm 3. This power density level is not high but comparing to the simple structure, its quite efficient. The power density decreases by about % for 3-layer structure. 6. Effect of Inverting the Input and Output Terminal A multilayer unipoled structure was designed and tested for studying the effect of inverting the electrical connections, which means the input and output connections shown in Fig. 3 are interchanged. For this study the dimensions of the one layer of the transformer were: Total diameter = 9.

7 Jpn. J. Appl. Phys., Vol. 3, No. 6A () S. PRIYA et al. 39 Step-up ratio (V/V) Load = kω 3 3 Temperature rise ( C) Step-down ratio (V/V) Load = Ω 6 Temperature rise ( C) Load = kω Load = Ω Fig.. Step-up ratio and temperature rise for three layer transformer at matching impedance of k. Dimensions of the each layer of transformer are Input diameter = 9. mm, Output diameter = mm and thickness =. mm. Output power and efficiency of the same transformer. mm, Output diameter = mm and thickness =. mm. Fig. shows the step-up ratio and temperature rise for three-layer transformer at a matching impedance of k. A gain of. was obtained. In Fig. the output power and efficiency of the same transformer is shown. At a gain of., the efficiency of the transformer is 9% and the output power is about 9. W. Next the electrode connection of this transformer were reversed i.e. the electrical input is applied to the inner section and the output is taken from the outer section. In this case the dimensions of the each layer of transformer becomes Input diameter = mm, Total diameter = 9. mm and thickness =. mm. Figure 3 shows the step-down ratio and temperature rise for threelayer step-down transformer at matching impedance of. A step down ratio of..6 is obtained. Fig. 3 shows the output power and efficiency of the same transformer. Power levels of W with 9% can be realized. These results show that the unipoled transformer has the capability to function both ways, which provides some latitude in designing the transformer with suitable equivalent circuit parameters. Fig. 3. Step-down ratio and temperature rise for three-layer transformer by inverting the electrical connections of the structure of Fig. at matching impedance of. Dimensions of the each layer of transformer are Input diameter = mm, Output diameter = 9. mm and thickness =. mm. Output power and efficiency of the same transformer. 7. Results and Discussion A piezoelectric transformer converts the electrical energy into mechanical energy at the input terminal and mechanical to electrical energy at the output terminal. The conversion from electrical to mechanical is proportional to the vibration velocity of the material. A higher vibration velocity material will provide a higher power as given by the relation: k p P ¼ s E ð Þ! r k t out v p where v is the vibration velocity of the material and t out is the thickness of the output part. As can be seen from the above equation that the figure of merit for the transformer material is k p v. In this study APC 8 was selected as the transformer material, which has a high figure of merit of the order of.3 m /s (k p :6 and v p :9 m/s). Table I shows the equivalent circuit parameters for the one and three layer unipoled transformer having output diameter of mm and total size of each layer disk was 9 :6 mm. The floating electrode pattern was used in Table I. Equivalent circuit parameters for the one and three layer unipoled transformer with floating electrode pattern having output diameter of mm for a total size of each layer disk was 9 :6 mm. The floating electrode pattern was used in this case. No. of layers Input (Output short circuited) Output (Input short circuited) F r F a R L C a C b F r F a R L C a C b (khz) (khz) () (mh) (nf) (nf) (khz) (khz) () (mh) (nf) (nf)

8 3 Jpn. J. Appl. Phys., Vol. 3, No. 6A () S. PRIYA et al. Impedance (Ω) 3 input output Fig.. Short-circuited impedance spectrum of the input and output terminals for the 3-layered unipoled transformer with output diameter of mm and total size of 9: :6 mm. this case. From this table it can be seen that the equivalent circuit parameters approximately translate by a factor of 3 for the three-layer transformer. Figure shows the shortcircuited input and output impedance spectrum for the threelayer transformer. A clean curve without any spurious can be seen in this figure. These data show that each layer of the three-layer transformer is closely matched to each other. However, a maximum power of W was observed for the one layer case and 6 W for the three-layer case, providing a ratio or :7n. Similar measurement on the transformer with common ground electrode yielded a ratio of :76n. These results indicate that the heat dissipation and interlayer constraints affect the transformer performance. The impedance curve shown in Fig. and the equivalent circuit parameters derived from this curve are valid only under low field condition. At higher field, the elastic nonlinearities result in asymmetry in the impedance curve resulting in change in the shape and sharp variation in the resonance frequency. 7) This shift in resonance frequency is easily affected by the external conditions such as stress. The small difference in phase can further result in damping of the active vibrations causing decrement in the performance of the unit. This factor cannot be accounted for during the design time and will always be present. The results of this study conclusively indicate that a high efficiency- transformer can be designed using the multilayer unipoled structure Phase (deg) 8. Conclusions This paper proposes a novel multilayer unipoled transformer structure. This design can provide high gain and high power at low processing cost. Investigations were performed on the disk of size 9. mm. It was found that a three-layer structure of size 9: :8 mm could provide a gain of.8 with output power of 3 W with the common ground. The main reason for obtaining the maximum power level in a 3- layer laminated transformer less than three times than that of single layer transformer is associated with the heat dissipation problem. Additionally, interlayer electrical and mechanical mismatch contribute to this decrement. Acknowledgement This research was sponsored by the Office of Naval Research through contract no. N-99-J-7. ) Y. L. Lee, S. Y. Cheng, Y. Y. Chen and S. F. Liao: Ferroelectrics 6 (99) 9. ) Y. Kaname and Y. Ise: J. Acoust. Soc. Jpn. 3 (976) 7. 3) Y. Fuda, K. Kumasaka, M. Katsuno, H. Sato and Y. Ino: Jpn. J. Appl. Phys. 36 (997) 3. ) J. H. Yoo, Y. W. Lee, K. H. Yoon, H. S. Jung, Y. H. Jung and C. Y. Park: J. KIEEME (998) 89. ) K. Teranishi, S. Suzuki and H. Itoh: Jpn. J. Appl. Phys. () 76. 6) C. A. Rosen, K. Fish and H. C. Rothenberg: U. S. Patent,838,7 (98). 7) K. Kanayama, N. Maruko and H. Saigoh: Jpn. J. Appl. Phys. 37 (998) 89. 8) R. P. Bishop: US PATENT,83,88 (998). 9) T. Zaitsu, T. Inoue, O. Ohnishi and A. Iwamoto: Proc. IEEE INTELEC 9, 99, p. 3. ) T. Zaitsu, T. Inoue, O. Ohnishi and Y. Sasaki: IEICE Trans. Electron. 77-C (99) 8. ) O. Ohnishi, Y. Sasaki, T. Zaitsu, H. Kishie and T. Inoue: IEICE Trans. Fundamentals E77-A (99) 98. ) D. A. Berlincourt: U.S. Patent (973). 3) P. Laoratanakul, A. V. Carazo, P. Bouchilloux and K. Uchino: Jpn. J. Appl. Phys. () 6. ) P. Laoratanakul: PhD dissertation, Pennsylvania State University, PA (). ) H. Jeong, B. Choi, J. Yoo, I. Im and C. Park: Jpn. J. Appl. Phys. 38 (999) 66. 6) J. Zheng, S. Takahashi, S. Yoshikawa and K. Uchino: J. Am. Ceram. Soc. 79 (9) ) S. Priya, D. Viehland, A. V. Carazo, J. Ryu and K. Uchino: J. Appl. Phys. 9 () 69.