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									                    Seminar report on


Guided by                           Presented by

   Mrs. Jaseela M                       Resmara s

                                        Roll no 01105025
Piezoelectric transformers                                                 Seminar ‘04


                 I express my sincere gratitude to Dr. P.M.S Nambisan, Prof. and Head of

 Department of Electrical and Electronics Engineering, MES College of Engineering,

 Kuttipuram, for his cooperation and encouragement.

                 I would also like to thank my seminar guide Mrs.Jaseela.M (Lecturer,

 Department of Electrical and Electronics Engineering), Asst. Prof. Gylson Thomas (Staff

 in-charge Department of Electrical and Electronics Engineering), for their invaluable

 advice and wholehearted cooperation without which this seminar would not have seen the

 light of day.

                 Finally I would like to express my gracious gratitude to my family and

 friends for their valuable advice and encouragement.

MESCE, Kuttippuram                           1                                EEE Dept.
Piezoelectric transformers                                                     Seminar ‘04



          Small electronic devices which operate at high voltages require a compact

 transformer to step up the low voltages of available power supplies. Electromagnetic

 transformers, having thousands of wire turns around a ferrite core, have become an

 obstacle to the progress of miniaturization, as they are the most bulky devices on a

 circuit board. Here comes the importance of the new concept – piezoelectric


         Piezoelectric transformers are, in fact, not transformers. They have no wires or

 magnetic fields, so they are better categorized as dynamos. They form a better

 alternative to conventional electromagnetic transformers. This paper deals with its

 working principle. Their advantages and the disadvantages are also explained.

MESCE, Kuttippuram                           2                                    EEE Dept.
Piezoelectric transformers                          Seminar ‘04


           INTRODUCTION



                  o WORKING PRINCIPLE


                  o CONSTRUCTION

                  o THE ELECRICAL PARAMETER

                  o PT SCHEMATIC

                  o APPILICATIONS

                  o ADVANTAGES

                  o DISADVANTAGES

           A BRIEF ANALYSIS

                  o DESCRIPTION

                  o ANALYSIS


           CONCLUSION

           REFERENCE

MESCE, Kuttippuram                   3                EEE Dept.
Piezoelectric transformers                                                     Seminar ‘04


              With the onset of miniaturization, many applications in the electronics

 industry now require small, low profile components with a high efficiency of operation.

 Electromagnetic transformers, having thousands of wire turns around a ferrite core, have

 become an obstacle to the progress of miniaturization, as they are among the most bulky

 devices on a circuit board. Piezoelectric transformers have recently received some

 attentions as a possible alternative.

                Piezoelectric transformer is, in fact, not transformers. They have no wires or

 magnetic field, so they are better categorized as dynamos. These transformers work like a

 motor that is mechanically coupled to a generator.

MESCE, Kuttippuram                            4                                   EEE Dept.
Piezoelectric transformers                                                    Seminar ‘04


              Piezoelectricity is a coupling between materials mechanical and electrical

 behaviors. In the simplest of terms, when a piezoelectric material is squeezed, an electric

 charge collects on its surface. Conversely, when a piezoelectric material is subjected to a

 voltage drop, it mechanically deforms.

               Many crystalline materials exhibit piezoelectric behaviour. A few materials

 exhibit the phenomenon strongly enough to be used in application that take advantage of

 their properties. These include quarts, Rochelle salt; lead titanate zirconate ceramics (eg;

 PZT-4, PZT-5A, etc), barium titanate, and polyvinylide (a polymer film).

 On a nanoscopic scale, piezoelectricity results from a non uniform charge distribution

 within a crystal’s unit cells. When such a crystal is mechanically deformed, the positive

 and negative charge centers displace by different amounts. So while the overall crystal

 remains electrically neutral, he difference in charge center displacement result in an

 electrical polarization within the crystal. Electric polarization due to mechanical input is

 perceived as piezoelectricity.

                In a setup that wasn’t expected to work, piezoelectricity was well observed

 in Rochelle salt crystals. When the crystal were deformed (with the gentle tap of wood or

 hammer), short (on the order of 4 milliseconds) relatively high voltage (maximum 20 v

 peak to peak with 10M input Z to scope). It was surprising to see such a well-defined bursts

 of electricity (very low current).

MESCE, Kuttippuram                           5                                   EEE Dept.
Piezoelectric transformers                                                         Seminar ‘04


 Working Principle

              With the direct effect, placing a force or vibration (stress) on the piezoelectric

 element generates a charge. The polarity of this charge depends on the orientation of the

 stress compared with the direction of polarization in the piezoelectric element. During the

 manufacturing process, poling, or applying a high a dc field in the range of 45 KV/cm to

 the piezoelectric transformer, set the polarization direction. The inverse piezoelectric effect

 is the opposite of the direct effect. Applying an electric field, or voltage, to the

 piezoelectric element results in a dimensional change, or strain. The direction of the change

 is like wise linked o the polarization direction. Applying a field at the same polarity of the

 element results in a decrease. An increase in one dimension in a structure results in a

 decrease in the other two through Poisson’s coupling, or the fact that lateral strain results in

 longitudinal strain at Poisson’s ratio. This phenomenon is an important factor in the

 operation of the transformer.

                In a piezoelectric transformer, the direct and converse piezoelectric effects

 are used to acoustically transform power from one voltage and current level to another

 through a vibrating structure. The converse piezoelectric effect, in which an applied electric

 field produces a resulting strain in a body, is used to convert an oscillating electric field

 applied to the left half of a structure, such as a bar, into a vibrational mode of the entire bar.

 If driven at resonance standing wave distributions of large amplitudes of stress and strain

 result. The resonantly amplified strain in the right half of each bar is converted to a voltage

 across the output terminals by the direct piezoelectric effect. Depending upon geometry and

MESCE, Kuttippuram                              6                                     EEE Dept.
Piezoelectric transformers                                                      Seminar ‘04

 materials parameters, we can obtain voltage amplification of various magnitudes, with

 associated step-down in current levels.

               Piezoelectric devices work on two different modes of operation (or a

 combination of the two), called d33 or d31, depending on the direction of extraction

 relative to the direction of polarization. The relative displacement in the d33 mode is

 approximately 3 times larger than that of the d31 mode. Displacement in the d33 is an

 expansion in the same direction as the electrical field and poling direction. Displacement in

 the d31 mode is a contraction perpendicular to the electrical and poling direction.

  Many materials, such as quartz, lithium niobate, and lead zirconate lead titanate (PZT)

 exhibits some form of the piezoelectric effect. The piezoelectric transformer uses PZT,

 hence, it is a PZT transformer.


      Electrical input signals to the primary electrodes are piezoelectrically transferred to

 mechanical vibrations.

MESCE, Kuttippuram                            7                                   EEE Dept.
Piezoelectric transformers                                                       Seminar ‘04


               The piezoelectric technology has been object of a significant evolution to

 achieve current reliability in PTs based applications. Initially this technology suffered from

 serious instabilities and device failures related to,

    I. Immature materials fabrication technology.

   II. Mechanical reliability min the nodal point, and

  III. Driving circuits.

               These drawbacks have subsequently been fully addressed through

 improvements in materials, third mode vibrational excitation for reducing the stress in the

 central nodal point, and design of more stable power supplies incorporating self tracking

 feedback circuits and resonant converters.

               In spite of the induced modifications, the current state of the PTs still suffers

 from a few drawbacks. First, the current PTs includes an output and an input sections

 which each have different polarization (alternatively poled piezoelectric transformers), with

 several associated inconveniences.

    I. Different polarization requires a special preprocessing in order to provide separately

       polarized sections.

   II. Internal stress concentration is in the interface between transversal and longitudinal

       polarization. This in turn, used to cause internal cracks during electric polarization.

       This in turn, used to cause internal cracks during electric poling process or premature

       mechanical fatigue and breakdown during operation.

MESCE, Kuttippuram                              8                                  EEE Dept.
Piezoelectric transformers                                                  Seminar ‘04

              The second of the issue under significant research now a days, is the

 enhancement of the power capabilities of Rosen type double polarized PTs. Although

 piezoelectric transformers for CCFL invertors requiring a power in the range of 510 W has

 been successfully achieved, higher power applications are still limited to PTs. The

 conventional piezoelectric transformers have a lack of high output as well as low

 impedance characteristics, which are needed for use in lightning ballasts. Recently, new

 structures for piezoelectric transformers have been developed and proposed for high power

 and small load resistance applications. Their structures, however, are more complicated,

 causing more costly in mass production.

              One of the simplest designs to make a PT was proposed by Berlin court in

 1973. This design consisted in a PT where the input and output sections had the same

 polarization (“unipoled” piezoelectric transformers).

MESCE, Kuttippuram                           9                                EEE Dept.
Piezoelectric transformers                                                        Seminar ‘04


              The piezoelectric transformer is constructed of PZT ceramic, but more

 precisely it is a multilayer ceramic. The manufacturing of the transformer is similar to the

 manufacturing of ceramic of chip capacitors. The process prints layers of flexible, unified

 PZT ceramic tape with metallic patterns, then allighs and stacks the layers to form the

 required structure. The next step involves pressing, dicing, and firing the stacks to create

 the stacks to create the final ceramic device.

               The input section of the transformer has a multilayer ceramic capacitor

 structure. The pattern of the metal electrodes creates an interdigitated plate configuration.

 The output section of the transformer has no electrode plates between the ceramic layers, so

 firing produces a single ceramic output structure. Conductive materials which forms the

 output electrode for the transformer, coats the end of the output section.

                The next construction step establishes the polarization directions for the two

 halves of the transformer. Poling of the input section across the interdigitated electrodes

 results in a polarization direction that aligns vertically to the thickness. Poling of the output

 section creates a horizontal or length oriented polarization direction. Operating the

 transformer drives the input in thickness mode, which means that an applied voltage

 between the parallel plates of the input causes the input section to become thicker and

 thinner on alternative half of the sine wave. The change in input thickness couples through

 to the output section, causing it to lengthen and shorten and thereby generating the output

 voltage. The voltage set up ratio is proportional to the ratio of the output length and

 thickness of the input layers.

MESCE, Kuttippuram                             10                                    EEE Dept.
Piezoelectric transformers                                                 Seminar ‘04

 Figure 2.1 Piezoelectric element. This device is composed of two electrode plates and a

 piezoelectric ceramic material, such as barium titanate-based Ceramics.

  Figure 2.2 Longitudinal mode piezoelectric element. The direction of the operating

 stress, T, is parallel o the polarization direction, P, with a corresponding resonant


 Figure 2.3 Transverse mode piezoelectric element. The direction of the operating stress,

 T, is perpendicular to the polarization direction, P, with a corresponding resonant


MESCE, Kuttippuram                          11                               EEE Dept.
Piezoelectric transformers                                                  Seminar ‘04

 Figure 3.1 Rosen piezoelectric transformer.           This piezoelectric transformer is a

 combination of a transverse mode piezoelectric actuator (primary side) and a longitudinal

 mode piezoelectric transducer (secondary side).

  Figure 3.2 Thickness vibration piezoelectric transformers.            This piezoelectric

 transformer is a combination of a longitudinal mode piezoelectric actuator (primary side)

 and a longitudinal mode piezoelectric transducer (secondary side).

 Figure 3.3 Radial vibration mode piezoelectric transformer.            This piezoelectric

 transformer is a combination of a transverse mode piezoelectric actuator (primary side)

 and a transverse mode piezoelectric transducer (secondary side).

MESCE, Kuttippuram                          12                                 EEE Dept.
Piezoelectric transformers                                                    Seminar ‘04


              The equivalent circuit model for the piezoelectric transformer looks identical

 to that of its series resonant magnetic counter part. The difference, however, extend pasty

 the nominal values to the physical representations of the various components. The input

 and output capacitances are simply the result having a dielectric between two metal plates.

 The effective dielectric constant of PZT material is 400 to 5000, depending on composition.

 At this point, unfortunately, basic electronics ends. The rest of the components are more

 complicated. The inductances, Lm, are the mass of the transformer. The capacitance Cm is

 the compliance of the material, or the inverse of spring rates. Calculating the compliance

 requires using the applicable generalized beam equation and young’s modulus, which is a

 constant that expresses the ratio of unit stress to unit deformation. The resistor, Rm,

 represents the combination of dielectric loss and the mechanical Q of the transformer.

          The acoustic, as opposed to the electrical, resonant frequency is related to the

 product of the capacitance Lm. The transformer operates in length resonance, and the

 associated motions are identical to those of a vibrating string. The major difference

 between a PZT transformer’s frequencies are in the ultrasonic range and vary, by design,

 from 50 KHz to MHz. like the string, the transformer has displacement nodes and

 antinodes. Mechanically clamping a node prevents vibration, which reduces efficiency in

 the best case and prevents operation in the worst. Mounting the transformer is crucial, you

 simply can’t refolw solder the device to pc board.

MESCE, Kuttippuram                           13                                  EEE Dept.
Piezoelectric transformers                                                         Seminar ‘04

                                    PT SCHEMATIC

               The final model is the “ideal” transformer with ratio N. this transformer

 represents three separate transformations. The first is the transformation is the electrical

 energy into mechanical vibration. This transformation is a function of the piezoelectric

 constant, which is the electrical field divided by stress, the stress of area , and the electrical

 field length. The second transformation is the transfer of mechanical energy from input

 section to the output section and is a function of poisons ratio, or the ratio of lateral to

 longitudinal strain, for the material. The final transformation is the transfer of mechanical

 energy back into electrical energy, and the calculations are similar to those for input side.

                                             Figure 4

MESCE, Kuttippuram                             14                                     EEE Dept.
Piezoelectric transformers                                                     Seminar ‘04


              Thinner laptop computers and flat-screen TVs may be possible with a simple

 change in the geometry of piezoelectric transformer that can increase the conversion ratio

 without adding additional volume or weight.

              The researchers are, however, looking into developing piezoelectric

 transformers for use on the battlefield to replace the enormous transformers needed to

 operate X-ray equipment. These machines can require as much as 10 kilovolts, but not

 much current. In these applications, 20 or more disk transformers might be stacked and still

 take up only a fraction of the weight and the volume of conventional transformer. In the

 other direction, the researchers are looking at step-down applications for audio


              Applications of piezoelectric transformers include high voltage power

 supplies for ring laser gyroscope, cathode ray tubes, image intensifiers, and munitions fuses.

 A novel application involves separation of the primary and secondary part of the

 transformer for use as power embedded sensors or devices. In this way, the primary can

 also be used to monitor the load on the secondary component.

MESCE, Kuttippuram                           15                                   EEE Dept.
Piezoelectric transformers                                    Seminar ‘04

 Selected Markets in Which PT Technology Has Likely Application Today;

      Audio Equipment

      Cellular Phones

      Computer Data Transmission

      Computer power supplies

      DC-DC Converters

      Electric Light Ballasts

      Flat Panel Displays

      High Voltage gate Drivers

      Ignition systems for vehicles

      Invertors

      LCD Displays

      Motor Drives And Controls

      Power Transformers(up to 4 Amps)

      Radios

      Satellite transmitters and receivers

      Smart Appliance And Smart House Systems

      Televisions

      VCRs

MESCE, Kuttippuram                            16                EEE Dept.
Piezoelectric transformers                                                   Seminar ‘04


              Piezoelectric transformers are small in size and don’t require windings. So

 there is no short circuit possibility between the windings, and the transformer has the

 ability to generate a wide range of high voltage AC or DC outputs as well. The unique

 nature of these transformers enables innovative circuit design, such as operation above

 resonance for inductive behavior in order to achieve soft switching without compensating

 inductors. New models are being developed for calculating power density and

 voltage\current amplification, and for evaluating bulk piezoelectric materials for losses,

 high frequency performance, and vibration velocity limits for construction of a prototype


MESCE, Kuttippuram                         17                                  EEE Dept.
Piezoelectric transformers                                   Seminar ‘04


 High power capacity          PT works in more applications than any

                              other electromagnetic transformers

 Low Profile\small Size       Compact assembled package and product

 High efficiency              Energy conservation &compliance with


 Low EMI emission             Little or no interference with surrounding

                              circuitry   compact      packaging    with

                              geometric flexibility.

 Pure Sine Wave Output        Longer product life, such as lamps.

 Wide Design versatility      Recalibration simplified or eliminated for

                              different model types and products

 Fail Safe Design             No Winding to burn, break, or short open

                              circuit would not cause are induced


 No windings                  Low EMI

 High Breakdown Voltage       Simply achieved in PTs, so circuitry,

                              packing & manufacturing are facilitated

 Simple mounting              Facilitates automated assembly of boards

 Wide Performance Range       Versatility for high voltages ac or dc


MESCE, Kuttippuram           18                                 EEE Dept.
Piezoelectric transformers                                                    Seminar ‘04


               However those piezoelectric transformers are not necessarily the answer to all

 power problems. For one thing, in any transformer, as the voltage is increased, the current

 decrease, so transformer is only applicable where current is unimportant.

MESCE, Kuttippuram                          19                                   EEE Dept.
Piezoelectric transformers                                                      Seminar ‘04




               Small electronic devices which operate at high voltages require a compact

 transformer to step up the low voltages of available power supplies. We have been

 exploring the feasibility of utilizing piezoelectric transformers (PTs) for use in low profile

 high voltage power supplies. The simplest design is the Rosen type PT has been

 theoretically modeled utilizing an equivalent circuit which accounts for both the electrical

 and mechanical behavior of transformer. The critical performance parameters of the

 transformer, such as voltage step-up ratio and efficiency, can be predicted from the

 equivalent circuit. To verify the equivalent circuit, we are constructing Rosen-type PTs and

 measuring their performance.



      A piezoelectric transformer is essentially an acoustic resonator\filter that is designed

 such that the output voltage is different from the input voltage. PTs like resonators can be

 classified according to their mode of vibration. The vibration mode that is most promising

 for high step-up ratio transformers is the length extensional mode. In this mode, along thin

 bar supports acoustic waves which propagate along its lengths. When the frequency of

MESCE, Kuttippuram                           20                                    EEE Dept.
Piezoelectric transformers                                                       Seminar ‘04

 vibration is such that an integer number of half wavelengths is equal to the length of the bar,

 the bar will be in mechanical resonance and large strains will appear in the bar.

              Accompanying the mechanical strain will be electrical fields due to the

 piezoelectric effect. The direction of the electric field will correspond to the direction in

 which the piezoelectric ceramic is poled. For a transformer, parts of the bar are poled in the

 length direction and other parts are poled in the thickness direction. Thus, the thickness

 poled portions of the bar will develop a voltage differential between the two large faces of

 the bar that is proportional to the thickness of the bar, and the length poled portions of the

 bar will develop voltage along the length of hat portion proportional to its length. To a first

 order, the voltage step-up ratio of the transformer will be proportional to the ratio of the

 thickness of the bar to the length of the bar.

                                             Figure 5

              A schematic of the Rosen transformer. The poling direction by arrows. The

 input half of the transformer is poled along its thickness while the output half is poled

 along its length.

MESCE, Kuttippuram                                21                                 EEE Dept.
Piezoelectric transformers                                                          Seminar ‘04

                                            Figure 6

              The complete equivalent circuit representing the Rosen transformer. The input

 electrodes are on the left side. The impedance is hyperbolic functions of the complex wave


               Possibly the simplest length extensional mode voltage step-up PT is the

 Rosen transformer (Figure 1) [1]. It consists of two portions, the first (input portion) is

 poled in the thickness direction, and the second (output portion) is poled along the bar’s

 length. This transformer is operated at its first harmonic frequency such that one full

 standing wave exists on the bar. This design requires three electrodes, two covering the

 large faces of the input section, and one on the end face of the output section.


               The standard method of analyzing acoustic resonators is by utilizing a Mason

 equivalent circuit [2]. The mechanical and electrical behaviors of the resonator are

 represented by parallel branches with the electromechanical conversion represented by an

 ideal transformer. An equivalent circuit was originally given by C. A. Rosen in his 1956

MESCE, Kuttippuram                            22                                      EEE Dept.
Piezoelectric transformers                                                      Seminar ‘04

 Ph.D. thesis and represents the behavior of the transformer under the assumption that the

 mechanical impedance of the two halves of the transformer are matched. This circuit is

 reproduced in (Figure 2) [1]. This circuit completely represents the transformer given the

 following assumptions: 1) the dimensions of the bar are such that no other resonance mode

 has a frequency near that of the operational mode, 2) the bar is sufficiently thin and narrow

 such that the transverse inertia of the bar is negligible, and 3) the dielectric losses in the

 material are negligible. Mechanical losses in the material are represented by the real

 component of the wave number (the argument in the hyperbolic impedances) which is

 describable in terms of the mechanical quality factor (or equivalently, the mechanical loss

 tangent). The mechanical quality factor (Qm) is determined by experiment, and in general

 this value decreases with frequency of vibration.

                                           Figure 7

 The at-resonance equivalent circuit of the Rosen transformer. This circuit is used to predict

 performance of the transformer.

MESCE, Kuttippuram                           23                                    EEE Dept.
Piezoelectric transformers                                                       Seminar ‘04

                                            Figure 8

              Theoretical transformer performance as a function of resistive load impedance

 without output matching circuitry. The efficiency peaks at a low load resistance while the

 power peaks at a substantially higher load.

                A more useful circuit is the near-resonance circuit. If the mechanical

 impedances of the two halves of the bar are approximated to be identical (that is, the

 velocity of sound in the two halves are the same), the general circuit can be simplified (see

 Figure 3). The circuit can be further simplified by representing the impedances near

 resonance with a series LCR branch. The resonance of the impedance is given by the

 values of the inductor and capacitor, and the mechanical losses are represented by the

 resistor. This circuit is utilized in predicting the performance of the Rosen transformer.

MESCE, Kuttippuram                             24                                   EEE Dept.
Piezoelectric transformers                                                      Seminar ‘04

  The performance of the Rosen transformer can be seen in Figure 4. Equations for voltage

 gain, efficiency, and power transfer derived from the at-resonance circuit have been plotted

 using typical values for transformer dimensions and material properties. As is evident from

 Figure 4, the performance is strongly load dependent. The gain increases with increasing

 load and reaches a maximum at infinite load (open circuit). Power peaks at a moderate

 load, and efficiency peaks at a relatively low load. For applications that demand high

 efficiency, the transformer is limited to operate within a small load range that corresponds

 to low values of power transfer and voltage gain. The loss of efficiency is due to current

 passing through the output capacitor (labeled C02 in Figure 3). This current also passes

 through the resistor and contributes to power dissipation within the transformer but does

 not contribute to power transferred to the load. For both efficiency and power transfer to be

 simultaneously large and inductor would need to be placed in parallel with the load such

 that the inductor-capacitor parallel circuit would be at resonance at the operation frequency.

 In such a case, efficiency would increase asymptotically with load power transfer peaking

 at a load value corresponding to the mechanical loss resistor. Also, a capacitor could be

 placed in series with the load so as to cancel the negative capacitor allowing greater power

 transfer. Of course, the addition of the extra circuit elements may in part negate the size

 advantage of the PT, and any design alteration which would eliminate the need for extra

 circuit elements would be a great improvement.

MESCE, Kuttippuram                           25                                    EEE Dept.
Piezoelectric transformers                                                 Seminar ‘04


              A computer controlled data acquisition system has been assembled (see

 Figure9).It consists of a PC, digital function generator, digital oscilloscope, and an

 amplifier. The PC controls the function generator and oscilloscope and downloads the

 captured waveforms from the oscilloscope. These waveforms are then analyzed to

 determine the transformer impedance, input power, output power, and voltage gain. With

 this setup, the transformer can be quickly and precisely characterized.

                                           Figure 9

              A schematic of the data acquisition system. A PC controls an HP function

 generator and a Nicolet oscilloscope via a GPIB connection. The dotted boxes represent

 electromagnetic shielding.

MESCE, Kuttippuram                           26                              EEE Dept.
Piezoelectric transformers                                                   Seminar ‘04


                We have theoretically analyzed the Rosen transformer and have predicted

 its performance as a function of the load. It is evident that matching circuitry will be

 necessary in order for both efficiency and power transfer to be Satisfactory. We have

 developed a poling technique which allows us to successfully pole transformers without

 destructive electrical discharges. We are in the process of constructing and measuring the

 performance of Rosen transformers. Once the performance of the transformers has been

 characterized, we will be able to determine if the Rosen design is sufficient to replace

 magnetic transformers in field emission display power sources.

MESCE, Kuttippuram                         27                                  EEE Dept.
Piezoelectric transformers                                                   Seminar ‘04


      Dallago.E.Danioni, G.venchi, “Single chip, low voltage piezoelectric transformer

         controller”, IEEE Xplore Sept 2003 pp 273-276.

      Ray Lee Lin, “Piezoelectric transformer characterization and application”, Nov

         2001, pp 1-9.

      Gregory Ivensky, “Generic operational characteristics of piezoelectric transformer”,

         IEEE Transaction on Power Electronics, vol 17, Nov 2003 pp1049-1052.

      M.A. Smith “piezoelectric ceramic transformer for micro power supplies” 1997, pp


      Gregory ivenski, “Analysis and modeling of Piezoelectric transformer in high

         output voltage application” pp 1-2.



MESCE, Kuttippuram                             28                              EEE Dept.

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