Abstract
In this contribution, we present a review on the various bulk piezoelectric ceramic transformers based on planar vibration modes. The studied transformer shapes include rectangular bar, rings and discs (e.g. disc ring dot) homogeneously poled in the thickness direction. Electrical parameters like transformation ratio, efficiency and input and output power are measured and modelled as a function of frequency and resistive load in the secondary circuit. Analytical modelling has been performed for the ‘Rosen type’ and ‘ring dot’ disc or ring transformers as well as for the bar transformers and several other geometries. Finite element analysis modelling has been performed for the set of other more complicated disc transformer geometries. An overview of the results on the studied transformers is presented, including data on transformation ratio, efficiency and optimum load.
Introduction
Piezoelectric transformer (PT) is a piezoelectric resonator with electrodes divided into primary (input) and secondary (output) parts. The transformer is driven by an alternating current (ac) electrical signal at the input circuit, and it generates ac voltage in the output circuit. It employs a converse piezoelectric effect in the input circuit and a primary piezoelectric effect in the output circuit. Common mechanical deformation in the whole PT is responsible for the power transfer between the input and output circuits. In that sense, PT is similar to conventional electromagnetic transformers with a common magnetic field inside the transformer's core. However, PTs have very specific frequency dependence of operational parameters such as transformation ratio, efficiency, input and output power and impedance. The properties of PT reach maximum magnitudes at the resonant frequency, and they are much smaller outside the resonance range.
The first ceramic PT based on lead zirconate titanate (PZT) ceramics has been patented by Rosen and his group1 in 1958. Since that time, there have been numerous patents issued on PTs, mostly related to the accompanying specific application. Cold cathode fluorescent lamp electronics,2 high voltage generator for cold plasma3,4 and step down power transformers for mobile phone battery recharging5 are the most common PT applications. The applications of PT are frequently complex, including specific driving circuit electronics. Piezoelectric transformers are available commercially in Rosen type design (e.g. Fuji & Co., Japan), in planar mode based on THUNDER technology as ‘Transoner’ (Face Electronics, USA) or in multilayer structures (e.g. Noliac A/S, Denmark).
The main PT parameters are voltage transformation ratio (step up or step down), efficiency, input/output power (and power density) and input and output impedance/admittance. These parameters must fit the input/output electronics; otherwise, the PT could be damaged by the mechanical or electrical loss overload, causing mechanical breaks or overheating and loss of piezoelectric properties. Therefore, ‘hard’ PZT ceramic types must be used for PT. Transformation parameters are related to material properties such as electromechanical coupling factor k, mechanical quality Q and dielectric loss tan(δ). For more information on the typical driving conditions and their limits, see, for example, Kartashev et al.6,7 The voltage transformation ratio saturates at open circuit conditions contrary to the current transformation ratio. Efficiency is the best for an optimum impedance load in output circuit and could reach almost 100%.
Piezoelectric transformer design
The most common piezoelectric ceramic material for PT is PZT ceramics and its modifications. Owing to the resonant character of PT operation, hard PZT must be used for it. Resonance requires high mechanical quality Qm and high electromechanical coupling coefficients for the specific vibration mode used in input and output circuits. Driving electronics require a certain range of impedance magnitude, which is related to the dielectric permittivity of the ceramic element. Piezoelectric transformers also follow today's trend for lead free materials. Some of the lead free piezoelectric material compositions mostly based on doped (K1/2Na1/2)NbO3 ceramics have been studied in the literature.8–12
An interesting idea comes from Kozielski et al.13 in the ‘ring dot’ PT made from the composite of soft and hard PZT materials. The input circuit part of the PT body was made from hard PZT to allow the possibility of higher power driving in the input circuit. The output part of the PT body was made from soft PZT in order to get the best voltage response. Both materials were pressed together into a green body and cosintered during ceramic processing.
Special application PT was fabricated also on PMN-PT (Pb(Mg1/3Nb2/3)O3) single crystal in Rosen type design14 in order to take advantage of the extremely high electromechanical coupling coefficients in these single crystals (the k33 coefficient in properly oriented and poled crystals could reach values as high as 95%). A crystal plate cut in [011] direction was oriented in [100] direction along its length and in [0−11] direction along its width. It showed a transformation ratio as high as 134 at open circuit and an efficiency of ∼95% at optimum load. Modifications of the Rosen type design with multilayer input were also studied on PMN-PT crystal.15 Several other modifications were studied on PMN-PT crystals: length extensional PT16 and ring dot PT on circular plate.17,18 Similarly, an Mg doped LiNbO3 circular plate single crystal was used for the PT in ring dot design.19
Possible vibration modes of piezoelectric resonator are given by the piezoelectric coefficient tensor structure (in matrix form)
Electromechanical coupling and mechanical quality factors for hard PZT ceramic materials: data were taken from manufacturer material data sheets
The original Rosen type design1 PT is built on a rectangular PZT plate, with one part poled in the thickness direction (input part) and the second part poled longitudinally (output). Several modifications of the Rosen type design on discs and rings were patented at the same time1 (see Fig. 1). The Rosen type PT design uses k31 mode in input circuit and k33 mode in output circuit. It could be further modified to axially symmetrical electrodes for the Rosen type PT on a disc PZT plate, with the output part in the shape of ring poled radially.
Rosen type PT design: rectangular and circular1
The so called ring dot PT is another very effective PT design. It was proposed on a circular or rectangular PZT plate (see Table 2), and it uses planar vibration mode in both input and output circuits (kp mode). Parameters of the circular ring dot PT were calculated analytically in a one-dimensional resonator model20 as a function of PT dimensions, frequency and ceramic material properties. The planar vibration mode is also used in a Transoner PT design21 based on THUNDER technology. It uses very strong bonding between two PZT discs. Such transformers are capable of transforming high power (commercially available for the nominal powers of 1, 5, 7, 15 and 25 W). The planar vibration mode has been also used for the ‘moonie’ design of PT.22 The input part uses the kp mode, but the output part combines the longitudinal k33 and shear k15 modes in a non-homogeneously poled resonator. The ring dot design could be also applied to thin rectangular bar resonators (see Table 2). The circular PT with ring dot electrode design has been further modified on a ring or disc resonator with a divided ring electrode,23 so called the double ring dot design (see Table 2).
Typical results for studied PTs: transformation ratios are listed for various electrode sizes, other parameters for optimum resistive load
The thickness extensional vibration mode could be used for the transformation in multilayer or multistack resonators (reviews on various vibration modes,24,25 operation parameters26 and non-linear energy transfer management27 could be found elsewhere in the literature). Moreover, a longitudinal thickness shear mode PT has been proposed on multioutput PT.28,29 Both thickness extensional and thickness shear vibration modes exhibit a high transformation ratio, and they are possibly applicable to high power transformation.
A PT, as a resonant piezoelectric device, may have several vibration modes in its vibration spectrum with the fundamental frequency and series of higher overtones. Each vibration mode exhibits specific distribution of stress/strain inside the resonator's body and, therefore, different transformation properties. More vibration modes are present in a less symmetrical electrode pattern PT design. See the disc PTs with a different electrode pattern in Fig. 2 as an example. An effective PT symmetry increases from class 2 to the limiting class ∞m. A PT's frequency spectrum is reduced in the number of resonance modes accordingly. However, a PT is not capable of ac signal transformation at all resonance frequencies equally. The best transformation parameters (i.e. transformation ratio, efficiency) are not always met at the fundamental resonance. In some cases, the distribution of generated charge/voltage in output circuit is the best for some overtone. It is due to the modal distribution of stress/strain inside the PT body (see disc PT in Fig. 3 as an example).
Different electrode patterns for disc PT: effective PT symmetry changes from 2, m, mm2 to ∞m effective symmetry for ‘Jin–Jiang’, 60° ‘wedge’, 180° ‘wedge’ and ‘ring dot’ PT design (from left to right)
Transformation ratio as function of frequency for disc PTs with different symmetries: disc, APC841, diameter 20 mm, thickness 0·8 mm, open circuit
Results and discussion
A set of PTs with various electrode patterns and ceramic element sizes and shapes have been prepared and measured experimentally for PT parameters. For the typical results, see Table 2. The proper electrode size for the specific electrode pattern could be used for the tuning of a specific PT parameter according to the proposed application. Transformation ratio, efficiency and input/output impedance are strongly dependent on the frequency and output circuit load.
The parameters of a PT could be either calculated analytically or modelled by the finite element method (FEM).24 An analytical solution is, however, limited only to very simple PT shapes and electrode patterns, such as the Rosen type design (length extensional or thickness shear31) or ‘ring dot’ geometry.20 This also includes temperature field modelling inside a PT body by FEM.32
Analytical modelling of PT parameters could be done only in some very simple cases, especially for one-dimensional vibration modes and simple electrode patterns. One of the first successful analytical solutions was published for the rectangular Rosen type PT.30 It uses an analytical solution of wave equation for the longitudinal vibrations of thin bar poled transversally or longitudinally. The stress/strain solution in both PT parts is continuous at the interface of input and output segments. The ends of the PT bar are under longitudinal stress free conditions. The voltage U2 in the output circuit is a function of the input voltage U1 and transformer parameters. It is calculated using Maxwell's equation, equation of motion and piezoelectric equations of state.
The transformation ratio for the Rosen type PT30 (see Fig. 1)
A similar calculation strategy has been adopted for the analytical modelling of disc shaped ring dot PT.20 An analytical solution, however, includes special functions, that is, Bessel's functions of the first kind and zeroth and first order. Several other PT shapes and electrode patterns allowing for one-dimensional solution of equations of motion are shown in Fig. 4. The same calculation strategy is adopted for these PTs.
Other PT geometries with one-dimensional analytical solution
If an analytical PT parameter solution does not exist, we can simulate PT performance by using coupled fields FEM with electrical circuit option. Information such as mechanical stress/strain and voltage distribution is available for all model nodes as a result. Results could be compared with laser interferometry and infrared camera visualisation. Combined information from these methods can give us some suggestions on the vibration mode, mechanical clamping for PT and its heat generation management.
Electrical driving of PT is a challenging task, especially at higher transformed power. Resonator in its resonance is under non-linear deformation and power dissipation at higher power. Excessive mechanical deformation might even result in the mechanical crack of the PT element. A discussion on the operating parameters with respect to non-linearities, high mechanical strain, high power dissipation and other key issues for PT was done by Kartashev et al.6,7 Dissipated heat causes temperature change and related change of the mechanical, piezoelectric and dielectric coefficients. Resonance frequency might shift with the temperature as a result of it.
Conclusions
Piezoelectric transformers are superior in some applications (high voltage, high frequency, low power) due to their specific properties, such as non-flammability, no magnetic field generation and their compact and small size with the high power density. However, their application is not easy due to the strong frequency and load impedance dependence of the transformer parameters.
Footnotes
Acknowledgements
This work was supported by the Grant Agency of the Czech Republic (grant no. P102/10/1139).
This paper is part of a special issue on Piezoelectric Materials for End Users