Finite element simulation of piezoelectric transformers

• Published in: IEEE transactions on ultrasonics, ferroelectrics, and frequency control Vol. 48; no. 4; pp. 872 - 878
• Main Authors: Tsuchiya, T., Kagawa, Y., Wakatsuki, N., Okamura, H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2001; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Boundary conditions; Circuit simulation; Computer simulation; Electrical engineering. Electrical power engineering; Electrodes; Equivalent circuits; Exact sciences and technology; Finite element analysis; Finite element method; Finite element methods; Frequency; General equipment and techniques; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Mathematical analysis; Mathematical models; Physics; Piezoelectricity; Resonance; Studies; Surface impedance; Transducers; Transformers; Transformers and inductors; Vibrations; Finite element method; Electric transformer; Three dimensional model; Piezoelectric sensor; Modal analysis; Lumped parameter circuit; Equivalent circuit; Power supply; Numerical method; Piezoelectric resonator; Experimental study
• DOI: 10.1109/58.935703
• ISSN: 0885-3010

Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional finite element modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The finite element approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the finite element method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design.