Mathematical model of multisectional piezoelectric transformer with ring electrodes in secondary electrical circuits

Within power electronic electromagnetic transformers have been the dominating component for converting and transforming of electrical power. The trend of power converters goes in the direction of higher efficiency and smaller volume. Research has shown that piezoelectric transformers can compete with traditional electromagnetic transformers on both efficiency and power density. Currently, there are no reliable and valid methods of constructing of mathematical models of piezoelectric transformers, which could be used as a theoretical basis for characteristics and parameters calculating of this class of functional elements of modern piezoelectronics. The final goal of mathematical modeling of the vibrating piezoelectric elements physical condition is a qualitative and quantitative description of characteristics and parameters of existing electrical and elastic fields. The main provisions of this article can be fixed as follows. For the first time the scheme of mathematical model constructing of the four sectional disk piezoelectric transformer, which does not contain internal contradictions, is proposed. Proposed scheme maintains its logical structure in the wide range of the number of sections. The features of mathematical models constructing of multisectional transformers, which arise at group connected sections, are considered. According to the authors this article completes construction of the theory of piezoelectric transformers with radial oscillations in thin, polarized across the thickness, piezoelectric disks