Principles and methods of the calculation of transfer characteristics of disk piezoelectric transformers Part 2. The procedure of calculation of parameters and characteristics of the simplest disk piezoelectric transformer

With the help of a personal computer it is possible in a few hours to model many combinations of geometric, physical and mechanical parameters of specific design of piezoelectric transformer, and to find a combination thereof, which provides an implementation of the devices specified parameters. This allows to sharply reduce the number of natural experiments, which inevitably are carried out in the process of new devices development. In addition, using a mathematical model it is easy to determine the characteristics sensitivity of piezoelectric transformer to variations of the elements parameters of its design. With the access to these dependences, we can implement a rational choice of products manufacturing technology, i.e. choose the least expensive technology from a number of ones. Thus, high-quality mathematical model can significantly reduce the time and cost of the development of piezoelectric transformers new models. It is these sufficiently obvious circumstances that encouraged and encourage professionals to develop various aspects of the theory of piezoelectric transformers. In most papers the described methods of piezoelectric transformers models constructing are mostly based on the use of equivalent electrical circuits and it does not allow analyzing of stress-strain state of solids with piezoelectric effects. 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 calculating of characteristics and parameters of this class of functional elements of modern piezoelectronics. In this paper mathematical model of the simplest disk transformer is constructed. During the construction and subsequent study of mathematical model the following facts are determined:  disk piezoelectric transformer is a functional element of piezoelectronics with negative feedback; for primary evaluation of frequencies of maximum values of transformation ratio the results of the calculation of frequencies of electromechanical resonances of radially oscillating piezoceramic disk can be used; absolute values of transformation ratio substantially depend on the values of electric load impedance