Mathematical model of disk piezoelectric transformer with ring electrode in primary electrical circuit

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 (PT) can compete with traditional electromagnetic transformers on both efficiency and power density. PTs are therefore an interesting field of research. PTs are advantageous in DC-DC converter applications and in cold cathode fluorescent lamps (CCFL) drivers. The favorable attributes of the PT are low weight and size and potentially low cost. One additional important characteristic is the high voltage isolation of ceramic materials used to build PTs. The advantages of using piezoelectric transformers to light LCD monitor backlights include its thin thickness, a small temperature rise, and a low electromagnetic interference (EMI) noise. In addition, a piezoelectric transformer is more suitable for mass production than traditional, coil-based transformers. 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 the development of new devices. In addition, using a mathematical model it is easy to determine the characteristics sensitivity of piezoelectric transformer to variations of elements parameters of its design. With 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 developing of piezoelectric transformers new models. In most papers the described methods for constructing of piezoelectric transformers models are mostly based on the use of equivalent electrical circuits and it does not allow to analyze stress-strain state of solids with piezoelectric effects. Based on the above, it can be argued that currently there are no reliable and valid methods for 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. We can formulate the main results of this work as follows: mathematical model of piezoelectric transformer with ring electrode in primary electrical circuit is constructed; high sensitivity of frequency characteristic of piezoelectric transformer to the values of output impedance of electrical signal source in primary electrical circuit is demonstrated