Optimizing piezoelectric transformer for maximum power transfer

The piezoelectric transformer should be considered as not only a mechanical system but also an electrical fully coupled system, which uses finite structure resonance to perform voltage conversion. The traditional piezoelectric transformer uses an equivalent circuit concept to simulate its mechanical motion. Since the field equation of a piezoelectric transformer is a partial differential equation, an equivalent circuit developed based on an ordinary differential equation cannot express its performance thoroughly. Since the motion of the piezoelectric transformer is determined by both the mechanical and the electrical boundary conditions, the transfer function and electrical impedance of a piezoelectric transformer will vary with different electrical and mechanical conditions. However, it has been discovered that once an equivalent circuit is used to simplify the mechanical motion of the piezoelectric transformer, the coupling effects between the mechanical and the electrical properties will be averaged out and all spatial information will be lost. A fully coupled field equation is derived in this paper to examine the motion of the piezoelectric transformer by taking into account both the mechanical and electrical boundary conditions. It can be shown that by using this newly developed field equation, a new concept using a weighting function in the spatial domain can be adopted to optimize the electro-mechanical coupling effects. In this paper, both impedance and power transfer optimization of the source as well as the sink of the piezoelectric transformer, and the corresponding interface circuits, are verified theoretically and experimentally.