Abstract
A one-dimensional analytical model is developed from the three-dimensional equations of linear piezoelectricity for Rosen piezoelectric transformers operating with extensional vibration modes of non-uniform piezoelectric ceramic rods for generating high electric voltages. Free and forced vibration analyses are performed. Vibration frequencies and mode shapes are obtained showing the mechanism of Rosen transformers. Nodal point of the operating mode is determined for the purpose of mounting. The transforming ratio, input impedance, and the efficiency of Rosen transformers and their dependence on various parameters are examined. In particular, it is shown that the slenderness of Rosen transformers implies high voltage generation. The results are useful in the understanding and design of Rosen piezoelectric transformers.