New transmission line analogy applied to single and multilayered piezoelectric transducers

It is shown that a piezoelectric element vibrating in an extensional or shear mode can be modeled rigorously by systematic use of the transmission line analogy and the superposition theorem. A schematic representation of such an element which is in a way more intuitive than others representations is introduced. The stresses on the electroded faces are considered as sources of stress applied at the two ends of an acoustic transmission line, since the acoustical perturbations may be considered as originating on these faces. Using transmission line theory, a complete set of expressions is found for electrical impedance, acoustic stresses, and velocities. Computed results are exactly the same as those given by the classical method, even if the computation sequence is almost entirely different. An intuitive graphical model for a piezoelectric element is proposed. It is also shown that the acoustic velocities on opposite faces of an asymmetrical loaded piezoelectric plate are exactly equal at the antiresonance frequency when internal losses are neglected. The programs developed can be used efficiently for practical multilayered transducer design.