NEW TRANSMISSION-LINE ANALOGY APPLIED TO SINGLE AND MULTILAYERED PIEZOELECTRIC TRANSDUCERS

We show that a piezoelectric element vibrating in an extensional or shear mode can be modeled rigorously in a new different way by systematic use of the transmission line analogy, and the superposition theorem. We also introduce a new schematical representation of such an element which is in a way more intuitive than others, particularly that of Mason's model. 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. We propose a new intuitive graphical model for a piezoelectric element. It is also shown that the acoustic velocities on opposite faces of an asymmetrically loaded piezoelectric plate are exactly equal at the anti-resonance frequency when internal losses are neglected. The programs developed can be used efficiently for practical multilayered transducer design.