Constitutive Equations of Piezoelectric Layered Beams With Interdigitated Electrodes

This paper establishes the constitutive equations, or linear two-port models, of piezoelectric layered beams with interdigital electrodes (IDEs). The effect of the nontrivial field on the transduction is analyzed. Based on conformal mapping techniques, we derive new analytic expressions for the capacitance, the electric field, and the electromechanical coupling factor of an anisotropic dielectric with the IDE configuration on top. The IDE capacitance with an anisotropic permittivity can be treated as the one with an isotropic permittivity. The complex expression for the nonuniform field is simplified to a quadratic form. A correction is required for the transducer's coupling constant. All modifications are expressed analytically. The analytic models are verified against the finite element method. Finally, the two-port models help to compare the devices with other electrode configurations, such as beams with a top and bottom electrode.