Lumped element equivalent circuit for shear piezoelectric cylindrical resonators

The lumped element equivalent circuit for piezoelectric cylindrical resonators polarized axially and vibrating in a shear mode in the vicinity of their resonance is presented. Closed analytical expressions for the equivalent-circuit parameters L₁, C₁, R₁ and C₀ for free piezoelectric cylindrical resonator were established. All element values obtained are functions of material and geometrical properties of the resonator. Moreover, using the perturbation theory, the analytical formulas for additional elements L₂, C₂, R₂ contributed by the viscoelastic loading were established. The results obtained can be used in the design and development of the piezoelectric cylindrical resonators, sensors and filters.