Generalised Butterworth-Van Dyke equivalent circuit for thin-film bulk acoustic resonator

A generalised Butterworth-Van Dyke (GBVD) equivalent circuit model for a thin-film bulk acoustic resonator (FBAR), especially for a FBAR with a high electromechanical coupling constant (k_t²), is presented. The derivation starts from the ideal impedance formula for the FBAR, then acoustic loss, dielectric loss, and electrode electrical loss are introduced step by step. Results show that the widely used modified Butterworth-Van Dyke (MBVD) model is a special case of a GBVD model using a low k_t² approximation.