Accurate and Efficient Equivalent Circuit Modeling for Single-Port SAW Resonators

An optimized equivalent circuit modeling framework for single-port surface acoustic wave (SAW) resonators is proposed in this article, addressing key limitations of conventional Butterworth–Van Dyke (BVD) and modified BVD (MBVD) models in representing spurious resonances and packaging parasitics. It incorporates: 1) simplified parasitic circuits to quantify packaging effects and 2) explicit resonance loops for spurious modes. The extraction of equivalent circuit parameters within this framework is guided by an iterative strategy that combines analytical derivation and least-squares optimization. Model validation across 15 commercial SAW resonators (303–868 MHz) shows significantly improved precision: the fit MBVD model reduces root mean squared error (RMSE) by roughly one order of magnitude, while the extended MBVD (EMBVD) further lowers RMSE by 30%–50%. The parasitic-integrated BVD (PBVD) model achieves high-accuracy packaging characterization with a relative RMSE (RRMSE) of 15.1% and root-mean-squared relative error (RMSRE) of 0.51%. In practice, EMBVD prevents oscillation mode hopping by capturing spurious resonances, while PBVD guides the optimization of devices’ packaging and PCB layout. Furthermore, the extracted equivalent circuit parameters provide clear criteria for sensor-specific resonator selection: balancing sensitivity against resolution for mass-loading sensing, or prioritizing low motional resistance (${R}_{\text {m}}\text {)}$and static capacitance (${C}_{{0}}\text {)}$to ensure oscillation stability for viscoelastic sensing. The proposed framework is also extendable to two-port SAW resonators, further broadening its applicability. This work thus facilitates the transition from precise resonator characterization to robust system design.