Sensitivity analysis of one port and two port BAW and SAW resonator model parameters

A great deal has been written on the subject of equivalent circuit modeling of bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators and on the extraction of their equivalent circuit parameters from measured S-parameter data. However, it is often difficult to obtain reliable and repeatable extraction of the equivalent circuit parameters due to random errors in the measured data itself. Several factors contribute to measurement uncertainty including temperature variation, characterization of fixture parameters, instrument noise, and operator error. This paper first presents a theoretical sensitivity analysis of the extraction of equivalent circuit parameters for single port resonators. For two port resonators, measured S-parameter data was randomly perturbed to simulate the effect of white Gaussian noise in the measurement system. Algorithms were developed using this technique to develop prediction curves giving standard deviation to mean ratios of the extracted equivalent circuit parameters in terms of the noise standard deviation