An accurate direct extraction technique for the MBVD resonator model

A fast method for direct parameter extraction has been developed and applied for characterizing film bulk acoustic resonators (FBAR). The modified Butterworth-Van Dyke (MBVD) model has been used to this end. The measured FBAR data is fitted to an analytical expression containing a set of unknown coefficients, which are then calculated by means of minimizing an error function. Once the coefficients are calculated, the lumped circuit elements in the MBVD model can be readily extracted. Further, since the model is only valid at near resonance frequencies a weight function is proposed. The presented extraction method in this work is fast, easy to implement and readily lends itself to computer automation.