MTL Annual Research Report 2011

Thin Film Bulk Acoustic Resonators (FBARs) are widely used in the design of modern radio frequency components including duplexers, filters, and oscillators. The overall goal of this project is to incorporate the performance parameters of these resonators into the design flow of the overall system. As a first step, the frequency response of the fabricated devices is measured. Traditionally, an equivalent circuit is then built based on least squares fitting of the frequency response of a simple RLC network to the measured data ^[1] . Such a technique is fairly simple, and the resulting equivalent model does capture important performance parameters, such as quality factor and resonant frequency. However, this technique cannot capture spurious resonances and other second order effects, which quite often play a significant role in the overall performance of the device.

In this work, we are developing tools that will automatically generate accurate, compact, and passive dynamical models for FBARs. Given measured transfer function samples, we identify a rational transfer function model that minimizes the mismatch at the given frequencies. These dynamical models can be interfaced with commercial circuit simulators for time domain simulations of a larger interconnected system. To guarantee the stability of the overall simulation, we ensure the passivity of our generated models by enforcing semidefinite constraints during the fitting process as proposed in ^[2] . Figure 1 shows the 3D layout of an FBAR. Numerical results are presented for resonators configured to constitute a bandpass frequency response. Figure 2 compares the output of our identified models with the given measured data.