The Input–Output Equivalent Sources Method for Fast Simulations of Distributed Nonlinearities in Bulk Acoustic Wave Resonators and Filters

Abstract

This work presents a new method to analyze weak distributed nonlinear effects, with focus on the generation of harmonics (H) and intermodulation products (IMD) in bulk acoustic wave resonators and filters composed of them. The method consists of finding equivalent current sources (Input-Output Equivalent Sources) at the H or IMD frequencies of interest, that are applied to the boundary nodes of any layer that can contribute to the nonlinearities according to its local nonlinear constitutive equations. The new methodology is compared with the harmonic balance analysis, by means of a commercial tool, of a discretized nonlinear Mason model, which is the most used model for nonlinear bulk acoustic wave resonators. While the computation time is drastically reduced, the results are fully identical. For the simulation of a 7 th order filter, the Input-Output Equivalent Sources method is around 700 times faster than the harmonic balance simulations.

Distributed Nonlinear Model and Fast Analysis for In-Band IMD3 Prediction of Surface Acoustic Wave Resonators

“…The analysis of large distributed problems has been previously reported in [25] and [26] by taking advantage of the weak nonlinear behavior of these passive devices. According to the perturbation theory, the circuit can be linearly solved at the fundamental frequencies and then the perturbation solution can be obtained taking into consideration the nonlinear terms of the constitutive equations.…”

“…This section applies the IOES method of [25] to SAW resonators providing further details than those appearing in [26], where the IOES method was very briefly described. The new details are:…”

“…The IOES method has been validated trough comparisons with ADS [36] obtaining the same results. In all the cases a twotone experiment with 51 frequency points is performed and, for a fair comparison between both methods, all the possible H's and IMD products were considered including remix effects as it was done in [25].…”

“…The method we describe in this article allows to find the equivalent current sources that placed at the boundary nodes of a given network with many internal sources provide the same results. Reference [25] describes the application of this new method to analyze BAW resonators and filters, referred as Input-Output Equivalent Sources (IOES) method, which allows to perform extremely fast and robust simulations of large distributed weakly nonlinear circuits. The application of the IOES method to SAW resonators was initially introduced in [26].…”