Abstract
This work presents a new method to analyze weak distributed nonlinear (NL) effects, with a focus on the generation of harmonics (H) and intermodulation products (IMD) in bulk acoustic wave (BAW) resonators and filters composed of them. The method consists of finding equivalent current sources [input-output equivalent sources (IOES)] 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 NL constitutive equations. The new methodology is compared with the harmonic balance (HB) analysis, by means of a commercial tool, of a discretized NL Mason model, which is the most used model for NL BAW resonators. While the computation time is drastically reduced, the results are fully identical. For the simulation of a seventh-order filter, the IOES method is around 700 times faster than the HB simulations.
Highlights
THE analysis of nonlinearities occurring in passive devices, being weak, are payed a growing attention, due to their effects in the high demanded performance of nowadays receivers [1]
A proven good approach is to work with distributed nonlinear models in which the nonlinear effect is locally described, allowing to find shape and size-independent nonlinear material parameters that can be later used for the design of any device
The main drawback of this approach is that the device must be discretized in many unit-cells describing the nonlinearities locally, and it leads to a high computation time, especially if the device has a lot of potential distributed nonlinear components, such as multiplexers, which includes many resonators
Summary
THE analysis of nonlinearities occurring in passive devices, being weak, are payed a growing attention, due to their effects in the high demanded performance of nowadays receivers [1]. This technique, based on a Volterra series analysis [14], was presented in [13] and it is briefly described in this article as an intermediate step towards the new IOES method, which is useful to unveil some concepts and equations that are later used. It describes the IOES method including a new description of the 4-port ABCD matrix of a nonlinear Mason circuit and all the algebraic manipulations that are required to figure out the equivalent sources These equivalent sources allow to solve big distributed weak nonlinear circuits much faster than the conventional HB techniques and the method described in [13]. The third example shows new simulations of a 7th filter to outline the main advantage of this technique, that is, the bigger the nonlinear problem, the faster the IOES method is in comparison with HB and [13]
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