Broyden-Based Input Space Mapping with Parameter Extraction Based on the Kullback-Leibler Distance

Abstract

High-frequency and high-speed circuits are commonly used in different kinds of modern electronics applications, including consumer electronics, medical equipment, automotive circuitry, among others. For these high frequencies, regular lumped circuit models are inadequate, being necessary to use distributed-element models based on transmission line theory or even full-wave electromagnetic (EM) models. Typical radio frequency (RF) and microwave components can be implemented in a variety of general technologies, such as microstrip, stripline, coplanar waveguide, etc. Properly configured full-wave EM simulations are normally employed to validate the performance of these components. Optimizing the performance of these RF and microwave components by directly using full-wave EM simulators can be computationally very expensive and, in many cases, even unfeasible. The design optimization process of microwave circuits can be accelerated with the help of space mapping (SM) algorithms, which optimize highly accurate but computationally expensive models, also known as fine models, with the support of fast but not accurate enough models, known as coarse models. A critical sub-process of most SM algorithms is parameter extraction (PE), which consists of finding the coarse model parameters that create a coarse model response as similar as possible to the fine model response at each iteration of the SM algorithm. To measure the similarity between the coarse and fine model responses, classical norms, such as the Manhattan, Euclidean, and Chebyshev norms are widely used. This doctoral dissertation first presents a validation procedure of full-wave EM simulations of filters in microstrip technology which are subsequently used in PE and SM examples. Next, it proposes a numerical PE formulation based on the Kullback-Leibler (K-L) distance, making rigorous comparisons with objective functions based on classical norms. Furthermore, it proposes a Broyden-based input SM formulation with PE based on the K-L distance, which is the principal contribution of this PhD thesis. The overall results presented in this dissertation, illustrated by many examples, considering both synthetic examples and filters in microstrip technology whose full-wave EM simulation responses were used as fine models, demonstrate that SM with PE based on the K-L distance behaves similarly or better than SM with PE based on classical norms. Some future research opportunities related to these topics are also mentioned in this dissertation.