Space Mapping with Parameter Extraction Based on the Kullback-Leibler Distance Illustrated with Full-Wave EM and Equivalent Circuit Models for Microstrip Filters

Abstract

Space mapping (SM) techniques are commonly used for optimizing highly accurate models that require a large computational effort, known as fine models, by exploiting simplified physics-based models that are computationally fast but not accurate enough, known as coarse models. Most SM formulations require solving a parameter extraction (PE) sub-problem at each iteration. Typically, SM algorithms use classical l-th norms for the PE objective function. In this paper, we first apply a PE formulation based on the Kullback-Leibler (K-L) distance to microstrip filters using their full-wave electromagnetic (EM) responses as targets, performing a rigorous numerical comparison against PE using classical norms. We subsequently propose, for the first time, a Broyden-based input space mapping algorithm using the K-L distance as objective function for the PE sub-problem. We apply SM design optimization to several examples, beginning with a classical synthetic test example and following with some microstrip filters using their full-wave EM representation as fine models, and their equivalent distributed circuit as coarse models. A rigorous numerical comparison is also performed between classical l-th norms and the K-L formulation for PE within the corresponding SM design optimizations. Our results indicate that SM with PE using the K-L formulation outperforms that one obtained by using the classical l-th norm PE formulations within SM.