Direct Least-Squares Rational-Polynomial Lumped-Circuit Model Extraction and Group Theory

Given a measured frequency domain response, it is useful to determine the best fit rational polynomial transfer function and then synthesize a corresponding lumped network. Vector Fitting, an iterative algorithm, is often used for this purpose. Historically, certain avenues of vector fitting research have not been pursued due to numerical precision limitations. Here, we explore one such approach that is closed form, i.e., non-iterative, and is not limited by numerical precision. When a lumped model is desired, we synthesize the best fits of all networks possible that have up to five RLC elements. In the course of this work, a variety of previously unknown relationships between these networks was discovered, including 4651 transforms between these lumped networks. The entire library, closed-form model extraction, and all network-pair transforms have been implemented in MATLAB and is freely available. In conjunction with this work, RLC network transfer functions and networks are explored in terms of group theory.