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 researc...

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Published in:IEEE journal of microwaves Vol. 5; no. 5; pp. 1162 - 1175
Main Author: Rautio, James C.
Format: Journal Article
Language:English
Published: IEEE 01.09.2025
Subjects:
Fitting
Frequency measurement
group theory
Integrated circuit modeling
Least squares approximations
Least-squares
lumped model
Mathematical models
model extraction
networks
Numerical models
Polynomials
rational polynomial
reduced-order models
RLC circuits
Transfer functions
vector fitting
Vectors
ISSN:2692-8388, 2692-8388
Online Access:Get full text
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Abstract 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.
AbstractList 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.
Author Rautio, James C.
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10.1515/9783110498967-008
10.1109/temc.2003.815528
10.1109/61.772353
10.1109/tmtt.2007.909141
10.1109/tac.1963.1105517
10.1109/mmm.2019.2909516
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Snippet Given a measured frequency domain response, it is useful to determine the best fit rational polynomial transfer function and then synthesize a corresponding...
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StartPage 1162
SubjectTerms Fitting
Frequency measurement
group theory
Integrated circuit modeling
Least squares approximations
Least-squares
lumped model
Mathematical models
model extraction
networks
Numerical models
Polynomials
rational polynomial
reduced-order models
RLC circuits
Transfer functions
vector fitting
Vectors
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Title Direct Least-Squares Rational-Polynomial Lumped-Circuit Model Extraction and Group Theory
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