Removing the Froissart Doublets in a Rational Interpolation Based on Loewner Matrix

Authors

  • Haobo Yuan National Key Laboratory of Antenna and Microwave Technology Xidian University, Xi’an, 710071, China
  • Jungang Ren National Key Laboratory of Antenna and Microwave Technology Xidian University, Xi’an, 710071, China
  • Yujie Li Hangzhou Institute of Technology Xidian University, Hangzhou, 311200, China
  • Xiaoming Huang National Key Laboratory of Antenna and Microwave Technology Xidian University, Xi’an, 710071, China https://orcid.org/0000-0002-9441-1147

DOI:

https://doi.org/10.13052/2023.ACES.J.380109

Keywords:

finite element method, Froissart doublets, rational interpolation, S-parameter

Abstract

In order to implement wide band frequency sweeping, the S-parameters can be fitted with an adaptive rational interpolation based on Loewner matrix. However, the errors in the sampling data may lead to Froissart doublets, which look like spikes in the curve. In this paper, a novel technique is proposed to remove these doublets. At first, the rational expression is converted into the sum of partial fractions by solving two generalized eigenvalue problems. After that, the partial fraction term with the smallest imaginary part of the pole and relatively large absolute value is considered to generate the doublets. Removing this term results in a smooth rational polynomial, which is validated by the example of a passive circuit simulated by finite element method(FEM).

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Author Biographies

Haobo Yuan, National Key Laboratory of Antenna and Microwave Technology Xidian University, Xi’an, 710071, China

Haobo Yuan was born in Tianmen, Hubei, China, in 1980. He received his B.S., M.S., and Ph.D. degrees in Electromagnetic Fields and Microwave Technology from Xidian University, Xi’an, China, in 2003, 2006, and 2009, respectively. Since 2006, he has been with the School of Electronic Engineering, Xidian University, where he is an Associate Professor. He was a post doctoral researcher at Ohio State University in 2019. His current research interests include computational electromagnetics, antenna measurements, and electromagnetic compatibility.

Jungang Ren, National Key Laboratory of Antenna and Microwave Technology Xidian University, Xi’an, 710071, China

Jungang Ren was born in Xi’an, Shaanxi, China, in 1998. He received his B.Eng. degree in Electronic Information Engineering from Xidian University, Xi’an, China, in 2020. He is currently working towards an M.S. degree with Xidian University. His research interests are numerical techniques in computational electromagnetics.

Yujie Li, Hangzhou Institute of Technology Xidian University, Hangzhou, 311200, China

Yujie Li received her B.Eng. degree in Electronic Information Engineering from the North University of China, Taiyuan, China in 2017. She is currently pursuing an M.Eng. degree with Xidian University. Her research interests are antenna measurement techniques and numerical methods in computational electromagnetics.

Xiaoming Huang, National Key Laboratory of Antenna and Microwave Technology Xidian University, Xi’an, 710071, China

Xiaoming Huang received his B.Eng. degree in Electrical Engineering from Zhengzhou University, Henan, China, in 2021. He is currently pursuing an M.S. degree with Xidian University, Xi’an. His research interests are the numerical techniques in computational electromagnetics.

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Published

2023-01-31

How to Cite

[1]
H. . Yuan, J. . Ren, Y. . Li, and X. . Huang, “Removing the Froissart Doublets in a Rational Interpolation Based on Loewner Matrix”, ACES Journal, vol. 38, no. 01, pp. 60–66, Jan. 2023.

Issue

2023: Vol 38 Iss 1

Section

Antennas, Metasurfaces, and Testing Methodologies for 5G/6G Communication