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

作者

  • 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

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

关键词:

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

摘要

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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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.

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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.

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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.

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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.

参考

A. Karwowski, A. Noga, and T. Topa, “Computationally efficient technique for wide-band analysis of grid-like spatial shields for protection against LEMP effects,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 32, no. 1, pp. 87-92, 2017.

Y. Zhang, D. Huang, and J. Chen, “Combination of asymptotic phase basis functions and matrix interpolation method for fast analysis of monostatic RCS,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 28, no. 1, pp. 49-56, 2013.

S. M. Seo, C. Wang, and J. Lee, “Analyzing PEC scattering structure using an IE-FFT algorithm,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 24, no. 2, pp. 116-128,2009.

D. Schobert and T. Eibert, “Direct field and mixed potential integral equation solutions by fast Fourier transform accelerated multilevel Green’s function interpolation for conducting and impedance boundary objects,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 26, no. 12, pp. 1016-1023, 2011.

F. S. de Adana, O. Gutiérrez, L. Lozano, and M. F. Cátedra, “A new iterative method to compute the higher order contributions to the scattered field by complex structures,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 21, no. 2, pp. 115-125, 2006.

Y. Zhang, Z. Wang, F. Zhang, X. Chen, J. Miao, and W. Fan, “Phased array calibration based on measured complex signals in a compact multiprobe setup,” IEEE Antennas and Wireless Propagation Letters, vol. 21, no. 4, pp. 833-837, 2022.

Z. Liu, R. Chen, D. Ding, and L. He, “GTD model based cubic spline interpolation method for wide-band frequency- and angular- sweep,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 26, no. 8, pp. 696-704,2011.

B. Gustavsen and A. Semlyen, “Rational approximation of frequency domain responses by vector fitting,” IEEE Transactions on Power Delivery, vol. 14, no. 3, pp. 1052-1061, Jul. 1999.

G. A. Baker, J. L. Gammel, and J. G. Wills, “An investigation of the Padé approximant method,” Journal of Mathematical Analysis & Applications, vol. 2, no. 1, pp. 405-418, 1961.

B. Essakhi and L. Pichon, “An efficient broadband analysis of an antenna via 3D FEM and Padé approximation in the frequency domain,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 2, no. 1, pp. 143-148, 2006.

A. C. Antoulas, J. A. Ball, J. Kang, and J. C. Willems, “On the solution of the minimal rational interpolation problem,” Linear Algebra and its Applications, vol. 137-138, no. 4805, pp. 511-573, 1990.

H. Yuan, W. Bao, C. Lee, B. F. Zinser, S. Campione, and J. Lee, “A method of moments wide band adaptive rational interpolation method for high-quality factor resonant cavities,” IEEE Transactions on Antennas and Propagation, vol. 70, no. 5, pp. 3595-3604, May, 2022.

B. Beckermann, G. Labahn, and A. C. Matos, “On rational functions without Froissart doublets,” Numerische Mathematik, vol. 138, pp. 615-633, 2018.

P. Gonnet, S. Guttel, and L. N. Trefethen, “Robust Padé approximation via SVD,” SIAM Review, vol. 55, pp. 101-117, Mar. 2013.

J. Gilewicz and Y. Kryakin, “Froissart doublets in Padé approximation in the case of polynomial noise,” Journal of Computational and Applied Mathematics, no. 153, pp. 235-242.

R. P. Brent, F. G. Gustavson, and D. Y. Y. Yun, “Fast solution of Toeplitz systems of equations and computation of Padé approximants,” Journal of Algorithms, vol. 1, pp. 259–295, 1980.

D. Belkić and K. Belkić, “Padé–Froissart exact signal-noise separation in nuclear magnetic resonance spectroscopy,” Journal of Physics B, vol. 44, pp. 1-19, 2011.

D. Bessis, “Padé approximations in noise filtering,” Journal of Computational and Applied Mathematics, vol. 66, pp. 85–88, 1996.

Y. Nakatsukasa, O. Sète, and L. N. Trefethen, “The AAA algorithm for rational approximation,” SIAM Journal on Scientific Computing, vol. 40, no. 3, pp. A1494-A1522, 2018.

J. Gilewicz and M. Pindor, “Padé approximants and noise: A case of geometric series,” Journal of Computational and Applied Mathematics, vol. 87, pp. 199-214, 1997.

J. Gilewicz and M. Pindor, “Padé approximants and noise: Rational functions,” Journal of Computational and Applied Mathematics, vol. 105, no. 1, pp. 285-297, 1999.

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已出版

2023-01-31

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[1]
H. . Yuan, J. . Ren, Y. . Li, 和 X. . Huang, 《Removing the Froissart Doublets in a Rational Interpolation Based on Loewner Matrix》, ACES Journal, 卷 38, 期 01, 页 60–66, 1月 2023.

期

2023: Vol 38 Iss 1

栏目

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