Analysis of the High-Frequency Response of Thin Wires Irradiated by Electromagnetic Waves Through Tikhonov Regularization Technique

Yin Zhang,Yuping Shang,Wei Du,Cheng Liao,Rui Huan

doi:10.1109/access.2019.2960404

Yin Zhang, Yuping Shang + Show 3 more

Open Access

https://doi.org/10.1109/access.2019.2960404

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Abstract

The formula for analyzing the response characteristics of the induced current on a transmission line (TL) excited by high-frequency electromagnetic (EM) waves is a mixed integral-differential equation. The integral part is the Fredholm integral equation of the first kind with serious ill-posedness, which causes difficulty in solving it stably. The regularization technique is a useful method for the analysis of the ill-posed problems. Therefore, in this paper, a method based on the Tikhonov regularization technique is proposed to analyze the high-frequency electromagnetic response of a finite length TL illuminated by external EM waves. The integral operator is discretized by the Simpson formula. The validity and correctness of the proposed method have been verified by numerical examples and the applicability of the proposed method at different errors has been analyzed via the TL with different height.

Highlights

A transmission line (TL) is an important connecting component that carries the function of transmitting signals and energy in modern electronic and electrical equipment
The three equations in (8) belong to the Fredholm integral equation of the first kind and are difficult to be solved stably, which means an unacceptable error may occur in the final result when the observed data at the right of the equation change slightly
The high-frequency electromagnetic (HFEM) response of a TL irradiated by EM waves can be expressed by solving the general TL model

Summary

INTRODUCTION

A transmission line (TL) is an important connecting component that carries the function of transmitting signals and energy in modern electronic and electrical equipment. Y. Zhang et al.: Analysis of the High-Frequency Response of Thin Wires Irradiated by Electromagnetic Waves example of multi-conductor transmission line (MTL) [16]. The enhanced transmission line (ETL) model is a useful method for the analysis of the response characteristics of the TL irradiated by HFEM waves, but there is a big difference between it and the classic TL model [17]. It is noted that the response characteristics of the TL illuminated by HFEM waves can be expressed by a mixed integral-differential equation. The Tikhonov regularization technique is adopted to solve the mixed integral-differential equation and analyze the HFEM response characteristics of the TL in this study. VOLUME 7, 2019 propagation direction of the EM waves is K and is defined by the pitch angle φ, azimuth angle γ , and polarization angle θ

DERIVATION OF THE MIXED INTEGRAL-DIFFERENTIAL EQUATION

PROCESS OF TIKHONOV REGULARIZATION

DEFINITION OF REGULARIZATION PARAMETER

NUMERICAL EXAMPLES

Findings

CONCLUSION