Skin Effect Modeling in Conductors of Arbitrary Shape Through a Surface Admittance Operator and the Contour Integral Method

TL;DR

This paper introduces a surface-based method using a surface admittance operator and contour integral technique to accurately model skin effect in conductors of any shape, improving efficiency and versatility over traditional eigenfunction-based methods.

Contribution

The paper presents a novel surface formulation for skin effect modeling in arbitrary-shaped conductors using the Dirichlet-Neumann operator and contour integral method, applicable to complex geometries.

Findings

Method accurately models skin effect in various conductor shapes.

Algorithm is simple to implement and computationally efficient.

Numerical results confirm high accuracy and versatility.

Abstract

An accurate modeling of skin effect inside conductors is of capital importance to solve transmission line and scattering problems. This paper presents a surface-based formulation to model skin effect in conductors of arbitrary cross section, and compute the per-unit-length impedance of a multiconductor transmission line. The proposed formulation is based on the Dirichlet-Neumann operator that relates the longitudinal electric field to the tangential magnetic field on the boundary of a conductor. We demonstrate how the surface operator can be obtained through the contour integral method for conductors of arbitrary shape. The proposed algorithm is simple to implement, efficient, and can handle arbitrary cross-sections, which is a main advantage over the existing approach based on eigenfunctions, which is available only for canonical conductor's shapes. The versatility of the method is illustrated through a diverse set of examples, which includes transmission lines with trapezoidal, curved, and V-shaped conductors. Numerical results demonstrate the accuracy, versatility, and efficiency of the proposed technique.