RLC Parameters of a Two-Wire Line with the Finite Element Method

TL;DR

This work develops a three-field finite-element approach to extract per-unit-length DC/low-frequency RLC parameters for a pair of insulated parallel wires. It couples electrostatics in the insulator, electrokinetics in the conductor, and magnetostatics in the domain, solved with weak formulations in an open-boundary 3D setting using ONELAB/GetDP. An exact open-domain treatment is achieved via cylindrical shell transformations (with $r_b$ and $r_e$) or alternative IABC boundaries, enabling accurate energy and power integrals for RLC extraction, even with a geometric defect. Validation against analytical results for uninsulated wires and against Altair Flux confirms accurate $R$, $L$, and $C$ per unit length and demonstrates the influence of insulation and defects, providing an open-source, end-to-end workflow for 3D RLC extraction in complex conductor geometries.

Abstract

This tutorial paper shows how to compute the DC (or low-frequency) resistance, inductance and capacitance of a pair of parallel wires using the finite element method. A three-dimensional infinite domain (open boundary) modeling of electrostatic and magnetostatic fields is presented, along with the electrokinetic formulation for the current flow inside the wires. The effects of the insulation and of a proposed physical defect in the wires are also considered. The open-source ONELAB software is used to perform the simulations and the code listing is provided. Comparisons using analytical models (when applicable) and the Altair Flux software are performed to help validate the simulations.

Figures (16)

• Figure 1: Geometry and electromagnetic constants of the wirepair's conductors and insulators.
• Figure 2: The wirepair segment to be analyzed (between $z=0$ and $z=\ell$).
• Figure 3: Geometrical constants (wirepaircommon.pro).
• Figure 4: Insulated wire with defect (top half of wire 2, partial 2D mesh).
• Figure 5: Group and Function objects (wirepair.pro, part 1 of 7).