2D Transmission Line Field Solver

by Henrik Forstén | Source code & issues

Version: 2026-08-22 (d118b28)

A quasi-static and full-wave 2D field solver for transmission line analysis with adaptive mesh refinement.

Methodology

Quasi-static solver computes the characteristic impedance and propagation parameters of transmission lines by solving Laplace's equation for the electric potential distribution in the cross-section. This assumes that E-field doesn't change as function of frequency, which is strictly valid only for uniform dielectric transmission lines such as stripline. In practice it gives accurate results for many practical transmission line structures.

Full-wave solver solves Maxwell's equations for the guided mode as an eigenvalue problem (using Nédélec elements) capturing dispersion effects that quasi-static solver misses. This is a more accurate solver, but also much slower. Conductor loss uses a magneto-quasi-static (MQS) solve: instead of treating the metal as a surface impedance, it meshes the conductor interior at finite conductivity and solves for the eddy currents the mode drives inside it, resolving skin and proximity effects directly to give resistive loss and the internal inductance. Surface roughness and plating is applied as post-processing.

Rectangular Waveguide

The rectangular waveguide is not TEM or quasi-TEM. It has a single conductor, so there is no static solution. It is solved as a pure eigenmode problem on the full-wave backend, and only the lowest (fundamental) mode is reported, TE₁₀ when the broad wall is wider than the narrow one. Below the cutoff frequency that mode is evanescent and only its attenuation is meaningful. Above the second cutoff the guide is over-moded and the higher-order modes it also supports are not included in the results. The Modes tab shows all the modes.

S-Parameters

S-parameters are computed from the RLGC transmission line model using standard ABCD matrix (T-parameter) formulation. For differential lines, modal decomposition separates odd and even modes, which are then combined into 4-port S-parameters.

Adaptive Mesh Refinement

The solver uses adaptive mesh refinement to concentrate grid points where the field gradients are highest (near conductor edges and dielectric interfaces), improving accuracy while keeping computation tractable.