Macro Basis Functions for Wire and Cable Coupling Analysis

Dense interconnected cables transmitting communication signals and power between components, such as sensors, motors, antennas and controllers, must operate in tightly controlled electromagnetic (EM) environments to ensure reliable radio frequency (RF) operations. Measurements can detect unwanted signals, but are often complicated, time consuming and expensive to perform. To predict and mitigate interference sources at the design phase, full-wave numerical models are required. The method of moments (MoM) is commonly used for radiating problems; however this type of geometry presents a computational challenge. The cable/wire cross section is sub-wavelength sized while its length and the external geometry is often on the order of wavelengths. Resolving these multi-scale features is computationally expensive and the resulting systems could be ill-conditioned. This dissertation proposes sets of macro basis functions (MBFs) for representing currents on wires and fields inside coaxial cables, to reduce the computational cost while preserving full-wave accuracy. MBFs reduce the solution space by forming a new basis through linear combinations of the underlying lower-order basis functions (LBFs). Conventionally, wires are modelled in the MoM with circumferentially-invariant axially-directed tubular rooftop basis functions where no higher order variations are considered. The proposed wire MBFs include the thin-wire rooftop function, as well as sinusoidal axial and circumferential components, to provide an intermediate approach between conventional thin-wire solvers and full-wave surface MoM. An additional set of MBFs are introduced to support junctions onto external geometry and end-caps. The initially proposed formulation aimed at electrically thick wires only represents solenoidal current flow approximately. This leads to spurious solutions for electrically very thin wires. A stabilized set of MBFs is subsequently proposed to ensure that solenoidal current flow can be exactly represented, thereby resolving the occurrence of spurious solutions. The efficiency and accuracy of the scheme are demonstrated through a range of transmission line problems and shown to be more reliable than existing methods for wire coupling analysis, e.g. transmission line theory (TLT) solvers and thin-wire MoM. A set of volume MBFs is proposed for representing the electric field inside coaxial cables, together with a finite element-boundary integral (FE-BI) formulation with an impedance boundary condition accounting for finite conductivity at cable shields. The volume MBFs are designed for exact representation of gradient fields, analogous to how the wire MBFs can exactly represent solenoidal currents. The use of surface and volume MBFs achieve more than a tenfold reduction in memory compared to the FE-BI with LBFs.

Grantor dc:publisher

Stellenbosch : Stellenbosch University

Year dc:date.issued

2026

Author dc:creator

• Dommisse, William Robertson

Advisors dc:contributor.advisor

• Botha, Matthys M.
• Rylander, Thomas

Language dc:language.iso

en

Repository record dc:identifier.uri

https://scholar.sun.ac.za/handle/10019.1/135757

OAI identifier oai:identifier

oai:scholar.sun.ac.za:10019.1/135757