Development of spectral domain techniques for the analysis of printed transmission lines with nonzero conductor thickness

Abstract

Sub-millimetre wave applications have gained increasing attention in antenna engineering due to their potential for compact front-end designs and wide-band communication channels. Applications include wireless communication, radar systems, astronomical instrumentation, and security imaging. The design of such systems requires accurate modelling of parameters such as input impedance, radiation patterns, and mutual coupling.

Traditional design approaches rely on commercial full-wave solvers, which are flexible but computationally expensive. High-frequency methods such as Physical Optics (PO) and Geometrical Optics (GO) have been used to reduce computational cost, particularly for lens antennas. However, these asymptotic methods become inaccurate when structures are electrically small or when curvature dimensions are comparable to the wavelength. This limitation is especially relevant for modern integrated systems, where small dielectric lenses are used in arrays or core-shell configurations.

To overcome these challenges, dedicated numerical methods based on the Method of Moments (MoM) have been developed for dielectric lens analysis. Although volumetric MoM approaches can accurately model structures of a few wavelengths in size, they become computationally infeasible when applied to finely detailed feeding structures with micrometre-scale features. This leads to extremely large numbers of unknowns and prohibitive memory requirements.

To address this multi-scale problem, hybrid and auxiliary modelling strategies have been introduced. These approaches separate the analysis of the feeding structure and the lens by using equivalent or auxiliary sources that preserve the radiating behaviour while reducing geometric complexity. This enables efficient coupling between simplified feeds and coarse lens models while maintaining acceptable accuracy.

In parallel, accurate modelling of planar transmission lines used in integrated technologies requires explicit consideration of conductor thickness and material losses, especially at sub-millimetre wavelengths where skin depth effects become significant. Conventional surface-based formulations are insufficient in this regime. Therefore, volumetric formulations and spectral-domain techniques are employed to account for finite conductivity and dispersion effects in microstrip and related transmission lines.

Within this context, the work develops and improves numerical tools for modelling printed transmission structures and integrated antenna feeds in stratified media. It focuses on improving both computational efficiency and numerical accuracy, particularly for structures that are not well represented by structured discretisations.

The thesis contributes to the development and optimisation of volumetric electromagnetic simulation tools, including improvements in numerical integration, computational performance, and grid-based modelling accuracy. These developments enable more reliable simulation of integrated sub-millimetre wave antenna systems, particularly for lens-based architectures and planar feeding networks.

Overall, the work supports the design of compact high-frequency antenna systems by providing improved numerical methods that bridge the gap between full-wave accuracy and computational feasibility in multi-scale electromagnetic problems.