UBC Theses and Dissertations

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UBC Theses and Dissertations

A versatile and accurate 2-D solution of finite and infinite extent coplanar waveguide Dunsmore, Marnie


Two rapidly converging 2-D models are proposed for the CPW static field problem. Numerical solution of the Finite-Extent CPW static field problem yields two singularities, one due to the edge singularity behavior of the charge, and the other due to the Green's function singularity when the source point x and field point x' are coincident. The infinite extent CPW static field problem has both these singularities as well as a Green's function singularity in the limit as the field point x' —>o°. The rapid convergence of these problems is obtained by extracting the Green's function singularities and then treating the charge edge singularities using Gauss-Chebychev quadrature. These models are easily adapted to different dielectric substrate configurations, including, but not confined to conventional free standing CPW and conductor-backed CPW. This is achieved using a complex image space domain Green's function which is both accurate and rapidly converging. Using the complex image Green's function, the extraction of singularities and Gauss-Chebychev quadrature, the Finite-Extent and infinite extent CPW static field problems are solved for the charge distribution, characteristic impedance and effective dielectric constant. The characteristic impedance and effective dielectric constant results are compared against conformal mapping results. The charge distribution results are compared against results obtained from electrooptic sampling. It is demonstrated that the models in this thesis are accurate and show an improvement in convergence time of between one and two orders of magnitude compared to existing CPW models.

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