The Analysis of Dielectric Loss in Co-Planar Waveguide Structures Using Generalized Transverse Resonance

There are several methods for the full-wave characterization of waveguide discontinuities; Finite Element Method (FEM), Finite Difference Technique (FDT), and Method of Moments (MoM) are popular. However, these methods are not easily applied when studying the ‘modal anatomy’ of a discontinuity. Other full-wave techniques are better suited. This dissertation discusses the formulation of a technique known as Generalized Transverse Resonance (GTR), which is a subset of Method of Moments. Generalized Transverse Resonance is a hybrid method combining the Transverse Resonance Method (TRM) with the Mode Matching Technique (MMT). The understanding of the generalized transverse resonance method starts with a discussion of Longitudinal Section Waves and from this derives the transverse resonance method for layered media para1lel to the wave propagation. It is shown that Maxwell’s equations can be represented as a mode function and voltage or current. This representation is used to reduce to the problem of merging the TRM and MMT into the GTR method by using network theory. The propagation constant is found by solving the wave equation, as an eigenvalue problem, subject to the boundary conditions. Discussed viii is the relative convergence phenomenon followed by the optimization strategy. Once the propagation constant is found, the cross sectional fields can be solved and from the fields the characteristic impedance is found. Theoretical data is compared to measure data to show the accuracy of the GTR method. Presented is an understanding of the propagation characteristics of a CPW transmission line in proximity with high and low loss silicon. This data will show the loss and propagation characteristics for four CPW structures using two separate silicon lids at six different heights above the transmission line. Two modes have been clearly identified and will be explained. Also presented is a comparison between measured data and simulated data for two CPW structures fabricated on a layered BCB/silicon substrate. Three silicon resistivities were used which clearly show the two modes from the proximity experiment, in addition to a third mode. This third mode is identified and explaine