Finite Difference Mode Matching
Isaak, David Delbert
The high frequency communication and high-speed electronic industries are demanding increasingly more sophisticated CAD software. Approximate calculations combined with a series of prototypes are becoming less and less practical, if not altogether impossible, as in the case of integrated circuit design. As the speed and complexity of electronics continues to escalate, theoretical techniques that are based on various simplifying approximations to predict the electromagnetic behavior of a device will become invalid. Rigorous numerical methods that depend heavily on powerful computers are fast emerging as the tools most likely to meet the needs of electronic design engineers. The finite difference method is the least analytical of these methods. It requires only the relevant partial differential equations and boundary conditions. The mathematical preprocessing is minimal, and the method can be applied to a wide range of structures including those with odd shapes. The mode matching method is typically applied to scattering from waveguide discontinuities with well defined boundary conditions. The thesis proposes a new hybrid method, finite difference mode matching (FDMM). In FDMM, the structure is sub-divided into regions with uniform crosssection. The orthogonal modes in these regions are found by planar finite difference techniques. The mode matching technique is then applied to the discretized finite difference solutions at the discontinuity. The advantages over other methods for characterizing three-dimensional structures is the discretization is planar and may be solved one region at a time; and unlike traditional mode matching, can be applied to any arbitrarily shaped discontinuity. This can give a considerable improvement in flexibility of application, computation speed and storage efficiency.