Keywords
direct boundary methods
boundary element method
planar transmission lines
Abstract
The paper presents algorithm of the hierarchical parasitic capacitance extraction of planar transmission lines. The algorithm utilizes direct Trefftz-Kupradze method which is derived from variational formulation. This approach lets one compare and contrast direct Trefftz-Kupradze method with popular Boundary Element and common formulation of both methods (the same boundary discretization, the same potential and flux interpolation, the same form of boundaryintegral equations). Considerations are reduced to 2D geometries and discretizations.are carried out by hierarchical binary decomposition. Boundary-integral equations for Laplace problem are formulated by appropriate method for each leaf-subdomain. Then, they are transformed into so-called Boundary Capacitance Matrices. In the process of tree traversal Boundary Capacitance Matrices are merged together. This matrix combining is done via Schur’s complement method. Finally, the last transformation of Boundary Capacitance Matrix yields General Capacitance Matrix of the system of conductors. Binary decomposition of the considered structures gives opportunity to build library of Boundary Capacitance Matrices for specific subdomain geometries and their utilization without the need of recalculation. By the means of proposed algorithm the influence of the distance of shifted collocation nodes (the feature specific for Trefftz-Kupradze method) is studied experimentally. The research yields quasi-optimal value of the distance, that is used in further numerical experiments. The obtained results are compared to analytical solutions and to the results given by Linpar application (method of moments). Keywords: parasitic capacitance, direct boundary methods, boundary element method, planar transmission lines.