Finite-element analysis of microstrip systems in the vicinity of a substrate edge and approximate formulas for capacitance

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The TEM electrical characteristics of a microstrip system in the vicinity of a dielectric edge are investigated via a series of numerical simulations and empirical formulas based on the simulations derived. A finite-element routine is used as the basis for the simulations that solve the Maxwell equations (/spl nabla//spl middot/D=/spl rho//sub f/) subject to the appropriate electromagnetic boundary conditions. The geometric and electrical parameters used in the simulation are selected to be representative of those found typically in printed circuit board fabrications (microstrip features /spl sim/10-30 mils). An empirical formulation for the capacitance of the microstrip is developed and shown to be in good agreement with the simulations (maximum difference of 1070). The formulation is also compared to measurements. Several plots of the vector electric-field intensity are presented. These plots identify the general structure of the electric-field intensity near the edge of the dielectric; thereby providing the design engineer with insight into the typical field fringing expected.>