The finite element method is used to analyze open three-dimensional transmission line structures in the quasi-TEM regime. Starting from the general solution of the Laplace equation in spherical coordinates, a set of asymptotic boundary conditions are derived for three-dimensional quasi-static problems for a spherical outer boundary. The second-order boundary condition is generalized to a box-shaped outer boundary and implemented in the finite element method to solve the potential problem of a rectangular microstrip patch. Numerical results show that the asymptotic boundary conditions yield more accurate results than those obtainable with a perfectly conducting shield placed at the same location.>
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Khebir et al. (1990) studied this question.
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