Lumped capacitance and open end effects of striplike structures in multilayered and anisotropic substrates

An accurate calculation of the lumped capacitance of a rectangular microstrip patch and the edge capacitance of an open-circuit microstrip or stripline is carried out. Variational expressions in the spectral domain are developed to analyze these conductors when they are embedded in a multilayered anisotropic substrate. A recurrence algorithm, easy to compute, is proposed to determine the three-dimensional spectral Green´s function characterizing the sort of substrates employed. The method makes it possible to study biaxial substrates in the case of the rectangular patch and uniaxial substrates with tilted optical axis in the transverse plane in the case of open-circuit striplike transmission lines. A detailed study of trial functions to approximate the charge density on the conductors is carried out, taking into account the physical features of each problem. The results obtained are compared with those appearing in the literature. Original design graphs are presented, with special emphasis on the use of inhomogeneous and anisotropic substrates