Calculation of quasi-static parameters of arbitrarily-shaped /spl mu//spl epsi/-anisotropic planar structures

Planar structures realized as, for example, microstrips, slotlines, coplanar waveguides and coupled transmission lines are widely used in microwave integrated circuits (MICs) such as directional couplers, interdigital filters and phase shifters. Although generally the electromagnetic fields in these structures are hybrid, the longitudinal components are neglected in quasi-static analysis, and the fields are assumed to be purely TEM. The quasi-static parameters of planar structures have been calculated by many authors. In these calculations, however, the involving /spl mu/ and /spl epsiv/ are assumed to be isotropic and the relative permeability /spl mu//sub r/ is taken to be unity. Furthermore, the underlying inductance matrix L is found by merely inverting the capacitance matrix C which is calculated for an /spl epsiv//sub r/ value of unity. In our present work we show that none of the above-mentioned restrictions is necessary to perform the calculations. We employ the boundary-element method (BEM) and the method of moments (MOM), for a direct calculation of the inductance and capacitance matrices of a system of multiconductor transmission-lines with arbitrary cross-sections, in a medium with anisotropic /spl mu/ and /spl epsiv/ tensors.