Finite and infinite element analysis of coupled cylindrical microstrip line in a nonhomogeneous dielectric media

Abstract

An effective method for computing the parameters of a coupled cylindrical microstrip line system is presented in this paper. Consider a cylindrical microstrip line cross-sectional configuration consisting of two concentric cylindrical dielectric substrates. Two arbitrary number C/sub 1/ and C/sub 2/ of infinitesimally thin arc strips of the arbitrary size (/spl alpha//sub 1//spl les/S/sub 1//spl les//spl beta//sub 1/) and (/spl alpha//sub 2//spl les/S/sub 2//spl les//spl beta//sub 2/) are clad on the dielectric cylindrical interfaces. The dielectric cylinders are characterized by real scalar permittivity /spl epsiv//sub i/ and permeability /spl mu//sub 0/ while the region outside of the dielectric cylinders is free space providing constitutive parameters /spl epsiv//sub 0/ and /spl mu//sub 0/, respectively. The two conductors are charged by V/sub 1/ and V/sub 2/ while the C/sub 0/ is grounded. The analysis is based on finite and infinite element methods and the quasi-static TEM mode approximation. The quasistatic TEM is essentially a low frequency model of a microstrip line that can be concerned with the existence of electric and magnetic fields separately. The microstrip line system is analyzed with both the ordinary finite to discretize the /spl Omega//sub i/ bounded region and global exterior infinite element to cover the /spl Omega//sub 0/ unbounded domain. The potential and field distribution in the cross section of the microstrip line are determined by minimizing the energy functional of the Laplace's equation using the variational principle. Then it can be used to calculate the Maxwellian capacitance or inductance matrix per unit length of the microstrip line. The parameters of the microstrip line can be determined in terms of the capacitance or inductance matrix. The equivalent circuit for the coupled microstrip lines is developed and its application to the solution of wave propagation modes is demonstrated. In this investigation, the accurate solution of characteristic impedance, effective dielectric constant, attenuation, coupling, propagation constant, and so on has been analyzed in terms of the capacitance matrix. These parameters are important in the design of microstrip lines, strip lines, and transmission lines.