Using of the finite element method for calculating the partial capacity distribution in the microstrip line

Authors: Rubanovich M. G., Vagin D. V., Hrustalev V. A., Bogomolov P. G., Stolyarenko A. A.

Annotation: The paper considers two methods for calculating the partial capacity distribution in the cross section of the microstrip line: 1) direct solution of two-dimensional boundary-value problem by the finite element method; 2) calculation with preliminary conformal mapping of the computational domain. In both cases, elliptic boundary-value problem with Laplace operator is solved to find the electric field potential. In the first case, rectangular finite elements with bilinear basis functions are used. In the second case, triangular finite elements with linear basis functions are used because of the complex boundary between air and dielectric in the computational domain. Upon receipt of the potential distribution, values of the electric field near the surface of the microstrip line are calculated. Then we define the charge distribution on the microstrip line surface by means of Gauss theorem. The developed algorithms are used to determine the partial capacity on any discrete interval of the asymmetric stripline cross-section disposed on a dielectric substrate. For the second method we calculated error estimation of the total capacity. The same estimation is made for the total capacity calculation by the formulas, proposed by the authors.

Keywords: microstrip, capacity, two dimensional electrostatic problem, effective permittivity, wave resistance, boundary problem, finite element method, conformal area mapping