Modeling and Computation of Capacitance Matrix for Shielded Vertical Microstrip-Lines using FEM

This paper presents the design analysis of five vertical shielded microstrip lines. The vertical microstrip transition solves the problem of discontinuity between two microstrip lines in different layers of microwave circuit. The main objective of this paper is to compute the capacitance and other relevant parameters like potential distributions of five shielded vertical microstrip line by using finite element technique. the computational and simulation work is carried out with the help of FEM based COMSOL multiphysics software. it has been used in a wide variety of problems like modeling wave guide and transmission lines, cavities etc. To improve the design further, adaptive mesh technique is applied to obtain more accurate result. The two methods commonly used for analyzing shielded microstrip lines are quasi-static method and full wave methods. While working on higher microwave frequencies, full-wave methods have to be exploited for the analysis. This method is based on the direct solution of Maxwell's equations. The quasi-static methods used in this work are based on assumption that the dominant mode of the wave, which propagates along the transmission line, can be approximated (with good accuracy) by the transversal electromagnetic wave (4). The field values can then be used to evaluate the potentials and the characteristic impedance (9). The quasi-static analysis can be performed by modelling the strip lines using computationally efficient Finite Element Method (FEM) (5). The principle of FEM is based on division of the solution domain into small domains, called finite elements. These domains can be of different sizes such that; in region where anticipation of larger variations in fields, number of elements and their sizes can be changed to obtain higher element densities. The model of shielded vertical microstrip lines are designed under the electrostatics surrounding in COMSOL Multiphysics. It facilitates all steps in the modelling process definite geometry, meshing, specifying physics solving and then visualising results. The characteristics impedance of lossless transmission line is: