Uma ferramenta computacional para a análise de linhas de transmissão utilizando o método dos elementos finitos

Abstract

The main topic of study of this work is the analysis of transmission lines with coaxial geometry with the finite element method. Initially, the transmission line is modelled as an equivalent circuit, which is discussed and the mathematical formulation is presented. This study includes a complete analysis of the differential equations for the equivalent circuit, its behaviour for different terminations, the application of boundary conditions in the solution of the wave equation, and the derivation of the equivalent distributed parameters: series resistance (R), shunt conductance (G), shunt capacitance (C) and series inductance (L). The differential equation has been solved with the application of the finite element method (FEM), which consists on the discretization of the geometry and on the application of the appropriate boundary conditions. A system of linear equations must be solved to determine the voltage distribution along an arbitrary transmission line. The analysis of the results is done graphically with Matlab software and includes the plotting of the attenuation and the phase variation in coaxial cables for different physical lengts. Finally, the results have been validated with the predictions obtained with the Txline software for different operating frequencies.