New method of TEM mode analysis of shielded transmission line with cylindrical conductors

Abstract

Summary form only given. The present paper deals with a new method of analysis of a shielded multiconductor transmission line, operating in the TEM mode regime. It is assumed that the cross section of conductors can have a form of circle or circular arc and the shield is grounded circular cylinder. The TEM mode analysis of a perfectly conducting transmission line is completely characterized by the solution of a two-dimensional electrostatic problem. Direct numerical methods usually meet difficulties when the geometry being investigated has sharp edges. The method developed in this work allows to take into account condition and to reach high accuracy in numerical calculations. This method is based on an integral equation for surface charge densities on conductors. The kernel of this integral equation is the Green function of Dirichlet problem for the internal region of a circle. The integral equation is reduced to a system of linear algebraic equations (SLAE), applying the Galerkin method. For the conductors with a circular cross section, the trigonometric functions can be used as a system of basis and weight functions. For the conductors with cross section in a form of circular arc, the full system of Chebyshev polynomials with proper weight is the most suitable, because the weight has the same singularity near the edge of conductor as a surface charge density. Two numerical examples illustrate the efficiency of this method. The first is a transmission line with a single cylindrical conductor. Another example is a transmission line with a conductor having sharp edges. The results of wave impedance calculations are presented. High accuracy and high convergence rate are achieved without limitations on conductors dimensions.