Алгебраические модели полосковых линий в многослойной диэлектрической среде

Abstract

The electrodynamic problem is reduced to an integral equation with respect to the current density on the strip conductor. It is solved by the projection method using the Chebyshev basis. A homogeneous system of linear algebraic equations (SLAE) is described with respect to the coefficients of the expansion of the longitudinal and transverse components of the current density in terms of Chebyshev polynomials with weight functions that take into account the specificity of the field at the edges of the strip conductors. On the basis of the condition that the determinant of this system is zero the constants of the natural waves propagation are determined by numerical methods. A procedure for improving the convergence of slowly convergent series for the matrix coefficients of SLAE is carried out. The problem of high-accuracy calculation of the functions represented in the form of infinite slowly convergent series, by means of which the matrix coefficients are determined, is solved. A universal formula independent of the number of layers for calculating the wave impedances of natural waves is obtained. The use of the Chebyshev basis and the improvement of the series convergence made it possible to develop an effective algorithm for calculating the basic electrodynamic parameters of the strip lines - the propagation constants and the wave impedances of the natural waves. The constructed algebraic models of strip lines allow computer simulation to obtain numerical results quickly and with high accuracy irrespectively of the number of dielectric layers and their parameters. On the basis of the developed algorithm we created a set of computer programs for calculating the propagation constants, the coefficients of the current density decomposition in terms of Chebyshev weighted polynomials and the wave impedances of screened strip lines of various types: a single and connected microstrip lines (with side and face communication); coplanar strip line; slit line and coplanar waveguide. These programs allow determining the electrodynamic parameters of the main wave and up to 50 waves of higher types. The results of a numerical analysis of the convergence of the developed algorithm for the calculation of natural waves are presented. This confirms the effectiveness of the constructed models. Numerical results obtained without the procedure for improving the convergence of series for matrix coefficients and results obtained by the projection method using the trigonometric basis are given.