DETERMINATION OF THE TRANSMISSION LINE RESISTANCE MATRIX WITH DEVIATIONS OF DESIGN PARAMETERS FROM NOMINAL

Abstract

Context. UHF transmission systems make extensive use of transmission line segments, the characteristics of which have a significant impact on the performance of various information technologies. One of the problems of production of transmission lines is to obtain a given wave impedance, which significantly affects the electrical and information characteristics of the entire set of equipment. Currently, there is a burning issue of estimating the influence of disturbing factors on various electrical characteristics of long line segments. To date, the most fully developed methods for assessing the effect of disturbing factors on the wave impedance of a homogeneous line (the wave impedance is constant) under regular perturbations. In this case, the influence of perturbations on the reflection coefficient of matched lines was mainly considered. The effect of perturbations on the other characteristics of homogeneous and, especially, inhomogeneous lines has not been sufficiently studie Objective. The purpose of this paper is to determine the effect of wave impedance perturbations on the transmission line impedance matrix. Knowing the perturbed impedance matrix, it is possible to determine the distortion of the characteristics of any device built on transmission line segments. Method. The paper uses the method of perturbation theory of linear differential operators applied to equations describing processes in inhomogeneous long lines. Results. The obtained results make it possible to estimate the influence of regular and irregular perturbations of the wave resistance (wave conductance) on the transmission line matrix considered as a quadrupole. Such matrix can be any quadrupole matrix: resistance matrix, conductance matrix, circuit matrix. This makes it possible, according to the desired function of the circuit (gain, input impedance, reflection coefficient), to determine the allowable deviation of the wave impedance from the nominal value in order to select a tolerance for reproducing the wave impedance. Conclusions. The proposed criterion for estimating line parameter deviations using the norm of the four-pole matrix is inherently an integral criterion and can be used to preliminarily estimate the frequency domain of the strongest distortions, regardless of the functional purpose of the transmission line segment. The developed approach is applicable to both homogeneous and heterogeneous transmission lines and covers both regular and irregular wave impedance perturbations.