Steady-State Response of a Well-Balanced Wire Pair to Distributed Interference

The problem of computing the steady-state response of a multiconductor system has received considerable attention in the literature. Carson and Hoyt 1 developed the classical transmission line equations and S. 0. Rice 2 developed the mathematical techniques necessary for their solution. Even so, the complexities introduced by a large number of conductors tend to limit the amount of basic understanding of fundamental problems, such as the effects of longitudinal induction and longitudinal-to-metallic conversion, that can be obtained by pursuing 653 the multiconductor problem. Moreover, a large number of conductors are necessarily described by a large number of parameters upon which there is often a paucity of data. We present an in-depth analysis of the steady-state response of a well-balanced wire pair to distributed interference. This simplification of the general problem enables the analysis to continue beyond the formal solution to develop both an intuitive feel for the problem and a simple model for use in engineering applications. The effect of other pairs can be approximated in the one-pair model by a judicious choice of model parameters. Historically, the primary emphasis has been on characterizing the longitudinal and metallic voltage at the subscriber's telephone set because of the impact of these voltages on the quality of the communication's path. 6 - 7 More recently, the use of electronic loop terminating equipment has generated interest in the longitudinal current at the central office.