Efficient Estimation of Crosstalk Statistics in Random Wire Bundles With Lacing Cords

Abstract

This paper deals with crosstalk estimation in a set of individually insulated wires laced together to form a bundle, and running above a ground plane. A simplified and numerically efficient multiconductor transmission line model is developed, involving a single reference cross section with pseudocircular shape and staircase approximation for the wire trajectories. The presence of lacing cords along the bundle is modeled as a sinusoidal modulation of the reference cross-section dimension. It is shown that crosstalk in wire bundles is mainly affected by the relative positions of the generator and receptor wires, whose paths are to be accurately represented as smooth curved trajectories, whereas it results to be substantially insensitive to rough modeling of the paths of the remaining wires. The weak random nonuniformity of the generator and receptor wires proves to be the fundamental property to be reproduced in order to obtain physically sound crosstalk predictions. This is enforced by deducing the staircase approximation of the generator and receptor wires from a preliminary representation of only that wire pair in terms of splines with a very small number of nodes. Differently, the staircase trajectories of the remaining wires are obtained by direct mapping onto the reference cross section. Model performance is assessed by comparing crosstalk predictions versus measurement data and theoretical results available in the technical literature. Predictions compare appreciably well with measurements, also in the most critical case of high-impedance loads. The coupling distribution shows nonsymmetrical structure and a long tail to the right, as several other crosstalk analyses have shown.