Eliminating crosstalk problems in a complex system requires methods that quickly predict where problems may occur and that give intuitive feedback on how best to solve these problems. Solutions for the maximum crosstalk are often used for this purpose. Limit lines for maximum crosstalk in the frequency domain are available in the literature when signal lines are electrically small and weak coupling is assumed; however, little research has been performed for the case where signal lines are electrically large. This paper provides derivations for maximum crosstalk in the frequency domain when signal lines are electrically large and weak coupling applies. The coupling mechanisms are represented by distributed voltage and current sources. These sources result from aggressor circuit voltages and currents as well as mutual terms in the transmission line per-unit-length parameters. The maximum crosstalk expressions for the victim loads are represented by piecewise expressions dependent on the total electrical length of the aggressor circuit and the electrical length of the coupling region. Measurements and simulations are presented, which show the maximum crosstalk estimates can predict the maximum envelope of crosstalk within a few dB.

No abstract

In earlier papers, analytical formulas were derived to estimate the maximum crosstalk in the frequency domain for systems with electrically long signal lines. These formulas were developed to give designers intuitive feedback as to the causes for crosstalk problems and methods for maximum crosstalk reduction. In one of these papers, the maximum crosstalk estimates are based on intuitive relationships for infinitely long transmission lines. While the resulting model is quite simple and easy to understand, its limitations are poorly understood. In another paper, the maximum crosstalk estimates are based on a mathematically rigorous integral formulation, but the resulting model is relatively complex. This rigorous model is derived assuming the signal lines are weakly coupled and the transmission line characteristic impedances are approximately the same over the entire lengths of the aggressor and victim circuits. The following paper illustrates how the less rigorously developed estimates, based on infinitely long transmission lines, may be derived from the mathematically rigorous maximum crosstalk estimates for lossless and homogeneous transmission lines in the frequency domain. The resulting derivation provides insight into the limitations and mathematical validity of the less rigorous estimates that are not available in the original paper. The mathematically rigorous maximum crosstalk estimates are shown to have fewer and less restrictive assumptions than the estimates based on infinitely long transmission lines. Measurements and simulations are presented that validate results and illustrate maximum crosstalk estimate limitations.Index Terms-Cabling and transmission systems, crosstalk, frequency domain techniques, modeling techniques, transmission line theory. 0018-9480

No abstract

We analytically model single-, two-, and three-wires above ground to determine the decay lengths of common and differential modes induced by an E1 high-altitude electromagnetic pulse (HEMP) excitation. Decay length information is pivotal to determine whether any two nodes in the power grid may be treated as uncoupled. We employ a frequency-domain method based on transmission line theory named ATLOG-Analytic Transmission Line Over Ground to model infinitely long and finite single wires, as well as solve the eigenvalue problem of a single-, two-, and three-wire system. Our calculations show that a single, semi-infinite power line can be approximated by a 10 km section of line and that the second electrical reflection for all line lengths longer than the decay length are below half the rated operating voltage. Furthermore, our results show that the differential mode propagates longer distances than the common mode in two-and three-wire systems, and this should be taken into account when performing damage assessment from HEMP excitation. This analysis is a significant step toward simplifying the modeling of practical continental grid lengths, yet maintaining accuracy, a result of enormous impact.