Maximum Crosstalk Estimation in Weakly Coupled Transmission Lines

Abstract

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.

Maximum Crosstalk Estimation in Lossless and Homogeneous Transmission Lines

“…Several recent efforts have focused on the estimation of maximum crosstalk [6]- [10]. An effort was made in [8], [9] to predict maximum crosstalk at "high frequencies," where the signal lines were electrically large, in a homogeneous medium, and weak coupling was assumed.…”

“…Although the results in [8] were shown to predict the crosstalk well, the maximum crosstalk formulations did not account for transmission line loss and lacked mathematical rigor. Mathematical derivations for new maximum crosstalk formulas were presented in [10] that addressed many of the shortcomings of [8]. The estimates in [10] were based on a mathematically rigorous integral formulation where the transmission lines could be lossy and in an inhomogeneous medium.…”

“…Mathematical derivations for new maximum crosstalk formulas were presented in [10] that addressed many of the shortcomings of [8]. The estimates in [10] were based on a mathematically rigorous integral formulation where the transmission lines could be lossy and in an inhomogeneous medium. The estimates in [10] were formulated in the frequency domain where the signal lines were assumed to be weakly coupled, and the transmission line characteristic impedances were approximately the same over the entire lengths of the aggressor and victim circuits.…”

“…One objective of this paper is to show how the general maximum crosstalk estimates in [10] can be simplified for the specific case of lossless transmission lines and a homogeneous medium assumption. Another objective is to illustrate the limitations and mathematical validity of the estimates in [8], which are not available in the original paper.…”

“…Another objective is to illustrate the limitations and mathematical validity of the estimates in [8], which are not available in the original paper. It is shown that the maximum crosstalk estimates in [8] can be derived from the formulas in [10] under the correct conditions. This paper provides rigorous derivations for the maximum crosstalk estimates in [8], which were originally formulated from an intuitive basis.…”