Maximum Crosstalk Estimation in Lossless and Homogeneous Transmission Lines

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.