Crosstalk analysis at near-end and far-end of the coupled transmission lines based on eigenvector decomposition

In this paper, a new analytical method is proposed to accurately estimate the near-end and far-end crosstalk of a coupled Transmission Lines (TLs) based on eigenvector decomposition. For a non-homogenous two coupled lines, the related linear differential equations system (LDES) is derived for distributed voltage and current and then using matrix analysis, its four distinct eigenvalues and their associated eigenvectors are determined. It is shown that the two eigenvalues represent the self-propagation constant, while the other ones are linked to the mutual propagation constant of the coupled lines. In addition to, for these lines a closed form expression for near-end and far-end crosstalk is presented. In special case of homogenous coupled lines, the LDES is also determined and it is shown that they provide two couples of eigenvalues. Using the concept of generalized eigenvalues, the solution of these systems is derived and a closed form formula is derived for crosstalk. In order to verify the accuracy of the proposed method a few types of coupled lines, including homogeneous or non-homogeneous are investigated and the amount of crosstalk is estimated. The calculated crosstalk is presented and compared with those obtained by numerical investigation. It is shown that a good agreement is obtained between the calculated and measured results.