Limitation of the Weak-Coupling Assumption for Crosstalk Analysis in an Inhomogeneous Medium

摘要

The limitation of the weak-coupling assumption for the case of two transmission lines with a common ground in an inhomogeneous medium is carefully examined in this paper. All loss is neglected and the lines are assumed to be symmetric. The analysis is based on the mathematical structure of solutions to the telegrapher's equations, and therefore quasi--TEM propagation is assumed. A relationship is found between the propagation constants associated with both the fully coupled and the weakly coupled forms of these equations which leads to a necessary condition for the validity of weak-coupling in an inhomogeneous medium. Although satisfying this condition does not prove that the lines will be weakly coupled, it is anticipated that it will be the limiting factor for many applications of general interest, such as the crosstalk of digital signals on circuit boards. Theoretical and experimental results are given in both the frequency and time domains for several stripline geometries. Closed-form solutions to the telegrapher's equations based on weak-coupling in an inhomogeneous medium are provided. 11 refs., 10 figs.