Analysis of Nonuniform Transmission Lines With an Iterative and Adaptive Perturbation Technique

This paper presents an iterative and adaptive perturbation technique for the analysis of nonuniform transmission lines. Place-dependent variations of the per-unit-length parameters are interpreted as perturbations with respect to their average values along the line. This allows casting the governing equations for the corresponding perturbations of the voltages and currents as those of a uniform transmission line with distributed sources. Therefore, standard transmission line theory is used to calculate these perturbation terms. Specifically, perturbations of increasing order are computed iteratively starting from the solution of the unperturbed line. The accuracy is adaptively adjusted by setting a threshold on the convergence of the solution. The algorithm turns out to be simple to implement and very accurate, yet faster than traditional approaches based on the discretization of the line into uniform sections. The technique is validated through the analysis of several nonuniform transmission line structures of relevance in EMC applications, namely uniformly and nonuniformly twisted wire pairs as well as a cable bundle with lacing cords.