Nonuniform Multiconductor Transmission Line Analysis by a Two-Step Perturbation Technique

Abstract

A two-step perturbation technique to model nonuni- form multiconductor transmission lines in the frequency domain is presented. In this method, nonuniformities are treated as per- turbations with respect to the nominal uniform multiconductor line. Starting from the Telegrapher's equations and applying two consecutive perturbations steps, at each step, we obtain second- order ordinary differential equations with distributed source terms. Solving these equations together with the appropriate boundary conditions provides the sought-for voltages and cur- rents along the interconnect structure. The method is validated by means of a frequency domain analysis of a ten-conductor microstrip line with random uniformities, confirming its accu- racy and efficiency. Additionally, the time-domain accuracy and efficiency is demonstrated by means of a high-speed packaging nonuniform interconnect with six signal conductors.