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

A two-step perturbation technique to model nonuniform multiconductor transmission lines in the frequency domain is presented. In this method, nonuniformities are treated as perturbations 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 currents 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 accuracy and efficiency. Additionally, the time-domain accuracy and efficiency is demonstrated by means of a high-speed packaging nonuniform interconnect with six signal conductors.