A Hybrid Perturbative-Stochastic Galerkin Method for the Variability Analysis of Nonuniform Transmission Lines

In this paper, a hybridization of the classical stochastic Galerkin method (SGM) with two perturbative solution techniques is proposed to speed up the statistical analysis of nonuniform multiconductor transmission line (MTL) structures with parameters affected by uncertainty. The first method leverages a recently developed deterministic perturbation technique (PT) to deal with nonuniformity affecting the SGM-augmented MTL equations. This approach is proven to be computationally more efficient than the traditional solution based on line subdivision into uniform cascaded sections, yet its performance is still affected by the so-called 'curse of dimensionality.' To further mitigate this issue, a second method is proposed, which resorts to the solution of uncoupled MTLs having the same size as the original structure, and where the effects of both nonuniformity and stochasticity are iteratively included by means of distributed sources. The accuracy and computational efficiency of the proposed approaches are assessed based on the statistical prediction of the mixed-mode S-parameters of microstrip-line structures with different numbers of random parameters. The test cases demonstrate that the hybrid SGM-PT approach is applicable to problems with a few tens of random variables, which is an unprecedented result for state-of-the-art SGM implementations.