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Efficiency of the Perturbative Stochastic Galerkin Method for Multiple Differential PCB Lines

This paper investigates the efficiency of a perturbative approach for the statistical assessment of differential transmission lines affected by random parameters. Within the polynomial chaos framework, the novel technique reformulates the so-called stochastic Galerkin method in a decoupled and iterative fashion. Instead of solving the classical, augmented and fully coupled transmission line equations, the new approach iteratively solves multiple uncoupled line equations with nominal per-unit-length parameters and suitable equivalent distributed sources accounting for their variability. The methodology is applied to a system of up to four PCB differential pairs. A computational advantage is observed against the classical stochastic Galerkin method for large problems in terms of number of random parameters and/or conductors.