Perturbative statistical assessment of PCB differential interconnects

Abstract

This paper presents a novel approach for the statistical analysis of differential interconnects with random parameters. The proposed method employs a perturbation technique to reformulate the augmented multiconductor transmission line (MTL) equations generated by the polynomial chaos based stochastic Galerkin method. The augmented MTL-like equations are recast as the equation for a deterministic MTL with average per-unit-length parameters and additional equivalent distributed sources that account for their variability. The process leads to multiple MTL problems of the same size as the original one, which are solved iteratively in the frequency domain. Moreover, for each iteration, the solution of each MTL problem is independent. The feasibility of the proposed approach is illustrated through the statistical analysis of a canonical PCB differential line with random geometrical parameters. Computational advantages with respect to the classical stochastic Galerkin and Monte Carlo methods are discussed along with the effect of the amount of variability on the performance.