A Hierarchical Approach to the Stochastic Analysis of Transmission Lines via Polynomial Chaos

Polynomial chaos-based techniques recently became popular tools for signal integrity investigations that include the effects of parameter variability. Most of the available approaches are limited by the "curse of dimensionality", apply only to Gaussian correlations, or they are hindered by the lack of explicit parametrization or knowledge of the input random parameters. This paper presents a hierarchical approach for transmission line analysis, according to which line voltages and currents are mod-eled as polynomial chaos expansions that are function of the per-unit-length parameters, rather than of the underlying geometrical and material parameters. This new approach exhibits some useful advantages such as non-parametricity (with respect to physical parameters), higher accuracy for low expansion orders, and a potential for dimensionality reduction. An application example involving the transient analysis of a stripline interconnect is used to illustrate the feasibility of the advocated approach and discuss its performance.