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An ME-PC Enhanced HDMR Method for Efficient Statistical Analysis of Multiconductor Transmission Line Networks

An efficient method for statistically characterizing multiconductor transmission line (MTL) networkssubject to a large number of manufacturing uncertainties is presented. The proposed method achieves its efficiency by leveraging a high-dimensional model representation (HDMR) technique that approximates observables (quantities of interest in MTL networks, such as voltages/currents on mission-critical circuits) in terms of iteratively constructed component functions of only the most significant random variables (parameters that characterize the uncertainties in MTL networks, such as conductor locations and widths, and lumped element values). The efficiency of the proposed scheme is further increased using a multielement probabilistic collocation (ME-PC) method to compute the component functions of the HDMR.

The ME-PC method makes use of generalized polynomial chaos (gPC) expansions to approximate the component functions, where the expansion coefficients are expressed in terms of integrals of the observable over the random domain. These integrals are numerically evaluated and the observable values at the quadrature/collocation points are computed using a fast deterministic simulator. The proposed method is capable of producing accurate statistical information pertinent to an observable that is rapidly varying across a high-dimensional random domain at a computational cost that is significantly lower than that of gPC or Monte Carlo methods. The applicability, efficiency, and accuracy of the method are demonstrated via statistical characterization of frequency-domain voltages in parallel wire, interconnect, and antenna corporate feed networks.