Time- and Frequency-Domain Evaluation of Stochastic Parameters on Signal Lines

This paper focuses on the derivation of enhanced transmission-line models allowing to describe, in time and frequency domain, a realistic interconnect with the inclusion of external uncertainties, like process variations or routing and layout uncertainties. The proposed method, which is based on the expansion of the well-known telegraph equations in terms of orthogonal polynomials, turns out to be accurate and more efficient than alternative solutions like Monte Carlo method in determining the transmission-line response sensitivity to parameters variability. Moreover, an implementation into standard circuit analysis tools such as SPICE is possible. Two application examples based on PCB structures of common use in commercial packages conclude the paper.