Response variability of high-speed interconnects via Hermite Polynomial Chaos

This paper focuses on the stochastic analysis of dynamical circuits via the Hermite Polynomial Chaos theory. The proposed approach facilitates the inclusion of external uncertainties, like tolerances or process variations, in the circuit analysis. The mechanics of the method amounts to expanding the output variables into a sum of a limited number of orthogonal basis functions and generating an extended matrix for the modified nodal analysis. The advocated method, while providing accurate results, turns out to be more efficient than the classical Monte Carlo technique in determining the circuit response sensitivity to parameters variability. A realistic application example involving a coupled-line structure concludes the paper.