Frequency and time domain variability analysis of an on-chip inverted embedded microstrip line using a macromodeling-based stochastic Galerkin method

In this contribution a novel stochastic Galerkin method is proposed to analyze the parameter variability of uniform on-chip interconnects. This efficient and accurate stochastic modeling method is made possible, specifically for on-chip interconnects, by first constructing parameterized macromodels of the per unit length transmission line parameters. The theory is illustrated by means of a numerical example, i.e. an inverted embedded microstrip line, of which the variability is analyzed in both the frequency and the time domain. A comparison with a standard Monte Carlo technique validates the new approach.