Impact on signal integrity of interconnect variabilities

In this paper, literature results on the statistical simulation of lossy and dispersive interconnect networks with uncertain physical properties are extended to general nonlinear circuits. The approach is based on the expansion of circuit voltages and currents into polynomial chaos approximations. The derivation of deterministic circuit equivalents for nonlinear components allows to retrieve the unknown expansion coefficients with a single circuit simulation, that can be carried out via standard SPICE-type solvers. These coefficients provide direct statistical information. The methodology allows the inclusion of arbitrary nonlinear elements and is validated via transmission-line networks terminated by diodes and driven by inverters.