Interval-valued reduced-order statistical interconnect modeling

We show how advances in the handling of correlated interval representations of range uncertainty can be used to approximate the mass of a probability density function as it moves through numerical operations and, in particular, to predict the impact of statistical manufacturing variations on linear interconnect. We represent correlated statistical variations in resistanceinductance-capacitance (RLC) parameters as sets of correlated intervals and show how classical model-order reduction methods-asymptotic waveform evaluation and passive reducedorder interconnect macromodeling algorithm-can be retargeted to compute interval-valued, rather than scalar-valued, reductions. By applying a simple statistical interpretation and sampling to the resulting compact interval-valued model, we can efficiently estimate the impact of variations on the original circuit. Results show that the technique can predict mean delay and standard deviation with errors between 5% and 10% for correlated RLC parameter variations up to 35%.