Predicting interconnect uncertainty with a new robust model order reduction method

As we scale toward nanometer technologies, the increase in interconnect parameter variations will bring significant performance variability. New design methodologies will emerge to facilitate construction of reliable systems from unreliable nanometer scale components. Such methodologies require new performance models which accurately capture the manufacturing realities. In this paper, we present a Linear Fractional Transform (LFT) based model for interconnect Parametric Uncertainty. This new model formulates the interconnect parameter uncertainty as a repeated scalar uncertainty structure. With the help of generalized Balanced Truncation Realization (BTR) based on Linear Matrix Inequalities (LMIs), the new model reduces the order of the original interconnect network while preserves the stability. This paper also shows that the LFT based model even guarantees passivity if the BTR reduction is based on solutions to a pair of Linear Matrix Inequalities (LMIs) which generalizes Lur´e equations.