NORM: compact model order reduction of weakly nonlinear systems

This paper presents a compact Nonlinear model Order Reduction Method (NORM) that is applicable for time-invariant and time-varying weakly nonlinear systems. NORM is suitable for reducing a class of weakly nonlinear systems that can be well characterized by low order Volterra functional series. Unlike existing projection based reduction methods by J. Roychowdhury et al. (1999), NORM begins with the general matrix-form Volterra nonlinear transfer functions to derive a set of minimum Krylov subspaces for order reduction. Direct moment matching of the nonlinear transfer functions by projection of the original system onto this set of minimum Krylov subspaces leads to a significant reduction of model size. As we will demonstrate as part of our comparison with existing methods, the efficacy of model order for weakly nonlinear systems is determined by the extent to which models can be reduced. Our results further indicate that a multiple-point version of NORM can substantially reduce the model size and approach the ultimate model compactness that is achievable for nonlinear system reduction. We demonstrate the practical utility of NORM for macromodeling weakly nonlinear RF circuits with time-varying behavior.