Projection-based approaches for model reduction of weakly nonlinear, time-varying systems

The problem of automated macromodel generation is interesting from the viewpoint of system-level design because if small, accurate reduced-order models of system component blocks can be extracted, then much larger portions of a design, or more complicated systems, can be simulated or verified than if the analysis were to have to proceed at a detailed level. The prospect of generating the reduced model from a detailed analysis of component blocks is attractive because then the influence of second-order device effects or parasitic components on the overall system performance can be assessed. In this way overly conservative design specifications can be avoided. This paper reports on experiences with extending model reduction techniques to nonlinear systems of differential-algebraic equations, specifically, systems representative of RF circuit components. The discussion proceeds from linear time-varying, to weakly nonlinear, to nonlinear time-varying analysis, relying generally on perturbational techniques to handle deviations from the linear time-invariant case. The main intent is to explore which perturbational techniques work, which do not, and outline some problems that remain to be solved in developing robust, general nonlinear reduction methods.