Model Order Reduction for Nonlinear IC Models

Model order reduction is a mathematical technique to transform nonlinear dynamical models into smaller ones, that are easier to analyze. In this paper we demonstrate how model order reduction can be applied to nonlinear electronic circuits. First we give an introduction to this important topic. For linear time-invariant systems there exist already some well-known techniques, like Truncated Balanced Realization. Afterwards we deal with some typical problems for model order reduction of electronic circuits. Because electronic circuits are highly nonlinear, it is impossible to use the methods for linear systems directly. Three reduction methods, which are suitable for nonlinear differential algebraic equation systems are summarized, the Trajectory piecewise Linear approach, Empirical Balanced Truncation, and the Proper Orthogonal Decomposition. The last two methods have the Galerkin projection in common. Because Galerkin projection does not decrease the evaluation costs of a reduced model, some interpolation techniques are discussed (Missing Point Estimation, and Adapted POD). Finally we show an application of model order reduction to a nonlinear academic model of a diode chain. Arie Verhoeven Eindhoven University of Technology (CASA), Den Dolech 2, 5600 MB Eindhoven, The Netherlands, e-mail: [email protected] Jan ter Maten NXP Semiconductors, e-mail: [email protected] Michael Striebel Technische Universität Chemnitz, e-mail: [email protected] Robert Mattheij Dept of Mathematics and Computer Science, TU Eindhoven, PO Box 513, 5600 MB Eindhoven The Netherlands, e-mail: [email protected]