Model Order Reduction for Neutral Systems by Moment Matching

Circuits with delay elements are very popular and important in the simulation of very-large-scale integration (VLSI) systems. Neutral systems (NSs) with multiple constant delays (MCDs), for example, can be used to model the partial element equivalent circuits (PEECs), which are widely used in high-frequency electromagnetic (EM) analysis. In this paper, the model order reduction (MOR) problem for the NS with MCDs is addressed by moment matching method. The nonlinear exponential terms coming from the delayed states and the derivative of the delayed states in the transfer function of the original NS are first approximated by a Padé approximation or a Taylor series expansion. This has the consequence that the transfer function of the original NS is exponential-free and the standard moment matching method for reduction is readily applied. The Padé approximation of exponential terms gives an expanded delay-free system, which is further reduced to a delay-free reduced-order model (ROM). A Taylor series expansion of exponential terms lets the inverse in the original transfer function have only powers-of-s terms, whose coefficient matrices are of the same size as the original NS, which results in a ROM modeled by a lower-order NS. Numerical examples are included to show the effectiveness of the proposed alQ. Wang ( ) · Y. Wang · E.Y. Lam · N. Wong Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong e-mail: [email protected] E.Y. Lam e-mail: [email protected] N. Wong e-mail: [email protected] Y. Wang Carnegie Mellon University Pittsburgh, 5000 Forbes Avenue, Hamerschlag Hall, Pittsburgh, PA, 15213 USA e-mail: [email protected] 1040 Circuits Syst Signal Process (2013) 32:1039–1063 gorithms and the comparison with existing MOR methods, such as the linear matrix inequality (LMI)-based method.