Coordinate-Transformed Arnoldi Algorithm for GeneratingGuaranteed Stable Reduced-Order Models of Arbitrary RLC Circuits

Since the rst papers on asymptotic waveform evaluation (AWE), Pad e-based reduced order models have become standard for improving coupled circuit-interconnect simulation eeciency. Such models can be accurately computed using bi-orthogonalization algorithms like Pad e via Lanczos (PVL), but the resulting Pad e approximates can still be unstable even when generated from stable RLC circuits. For certain classes of RC circuits it has been shown that congruence transforms, like the Arnoldi algorithm, can generate guaranteed stable and passive reduced-order models. In this paper we present a computationally ee-cient model-order reduction technique, the coordinate-transformed Arnoldi algorithm, and show that this method generates arbitrarily accurate and guaranteed stable reduced-order models for arbitrary RLC circuits. Examples are presented which demonstrate the enhanced stability and eeciency of the new method.

[1]  F. P. Lees,et al.  The determination of the moments of the impulse response of chemical processes from the basic transformed equations , 1969 .

[2]  A. Ruehli.  Equivalent Circuit Models for Three-Dimensional Multiconductor Systems , 1974 .

[3]  Gene H. Golub,et al.  Matrix computations , 1983 .

[4]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[5]  Michel S. Nakhla,et al.  Generalized moment-matching methods for transient analysis of interconnect networks , 1992, [1992] Proceedings 29th ACM/IEEE Design Automation Conference.

[6]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[7]  Ronald A. Rohrer,et al.  Interconnect simulation with asymptotic waveform evaluation (AWE) , 1992 .

[8]  Michel S. Nakhla,et al.  Simulating 3-D retarded interconnect models using complex frequency hopping (CFH) , 1993, ICCAD.

[9]  P. Dooren,et al.  Asymptotic Waveform Evaluation via a Lanczos Method , 1994 .

[10]  Lawrence T. Pileggi,et al.  RICE: rapid interconnect circuit evaluation using AWE , 1994, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[11]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[12]  Roland W. Freund,et al.  Reduced-Order Modeling of Large Linear Subcircuits via a Block Lanczos Algorithm , 1995, 32nd Design Automation Conference.

[13]  Andrew T. Yang,et al.  Stable and efficient reduction of substrate model networks using congruence transforms , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).