Block SAPOR: block Second-order Arnoldi method for Passive Order Reduction of multi-input multi-output RCS interconnect circuits

ABSTRACT

Recently model order reduction techniques for second-order systems have obtained many research interests for the simulation of RCS interconnect circuits employing susceptance elements. In this paper, we propose a Block SAPOR (Block Second-order Arnoldi method for Passive Order Reduction) for Multi-Input Multi-Output RCS Circuits. The proposed Block SAPOR algorithm can simultaneously guarantee passivity and achieve higher accuracy than the first order reduction technique PRIMA. Most importantly, the reduced system matrices obtained by the proposed method can preserve the structure of the original system matrices. Such a nice property makes it possible to construct an equivalent RCS circuit for the reduced system.

REFERENCES

• 1: D. Ling and A. Ruehli, Circuit Analysis, Simulation and Design - Advances in CAD for VLSI. Vol. 3, Part II, Chap. 11, Elsevier Science Publisher, 1987.
• 2: Anirudh Devgan , Hao Ji , Wayne Dai, How to efficiently capture on-chip inductance effects: introducing a new circuit element K, Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design, November 05-09, 2000, San Jose, California
• 3: Z. Zheng , L. Pileggi , M. Beattie , B. Krauter, Window-Based Susceptance Models for Large-Scale RLC Circuit Analyses, Proceedings of the conference on Design, automation and test in Europe, p.628, March 04-08, 2002
• 4: Hui Zheng , Lawrence T. Pileggi, Robust and passive model order reduction for circuits containing susceptance elements, Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design, p.761-766, November 10-14, 2002, San Jose, California [doi>10.1145/774572.774684]
• 5: A. Odabasioglu, M. Celik and L. Pileggi, PRIMA: Passive Reduced-Order Interconnect Macromodeling Algorithm. IEEE Trans. on CAD of Integrated Circuits and Systems, vol. 17, no. 8, pp. 645--654, Aug. 1998.
• 6: R. W. Freund, Reduced-Order Modeling Techniques Based on Krylov Subspaces and Their Use in Circuit Simulation. Numerical Analysis Manuscript, No. 98-3-02, Bell Laboratories, Feb. 1998.
• 7: L. Pillage, and R. A. Rohrer, Asymptotic Waveform Evaluation for Timing Analysis. IEEE Trans. on CAD of Integrated Circuits and Systems, Vol. 9, No. 4, pp. 352--366, Apr. 1990.
• 8: L. Miguel Silveira , Mattan Kamon , Ibrahim Elfadel , Jacob White, A coordinate-transformed Arnoldi algorithm for generating guaranteed stable reduced-order models of RLC circuits, Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design, p.288-294, November 10-14, 1996, San Jose, California, United States
• 9: Bernard N. Sheehan, ENOR: model order reduction of RLC circuits using nodal equations for efficient factorization, Proceedings of the 36th ACM/IEEE conference on Design automation, p.17-21, June 21-25, 1999, New Orleans, Louisiana, United States [doi>10.1145/309847.309855]
• 10: Z. Bai and Y. -F. Su, SOAR: A Second-Order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem. Computer Science Technical Report, CSE-2003-21, University of California, Davis, 2003. To appear in SIAM J. Matrix Anal. Appl.
• 11: Yangfeng Su , Jian Wang , Xuan Zeng , Zhaojun Bai , C. Chiang , D. Zhou, SAPOR: second-order Arnoldi method for passive order reduction of RCS circuits, Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design, p.74-79, November 07-11, 2004 [doi>10.1109/ICCAD.2004.1382546]
• 12: Z. Bai and Y. -F. Su, Dimension Reduction of Second-Order Dynamical Systems via a Second-Order Arnoldi Method. Computer Science Technical Report, CSE-2004-1, University of California, Davis, 2003. To appear in SIAM J. Sci. Comp.