A block rational Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks

ABSTRACT

Recent work in the area of model-order reduction for RLC interconnect networks has been focused on building reduced-order models that preserve the circuit-theoretic properties of the network, such as stability, passivity, and synthesizability. Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks. Non-passive reduced-order models may lead to instabilities even if they are themselves stable. In this paper, we address the problem of guaranteeing the accuracy and passivity of reduced-order models of multiport RLC networks at any finite number of expansion points. The novel passivity-preserving model-order reduction scheme is a block version of the rational Arnoldi algorithm. The scheme reduces to that of the PRIMA algorithm when applied to a single expansion point at zero frequency. Although the treatment of this paper is restricted to expansion points that are on the negative real axis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from expanding the original model around a single point. Nyquist plots are used to illustrate both the passivity and the accuracy of the reduced-order models.

REFERENCES

• 1: 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
• 2: R. W. Freund , P. Feldmann, Reduced-order modeling of large passive linear circuits by means of the SYPVL algorithm, Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design, p.280-287, November 10-14, 1996, San Jose, California, United States
• 3: J. Eric Bracken. Passive modeling of linear interconnect networks. Technical report, ECE, CMU, 1996. submitted for publication.
• 4: Kevin J. Kerns , Andrew T. Yang, Preservation of passivity during RLC network reduction via split congruence transformations, Proceedings of the 34th annual conference on Design automation, p.34-39, June 09-13, 1997, Anaheim, California, United States [doi>10.1145/266021.266031]
• 5: Altan Odabasioglu , Mustafa Celik , Lawrence T. Pileggi, PRIMA: passive reduced-order interconnect macromodeling algorithm, Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design, p.58-65, November 09-13, 1997, San Jose, California, United States
• 6: A. Ruhe. The rational Krylov algorithm for nonsymmetric eigenvalue problems iii: complex shifts for real matrices. BIT, 34:165-176, 1994.
• 7: K. Gallivan, E. Grimme, and P. Van Dooren. A rational Lanczos method for model reduction. Numerical Algorithms, 12:33-63, 1996.
• 8: E. A. Guillemin. Synthesis of Passive Networks. John Wiley and Sons, 1957.
• 9: S. Y. Kim, N. Gopal, and L. T. Pillage. Time-domain macromodels for vlsi interconnect analysis. IEEE Trans. on CAD, 13(10):1257-1270, October 1994.
• 10: J. Eric Bracken. Algorithms for passive modeling of linear interconnect networks. Technical report, ECE, CMU, 1996. submitted for publication.
• 11: Kevin J. Kerns , Andrew T. Yang, Stable and efficient reduction of large, multiport RC networks by pole analysis via congruence transformations, Proceedings of the 33rd annual conference on Design automation, p.280-285, June 03-07, 1996, Las Vegas, Nevada, United States [doi>10.1145/240518.240570]
• 12: P. Feldmann and R. W. Freund. Efficient linear circuit analysis by Pad@ approximation via the Lanczos process. IEEE Trans. CAD, 14:639-649, May 1995.
• 13: L. Miguel Silveira , Mattan Kamon , Jacob White, Efficient reduced-order modeling of frequency-dependent coupling inductances associated with 3-D interconnect structures, Proceedings of the 32nd ACM/IEEE conference on Design automation, p.376-380, June 12-16, 1995, San Francisco, California, United States [doi>10.1145/217474.217558]
• 14: E. Chiprout and M. S. Nakhla. Analysis of interconnect networks using complex frequency hopping (CFH). IEEE Trans. CAD, 14(2):186-200, February 1995.
• 15: L. T. Pillage and R. A. Rohrer. Asymptotic Waveform Evaluation for Timing Analysis. IEEE Trans. CAD, 9(4):352-366, April 1990.
• 16: E. Grimme. Krylov Projection Methods for Model Reduction. PhD thesis, Coordinated-Science Laboratory, University of Illinois at Urbana-Champaign, 1997.
• 17: C. D. Villemagne and R. E. Skelton. Model reduction using a projection formulation. Int. J. Control, 46:2141 - 2169, 1987.
• 18: Eli Chiprout. 1997. Private communication.

INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.1 PROCESSOR ARCHITECTURES
      C.1.2 Multiple Data Stream Architectures (Multiprocessors)
          Subjects: Interconnection architectures (e.g., common bus, multiport memory, crossbar switch)

Additional Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.1 Types and Design Styles
          Subjects: Advanced technologies

  C. Computer Systems Organization

General Terms:
Algorithms, Design, Measurement, Performance, Theory

Keywords:
model-order reduction, passivity, Arnoldi iteration, multipoint Pade' approximation