Semiconductors pp 115-130 | Cite as

Moment-Matching Approximations for Linear(Ized) Circuit Analysis

  • Nanda Gopal
  • Ashok Balivada
  • Lawrence T. Pillaget
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 58)

Abstract

Moment-matching approximations appear to be a promising approach for linear circuit analysis in several application areas. Asymptotic Waveform Evaluation (AWE) uses momentmatching to approximate the time- or frequency-domain circuit response in terms of a reducedorder model. AWE has been demonstrated as an efficient means for solving large, stiff, linear(ized) circuits, in particular, the large RC- and RLC-circuit models which characterize high-speed VLSI interconnect. However, since it is based upon moment-matching, which has been shown to be equivalent to a Pade approximation in some cases, AWE is prone to yielding unstable waveform approximations for stable circuits. In addition, it is difficult to quantify the time domain error for moment-matching approximations. We address the issues of stability and accuracy of momentmatching approximations as they apply to linear circuit analysis.

Keywords

Convolution Rosen Mellon 

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References

  1. [1]
    G. A. Baker, Jr. Essentials of Pade Approximants. Academic Press, 1975.MATHGoogle Scholar
  2. [2]
    G. A. Baker, Jr. and P. Graves-Morris. Encyclopedia of Mathematics and its Applications, volume 13. Addison-Wesley Publishing Co., 1981.Google Scholar
  3. [3]
    R. F. Brown. Model stability in use of moments to estimate pulse transfer functions. Electron. Lett., 7, 1971.Google Scholar
  4. [4]
    P. K. Chan. Comments on asymptotic waveform evaluation for timing analysis. Private correspondence.Google Scholar
  5. [5]
    C. Chen. Linear System Theory and Design. CBS Collge Publishing, 1984.Google Scholar
  6. [6]
    L. O. Chua and P. Lin. Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques. Prentice-Hall, Inc., 1975.MATHGoogle Scholar
  7. [7]
    E. J. Davison. A method for simplifying linear dynamic systems. IEEE Trans. Auto. Control, 11, Jan 1966.Google Scholar
  8. [8]
    J. F. J. Alexandra. Stable partial Pade’ approximations for reduced-order transfer functions. IEEE Trans. Auto. Control, 29, 1984.Google Scholar
  9. [9]
    L. G. Gibilaro and F. P. Lees. The reduction of complex transfer function models to simple models using the method of moments. Chem. Eng. Sc., 24, 1969.Google Scholar
  10. [10]
    N. Gopal and L. T. Pillage. Constrained approximation of dominant time constant(s) in RC circuit delay models. Technical Report TR-CERC-TR-LTP-91-01, Comp. Eng. Res. Ctr., U. Texas (Austin), Jan 1991.Google Scholar
  11. [11]
    N. Gopal, C. Ratzlaff, and L. T. Pillage. Constrained approximation of dominant time constant(s) in RC circuit delay models. In Proc. 13th IMACS World Congress Comp. App. Math., Jul 1991.Google Scholar
  12. [12]
    P. Henrici. Applied and Computational Complex Analysis. John Wiley & Sons, 1974.MATHGoogle Scholar
  13. [13]
    X. Huang. Pade1 approximation of linear(ized) circuit responses. PhD thesis, Carnegie Mellon Univ., Nov 1990.Google Scholar
  14. [14]
    X. Huang, V. Raghavan, and R. A. Rohrer. AWEsim: A program for the efficient analysis of linear(ized) circuits. In Proc. IEEE Int’I. Conf. Computer-Aided Des., Nov 1990.Google Scholar
  15. [15]
    M. F. Hutton and B. Friedland. Routh approximations for reducing order of linear timeinvariant systems. IEEE Trans. Auto. Control, 20, 1975.Google Scholar
  16. [16]
    S. M. Kendall and A. Stuart. The Advanced Theory of Statistics. MacMillan Pub. Co., Inc., 1977.MATHGoogle Scholar
  17. [17]
    S. P. McCormick. Modeling and Simulation of VLSI Interconnections with Moments. PhD thesis, Mass. Inst. Tech., June 1989.Google Scholar
  18. [18]
    J. Pal. Stable reduced-order Pade’ approximants using the Routh-Hurwitz array. Electron. Lett, 15, 1979.Google Scholar
  19. [19]
    L. T. Pillage. Asymptotic Waveform Evaluation for Timing Analysis. PhD thesis, Carnegie Mellon Univ., Apr 1989.Google Scholar
  20. [20]
    L. T. Pillage and R. A. Rohrer. Asymptotic waveform evaluation for timing analysis. IEEE Trans. Comp. Aided Design, 9, 1990.Google Scholar
  21. [21]
    PSPICE USER’S MANUAL. Version 4.03. Microsim Corp., Jan 1990.Google Scholar
  22. [22]
    C. L. Ratzlaff. A fast algorithm for computing the time moments of RLC circuits. Master’s thesis, The Univ. of Texas at Austin, May 1991.Google Scholar
  23. [23]
    C. L. Ratzlaff, N. Gopal, and L. T. Pillage. RICE: Rapid Interconnect Circuit Evaluator. In Proc. 28th ACM/IEEE Design Auto. Conf., Jun 1991.Google Scholar
  24. [24]
    R. H. Rosen and L. Lapidus. Minimum realization and systems modeling: Part I–Fundamental theory and algorithms. A. I. Ch. E. J., 18, Jul 1972.Google Scholar
  25. [25]
    Y. Shamash. Linear system reduction using Pade approximation to allow retention of dominant modes. Int’l. J. Control, 21 (2), 1975.Google Scholar
  26. [26]
    V. Zakian. Simplification of linear time-invariant systems by moment approximants. Int’l. J. Control, 18, 1973.Google Scholar
  27. [27]
    J. Zinn-Justin. Strong interaction dynamics with Pade’ approximants. Phy. Rep., 1970.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Nanda Gopal
  • Ashok Balivada
  • Lawrence T. Pillaget
    • 1
  1. 1.Computer Engineering Research Center, Department of Electrical & Computer EngineeringThe University of Texas at AustinAustinUSA

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