Advertisement

Circuit Simulation Techniques Based on Lanczos-Type Algorithms

  • R. W. Freund
Part of the Systems & Control: Foundations & Applications book series (PSCT, volume 22)

Abstract

A circuit is a network of electronic devices, such as resistors, capacitors, inductors, diodes, and transistors. Today’s integrated circuits are extremely complex, with up to hundreds of thousands or even millions of devices, and prototyping of such circuits is no longer possible. Instead, computational methods are used to simulate and analyze the behavior of the electronic circuit at the design stage. This allows us to correct the design before the circuit is actually fabricated in silicon. It is due to extensive circuit simulation that first-time correct circuits in silicon are almost the norm.

Keywords

Transfer Function Circuit Simulation Hankel Matrix Lanczos Algorithm Pade Approximants 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J.I. Aliaga, D.L. Boley, R.W. Freund, and V. Hernández. A Lanczos-type algorithm for multiple starting vectors. Numerical Analysis Manuscript. No. 96–18. Bell Laboratories. Murray Hill, NJ. 1996.Google Scholar
  2. [2]
    G.A. Baker, Jr. and P. Graves-Morris. Padé Approximants, Second Edition. New York: Cambridge University Press, 1996.MATHGoogle Scholar
  3. [3]
    A. Bultheel and M. Van Barel. Padé techniques for model reduction in linear system theory: a survey. J. Comput. Appl. Math. 14 (1986), 401–438.MathSciNetCrossRefGoogle Scholar
  4. [4]
    P. Feldmann and R. W. Freun. Efficient linear circuit analysis by Padé approximation via the Lanczos process. Proc. EURO-DAC 1994 with EURO-VHDL 1991 170–175.Google Scholar
  5. [5]
    P. Feldmann and R. W. Freund. Efficient linear circuit analysis by Padé approximation via the Lanczos process. IEEE Trans. Computer-Aided Design 14 (1995), 639–649.CrossRefGoogle Scholar
  6. [6]
    P. Feldmann and R.W. Freund. Reduced-order modeling of large linear subcircuits via a block Lanczos algorithm. Proc. 32nd Design Automation Conference 1995. 474–479.Google Scholar
  7. [7]
    R.W. Freund. Solution of shifted linear systems by quasi-minimal residual iterations. Numerical Linear Algebra. (L. Reichel, A. Ruttan, and R. S. Varga, W. de Gruyter, Eds.) Berlin: Springer-Verlag, 1993. 101–121.Google Scholar
  8. [8]
    R.W. Freund. Computation of matrix Padé approximations of transfer functions via a Lanczos-type proces. Approximation Theory VIII, Vol. 1: Approximation and Interpolation. (C. K. Chui and L. L. Schumaker, Eds.). Singapore: World Scientific Publishing Co., 1995. 215–222.Google Scholar
  9. [9]
    R.W. Freund and P. Feldmann, Small-signal circuit analysis and sensitivity computations with the PVL algorithm. IEEE Trans. Circuits and Systems-II: Analog and Digital Signal Processing 43 (1996), 577–585.CrossRefMATHGoogle Scholar
  10. [10]
    R.W. Freund and P. Feldmann. Reduced-order modeling of large passive linear circuits by means of the SyPVL algorithm. To appear Tech. Dig. 1996 IEEE/ACM International Conference on Computer-Aided Design 1996.Google Scholar
  11. [11]
    R.W. Freund, M.H. Gutknecht, and N.M. Nachtigal. An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices. SIAM J. Sci. Comput. 14 (1993), 137–158.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    R.W. Freund and M. Malhotra. A block-QMR algorithm for non-Hermitian linear systems with multiple right-hand sides. Numerical Analysis Manuscript No. 95–09. AT&T Bell Laboratories. Murray Hill, NJ, 1995. To appear Linear Algebra Appl.Google Scholar
  13. [13]
    K. Gallivan, E. Grimme, and P. Van Dooren. Asymptotic waveform evaluation via a Lanczos method. Appl. Math. Lett. 7 (1994), 75–80.CrossRefMATHGoogle Scholar
  14. [14]
    I. Gohberg, M. A. Kaashoek, and L. Lerer. On minimality in the partial realization problem. Systems Control Lett. 9 (1987), 97–104.MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    W.B. Gragg. Matrix interpretations and applications of the continued fraction algorithm. Rocky Mountain J. Math. 4 (1974), 213–225.MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    W.B. Gragg and A.Lindquist. On the partial realization problem. Linear Algebra Appl. 50 (1983), 277–319.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    E.J. Grimme, D.C. Sorensen, and P. Van Dooren. Model reduction of state space systems via an implicitly restarted Lanczos method. Numer. Algorithms 12 (1996), 1–31.MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    M.H. Gutknecht. A completed theory of the unsymmetric Lanczos process and related algorithms, part I. SIAM J. Matrix Anal Appl. 13 (1992), 594–639.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    X. Huang. Pade Approximation of Linear(ized) Circuit Responses. Ph.D. Dissertation. Carnegie Mellon University. Pittsburgh, Pennsylvania. 1990.Google Scholar
  20. [20]
    T. Kailath. Linear Systems, Englewood Clifffs: Prentice-Hall, 1980.MATHGoogle Scholar
  21. [21]
    H.M. Kim and R.R. Craig, Jr. Structural dynamics analysis using an unsymmetric block Lanczos algorithm. Internat. J. Numer. Methods Engrg. 26 (1988), 2305–2318.CrossRefMATHGoogle Scholar
  22. [22]
    H.M. Kim and R.R. Craig, Jr. Computational enhancement of an unsymmetric block Lanczos algorithm. Internat. J. Numer. Methods Engrg. 30 (1990), 1083–1089.MathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    C. Lanczos. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Standards 45 (1950), 255–282.MathSciNetCrossRefGoogle Scholar
  24. [24]
    L.T. Pillage and R.A. Rohrer. Asymptotic waveform evaluation for timing analysis. IEEE Trans. Computer-Aided Design 9 (1990), 352–366.CrossRefGoogle Scholar
  25. [25]
    T.-J. Su. A decentralized linear quadratic control design method for flexible structures. Ph.D. Dissertation. The University of Texas at Austin. Austin, Texas. 1989.Google Scholar
  26. [26]
    T.-J. Su and R.R. Craig, Jr. Model reduction and control of flexible structures using Krylov vectors. J. Guidance Control Dynamics 14 (1991), 260–267.CrossRefGoogle Scholar
  27. [27]
    A.J. Tether. Construction of minimal linear state-variable models from finite input-output data. IEEE Trans. Automat. Control AC-15 (1970), 427–436.MathSciNetCrossRefGoogle Scholar
  28. [28]
    J. Vlach and K. Singhal. Computer Methods for Circuit Analysis and Design, Second Edition. New York: Van Nostrand Reinhold, 1993.Google Scholar
  29. [29]
    G.-L. Xu and A. Bultheel. Matrix Pade approximation: definitions and properties. Linear Algebra Appl. 137/138 (1990), 67–136.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • R. W. Freund
    • 1
  1. 1.Bell LaboratoriesLucent TechnologiesMurray HillUSA

Personalised recommendations