Skip to main content

Circuit Simulation Techniques Based on Lanczos-Type Algorithms

  • Conference paper
Systems and Control in the Twenty-First Century

Part of the book series: Systems & Control: Foundations & Applications ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. G.A. Baker, Jr. and P. Graves-Morris. Padé Approximants, Second Edition. New York: Cambridge University Press, 1996.

    MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. 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. 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. 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.

    Article  MATH  Google Scholar 

  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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  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. K. Gallivan, E. Grimme, and P. Van Dooren. Asymptotic waveform evaluation via a Lanczos method. Appl. Math. Lett. 7 (1994), 75–80.

    Article  MATH  Google Scholar 

  14. I. Gohberg, M. A. Kaashoek, and L. Lerer. On minimality in the partial realization problem. Systems Control Lett. 9 (1987), 97–104.

    Article  MathSciNet  MATH  Google Scholar 

  15. W.B. Gragg. Matrix interpretations and applications of the continued fraction algorithm. Rocky Mountain J. Math. 4 (1974), 213–225.

    Article  MathSciNet  MATH  Google Scholar 

  16. W.B. Gragg and A.Lindquist. On the partial realization problem. Linear Algebra Appl. 50 (1983), 277–319.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  19. X. Huang. Pade Approximation of Linear(ized) Circuit Responses. Ph.D. Dissertation. Carnegie Mellon University. Pittsburgh, Pennsylvania. 1990.

    Google Scholar 

  20. T. Kailath. Linear Systems, Englewood Clifffs: Prentice-Hall, 1980.

    MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  24. L.T. Pillage and R.A. Rohrer. Asymptotic waveform evaluation for timing analysis. IEEE Trans. Computer-Aided Design 9 (1990), 352–366.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  28. J. Vlach and K. Singhal. Computer Methods for Circuit Analysis and Design, Second Edition. New York: Van Nostrand Reinhold, 1993.

    Google Scholar 

  29. G.-L. Xu and A. Bultheel. Matrix Pade approximation: definitions and properties. Linear Algebra Appl. 137/138 (1990), 67–136.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this paper

Cite this paper

Freund, R.W. (1997). Circuit Simulation Techniques Based on Lanczos-Type Algorithms. In: Byrnes, C.I., Datta, B.N., Martin, C.F., Gilliam, D.S. (eds) Systems and Control in the Twenty-First Century. Systems & Control: Foundations & Applications, vol 22. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-4120-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4120-1_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-8662-2

  • Online ISBN: 978-1-4612-4120-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics