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CHORAL — A One Step Method as Numerical Low Pass Filter in Electrical Network Analysis

  • M. Günther
  • P. Rentrop
  • U. Feldmann
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 18)

Abstract

Circuit simulation packages generate the network equations automatically. In time domain analysis this results in a system of differential-algebraic equations, which is solved numerically by BDF schemes and/or the trapezoidal rule. CHORAL, a charge-oriented Rosenbrock-Wanner method, has been developed as an alternative approach for digital circuits. By its successful implementation into TITAN, Infineon Technologies’ circuit simulator, a second integration scheme is available for the first time. Results for benchmarks and industrial circuits show that CHORAL is competitive with the standard ansatz. A careful analysis shows that CHORAL can be interpreted as a numerical (non-ideal) low pass filter with all its beneficial properties: oscillations of physical significance are preserved, but highly oscillatory perturbations are damped out very rapidly.

Keywords

Trapezoidal Rule Multistep Method Circuit Simulation Time Domain Analysis PMOS Transistor 
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.

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References

  1. 1.
    Estév ez Schwarz, D., Feldmann, U., Mär z, R., Sturtzel, S., Tischendorf, C.: Finding benificial DAE structures in circuit simulation. Submitted for publication.Google Scholar
  2. 2.
    Feldmann, U.; Wever, U.; Zheng, Q.; Schultz, R.; Wriedt, H.: Algorithms for modern circuit simulation. AEÜ 46, 274–285 (1992).Google Scholar
  3. 3.
    Feldmann, U., Gün ther, M.: Some remarks about regularization of circuit equations. Proc. ISTET’99, Sept. 6.-9. 1999 (Magdeburg), 343–348.Google Scholar
  4. 4.
    Günther, M.: Ladungsorientierte Rosenbrock-Wanner-Methoden zur numerischen Simulation digitaler Schaltungen. VDI Verlag, Düsseldorf, 1995.Google Scholar
  5. 5.
    Gün ther, M.: Simulating digital circuits numerically — a charge-oriented ROW approach. Num. Math. 79, 203–212 (1998).CrossRefGoogle Scholar
  6. 6.
    Günther, M.; Feldmann, U.: CAD based electric circuit modeling I: mathematical structure and index of network equations. Surv. Math. Ind. 8 97–129 (1999).zbMATHGoogle Scholar
  7. 7.
    Günther, M.; Feldmann, U.: CAD based electric circuit modeling II: impact of network structure and parameters. Surv. Math. Ind. 8, 131–157 (1999).zbMATHGoogle Scholar
  8. 8.
    Günther, M.; Hoschek, M.: ROW methods adapted to electric circuit simulation packages. J. Comp. Appl. Math. 82, 159–170 (1997).Google Scholar
  9. 9.
    Gün ther, M.; Hoschek, M.; Rentrop, P.: Differential-Algebraic Equations in Electric Circuit Simulation. Int. J. Electron. Commun. (AE) 54, 101–107 (2000).Google Scholar
  10. 10.
    Günther, M.; Hoschek, M.; Weiner, R.:. ROW methods adapted to a cheap Jacobian. To appear in Appl. Numer. Math.Google Scholar
  11. 11.
    Günther, M.; Kværnø, A.; Rentrop, P.: Multirate partitioned Runge-Kutta methods. To appear in BIT.Google Scholar
  12. 12.
    Hairer, E.; Wanner, G.: Solving ordinary differential equations II. Stiff and differential-algebraic problems. Springer-Verlag, Berlin, 1991.Google Scholar
  13. 13.
    Hoschek, M.: Einschrittverfahren zur numerischen Simulation elektrischer Schaltungen. VDI Verlag, Düsseldorf, 1999.Google Scholar
  14. 14.
    Hoschek, M.; Rentrop, P.; Wagner, Y.: Network approach and differentialalgebraic systems in technical applications. Surv. Math. Ind. 9, 49–76 (1999).MathSciNetzbMATHGoogle Scholar
  15. 15.
    März, R., Tischendorf, C.: Recent results in solving index 2 different algebraic equations in circuit simulation. SIAM. J. Sci. Comp. 18(1), 139–159 (1997).zbMATHCrossRefGoogle Scholar
  16. 16.
    G. Massobrio and P. Antognetti. Semiconductor device modelling with SPICE. McGraw-Hill, New York, 1993.Google Scholar
  17. 17.
    Nagel, W.: SPICE 2-a computer program to simulate semiconductor circuits. Dissertation. Berkeley, CA: UC Berkeley, 1975.Google Scholar
  18. 18.
    Rentrop, P.: ROW-type methods for the integration of electric circuits. In Bank, R. et al. (Eds): Mathematical modelling and simulation of electrical circuits and semiconductor devices, Basel, Birkhäuser Verlag, 59–71 (1990)Google Scholar
  19. 19.
    Rentrop, P.; Roche, M.; Steinebach, G.: The application of Rosenbrock-Wanner type methods with stepsize control in differential-algebraic equations. Num. Math. 55, 545–563 (1989).MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Simeon, B.: Order reduction of stiff solvers at elastic multibody systems. Appl. Numer. Math. 28, 459–475 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    van der Houwen, P.J., Sommeijer, B.P.: Explicit Runge-Kutta-Nyström methods with reduced phase errors for computing oscillating solutions. SIAM J. Numer. Anal. 24, 595–617 (1987).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • M. Günther
    • 1
  • P. Rentrop
    • 1
  • U. Feldmann
    • 2
  1. 1.Universität Karlsruhe (TH), Fachbereich MathematikInstitut für Wissenschaftliches Rechnen und Mathematische Modellbildung (IWRMM)Karlsruhe
  2. 2.Infineon TechnologiesMünchen

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