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Timestep control for charge conserving integration in circuit simulation

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Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 117))

Abstract

Charge oriented integration is necessary in general purpose circuit simulation for maintaining charge conservation. Generally, an approach derived by Ward and Dutton is implemented. Its drawbacks are higher expense for timestep control, loss of one integration order, and the fact that the user has no direct control of the variables which he really is interested in.

An error estimate is proposed which is closely related to error estimates given by Gear, Leimkuhler et al. for differential algebraic equations of index 2. A timestep control algorithm based on this estimate requires extra solutions of a linear system with the matrix of the Newton procedure. First results indicate that this additional overhead is compensated by a better adaption of the timesteps.

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References

  1. Brenan, K.E.; Campbell, S.L.; Petzold, L.R. (1989) Numerical solution of initial value problems in differential algebraic equations. (Elsevier, New York)

    MATH  Google Scholar 

  2. Cirit, M.A. (1989) The Meyer model revisited: why is charge not conserved? IEEE Trans. CAD 8. 1033–1037

    Google Scholar 

  3. Denk, G. (1990) An improved numerical integration method in the circuit simulator SPICE2-S. Int. Ser. Numer. Math. 93 (Birkhäuser, Basel), 85–99

    Google Scholar 

  4. Feldmann, U.; Wever, U.; Zheng, Q.; Schultz, R.; Wriedt, H. (1992) Algorithms for modern circuit simulation. AEÜ 46, 274–285

    Google Scholar 

  5. Gear, C.W. (1986) Maintaining solution invariants in the numerical solution of ODEs. SIAM J. Sci. Stat. Comput. 7, 734–743

    Article  MathSciNet  MATH  Google Scholar 

  6. Gupta, G.K.; Gear, C.W.; Leimkuhler, B.J. (1985) Implementing linear multistep formulas for solving DAEs. Rep. No. UIUCDCS-R-85-1205 (Univ. Illinois, Urbana)

    Google Scholar 

  7. Ho, C.W.; Ruehli, A.E.; Brennan, RA. (1975) The modified nodal approach to network analysis. IEEE Trans. CAS 22. 505–509

    Google Scholar 

  8. Kampowsky, W.; Rentrop, P.; Schmidt, W. (1992) Classification and numerical simulation of electric circuits. Surv. Math. Ind. 2, 23–65

    MathSciNet  MATH  Google Scholar 

  9. Leimkuhler, B.J. (1986) Error estimates for differential-algebraic equations. Rep. No. UIUCDCS-R-86-1287 (Univ. Illinois, Urbana)

    Google Scholar 

  10. Meyer, J.E. (1971) MOS models and circuit simulation. RCA Rev. 32, 42–63

    Google Scholar 

  11. Nagel, L.W. (1975) SPICE2: A computer program to simulate semiconductor circuits. Tech. Rep. ERL M520 (Univ. California, Berkeley)

    Google Scholar 

  12. Petzold, L.R. (1982) Differential/algebraic equations are not ODEs. SIAM J. Sci. Stat. Comput. 3, 367–384

    Article  MathSciNet  MATH  Google Scholar 

  13. Sacks-Davis, R. (1972) Error estimates for a stiff differential equation procedure. Math. Comp. 31, 939–953

    Article  MathSciNet  Google Scholar 

  14. Sakallah, K.A.; Yen, Y.T.; Greenberg, S.S. (1990) A first order charge conserving MOS capacitance model. IEEE Trans. CAD-9. 99–108

    Google Scholar 

  15. Sieber, E.-R. (1992) Schrittweitensteuerung bei der numerischen Integration in der Schaltkreissimulation. Dipl. thesis (Math. Inst. Tech. Univ, Munich)

    Google Scholar 

  16. Singhal, K.; Vlach, J. (1986) Formulation of circuit equations. In: Ruehli, A.E. (ed.) Circuit analysis, simulation and design. Part 1 (North Holland, Amsterdam), 45-70

    Google Scholar 

  17. Turchetti, C.; Prioretti, P.; Masetti, G.; Profumo, E.; Vanzi, M. (1986) A Meyer-like approach for transient analysis of digital MOS ICs. IEEE Trans. CAD 5. 499–507

    Google Scholar 

  18. Ward, D.E.; Dutton, R.W. (1978) A charge oriented model for MOS transistor capacitances. IEEE J. Solid-State Circuits SC-13, 703–708

    Article  Google Scholar 

  19. Yang, P. (1986) Capacitance modeling for MOSFETS. In: Ruehli, A.E. (ed.) Circuit analysis, simulation and design. Part 1 (North Holland, Amsterdam), 107–129

    Google Scholar 

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Author information

Authors and Affiliations

  1. TU Munich, Germany

    E.-R. Sieber

  2. Siemens AG, ZFE BT SE 43, 81739, Munich, Germany

    U. Feldmann

  3. Siemens Nixdorf AG, Munich, Germany

    R. Schultz

  4. Uni Hamburg, Germany

    H. Wriedt

Authors
  1. E.-R. Sieber
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  2. U. Feldmann
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  3. R. Schultz
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  4. H. Wriedt
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics, C-012, University of California, San Diego, La Jolla, CA, 92093, USA

    R. E. Bank

  2. Institut fĂĽr Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117, Berlin, Germany

    H. Gajewski

  3. Mathematisches Institut der TH MĂĽnchen, Postfach 20 24 20, D-80290, MĂĽnchen, Germany

    R. Bulirsch

  4. ZTI DES2 Siemens AG, Otto-Hahn-Ring 6, D-81739, MĂĽnchen, Germany

    K. Merten

  5. Siemens Corporate Research, Inc., 755 College Road East, Princeton, N. J., 08540, USA

    K. Merten

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© 1994 Springer Basel AG

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Sieber, ER., Feldmann, U., Schultz, R., Wriedt, H. (1994). Timestep control for charge conserving integration in circuit simulation. In: Bank, R.E., Gajewski, H., Bulirsch, R., Merten, K. (eds) Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices. ISNM International Series of Numerical Mathematics, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8528-7_8

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  • DOI: https://doi.org/10.1007/978-3-0348-8528-7_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9665-8

  • Online ISBN: 978-3-0348-8528-7

  • eBook Packages: Springer Book Archive

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