Skip to main content
SpringerLink
Log in
Book cover

Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering pp 99–116Cite as

Fast Switching Behavior in Nonlinear Electronic Circuits: A Geometric Approach

  • Chapter

  • 1105 Accesses

Part of the book series: Studies in Computational Intelligence ((SCI,volume 459))

Abstract

In this paper an outline about the geometric concept of nonlinear electronic circuits is given. With this geometric concept the fast switching behavior of circuits, i.e. the jumps in their state space, is illustrated and a jump condition is formulated. Furthermore, the developed geometric approach is adapted to MNA based systems of equations. This new method enables the simulation of such ill-conditioned circuits without regularization and presents an implementation approach for common circuit simulators like SPICE.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. IEEE Solid-State Circuits Magazine, 3(2) (2011)

    Google Scholar 

  2. Sandberg, I.W., Shichman, H.: Numerical integration of systems of stiff nonlinear differential equations. Bell Syst. Tech. J. 47, 511–527 (1968)

    MathSciNet  MATH  Google Scholar 

  3. Gear, W.: Simultaneous numerical solution of differential-algebraic equations. IEEE Transactions on Circuit Theory CT-18(1), 89–95 (1971)

    Google Scholar 

  4. Ihrig, E.: The regularization of nonlinear electrical circuits. Proceedings of the American Mathematical Society 47(1), 179–183 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  5. Sastry, S., Desoer, C.: Jump behavior of circuits and systems. IEEE Transactions on Circuits and Systems 28(12), 1109–1124 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chua, L.: Dynamic nonlinear networks: State-of-the-art. IEEE Transactions on Circuits and Systems CAS-27(11), 1059–1087 (1980)

    Google Scholar 

  7. Venkatasubramanian, V.: Singularity induced bifurcation and the van der pol oscillator. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 41(11), 765–769 (1994)

    Article  MATH  Google Scholar 

  8. Tikhonov, A.N., Vasil’eva, A.B., Sveshnikov, A.G.: Differential Equations. Springer, Heidelberg (1985)

    Book  Google Scholar 

  9. Knorrenschild, M.: Differential/algebraic equations as stiff ordinary differential equations. SIAM J. Numer. Anal. 29, 1694–1715 (1992), http://dx.doi.org/10.1137/0729096

    Article  MathSciNet  MATH  Google Scholar 

  10. Thiessen, T., Gutschke, M., Blanke, P., Mathis, W., Wolter, F.-E.: A numerical approach for nonlinear dynamical circuits with jumps. In: 20th European Conference on Circuit Theory and Design, ECCTD 2011 (2011)

    Google Scholar 

  11. Thiessen, T., Gutschke, M., Blanke, P., Mathis, W., Wolter, F.-E.: Differential Geometric Methods for Jump Effects in MOS Systems (presented). In: 2012 IEEE International Symposium on Circuits and Systems, ISCAS 2012 (2012)

    Google Scholar 

  12. Smale, S.: On the mathematical foundation of electrical circuit theory. Journ. Differential Geometry 7(1-2), 193–210 (1972)

    MathSciNet  MATH  Google Scholar 

  13. Mathis, W.: Geometric Theory of Nonlinear Dynamical Networks. In: Moreno-Díaz, R., Pichler, F. (eds.) EUROCAST 1991. LNCS, vol. 585, pp. 52–65. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  14. Thiessen, T., Mathis: Geometric Dynamics of Nonlinear Circuits and Jump Effects. International Journal of Computations & Mathematics in Electrical & Electronic Engineering (Compel 2011) 30(4), 1307–1318 (2011)

    Article  Google Scholar 

  15. Guillemin, V., Pollack, A.: Differential Topology. Prentice-Hall, Inc., Englewoods Cliffs (1974)

    MATH  Google Scholar 

  16. Mathis, W.: Theorie nichtlinearer Netzwerke. Springer, New York (1987)

    Book  Google Scholar 

  17. Ichiraku, S.: On singular points of electrical circuits. Yokohama Mathematical Journal 26, 151–156 (1978)

    MathSciNet  MATH  Google Scholar 

  18. Ichiraku, S.: Connecting Electrical Circuits: Transversality and Well-Posedness. Yokohama Mathematical Journal 27, 111–126 (1979)

    MathSciNet  MATH  Google Scholar 

  19. Tchizawa, K.: An Analysis of Nonlinear Systems with Respect to Jump. Yokohama Mathematical Journal 32, 203–214 (1984)

    MathSciNet  MATH  Google Scholar 

  20. Rozov, N.K.: Asymptotic theory of two-dimensional relaxation self-oscillating system. Mathematical Notes 37, 71–77 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  21. Andronov, A., Vitt, A., Khaĭkin, S., Fishwick, W.: Theory of oscillators. Dover books on electronics, electricity, electrical engineering. Dover (1987)

    Google Scholar 

  22. Mishchenko, E.F., Rozov, N.K.: Differential Equations with Small Parameters and Relaxation Oscillators. Plenum Press, New York (1980)

    Google Scholar 

  23. Thiessen, T., Plönnigs, S., Mathis, W.: A Geometric MNA Based Approach for Circuits with Fast Switching Behavior (presented). In: 2012 IEEE International Symposium on Circuits and Systems, ISCAS 2012 (2012)

    Google Scholar 

  24. Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, New York (1993)

    Google Scholar 

  25. Sarangapani, P., Thiessen, T., Mathis, W.: Differential algebraic equations of mos circuits and jump behavior (accepted). Advances in Radio Science

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Electrical Engineering, Leibniz University of Hanover, D-30167, Hanover, Germany

    Tina Thiessen, Sören Plönnigs & Wolfgang Mathis

Authors
  1. Tina Thiessen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sören Plönnigs
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wolfgang Mathis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tina Thiessen .

Editor information

Editors and Affiliations

  1. Inst. Intelligente Systemtechnologien, Universität Klagenfurt, Universitätsstr. 65-67, Klagenfurt, 9020, Austria

    Kyandoghere Kyamakya

  2. , Lehrgebiet Informationstechnik, FernUniversität in Hagen, Universitätsstraße 27, Hagen, 58097, Germany

    Wolfgang A. Halang

  3. FB Elektrotechnik, Inst. Theoretische Elektrotechnik, Universität Hannover, Appelstr. 9 A, Hannover, 30167, Germany

    Wolfgang Mathis

  4. , Lakeside Park, Alpen-Adria Universität Klagenfurt, Haus B04, Klagenfurt, 9020, Austria

    Jean Camberlain Chedjou

  5. Fernuniversität Hagen, Hagen, 58084, Germany

    Zhong Li

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Thiessen, T., Plönnigs, S., Mathis, W. (2013). Fast Switching Behavior in Nonlinear Electronic Circuits: A Geometric Approach. In: Kyamakya, K., Halang, W., Mathis, W., Chedjou, J., Li, Z. (eds) Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering. Studies in Computational Intelligence, vol 459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34560-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34560-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34559-3

  • Online ISBN: 978-3-642-34560-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation