"E pluribus unum" or How to Derive Single-equation Descriptions for Output-quantities in Nonlinear Circuits using Differential Algebra

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Gerbracht, Eberhard H. -A.;
  • Subject: Computer Science - Symbolic Computation | Mathematics - Classical Analysis and ODEs

In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear algebra to the system of differenti... View more
  • References (14)
    14 references, page 1 of 2

    [1] Giuseppa Carra` Ferro, “Computer Algebra, Nonlinear Differential Equations and Analog Circuit Design,” in Proceedings of the 5th International Workshop on Symbolic Methods and Applications in Circuit Design - SMACD '98, Kaiserslautern, October 8-9,1998, Dieter Pra¨tzel-Wolters, Ralf Sommer, and Eckhard Hennig, Eds., Kaiserslautern, 1998, pp. 49-56.

    [2] Angela M. Hodge and Robert W. Newcomb, “Semistate Theory and Analog VLSI Design,” IEEE Circuits and Systems Magazine, vol. 2, no. 2, pp. 30-51, Second Quarter 2002.

    [3] F. Boulier, D. Lazard, F. Ollivier, and M. Petitot, “Representation for the radical of a finitely generated differential ideal,” in Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, ISSAC '95, Montreal, Canada, July 10-12, 1995., A.H.M. Levelt, Ed., New York, 1995, pp. 158-166, ACM Press, https:// hal.archives-ouvertes.fr/ hal-00138020/en, viewed April 17th, 2008.

    [4] Franc¸ois Boulier, Etude et implantation de quelques algorithmes en alge`bre diffe´rentielle, Ph.D. thesis, Universite´ des Sciences et Technologies de Lille, 1994, http://tel.archives-ouvertes.fr/ tel-00137866/en, viewed April 17th, 2008.

    [5] Evelyne Hubert, E´ tude Alge´brique et Algorithmique des Singularite´s des Equations Diffe´rentielles Implicites, Ph.D. thesis, Institut National Polytechnique Grenoble, 1997, http://www-sop.inria.fr/cafe/ Evelyne.Hubert/Publi/EHubertThesis.ps.gz, viewed April 17th, 2008.

    [6] Evelyne Hubert, “The diffalg package,” http:// www-sop.inria.fr/cafe/Evelyne.Hubert/ diffalg, viewed April 17th, 2008.

    [7] Evelyne Hubert, “Basic concepts in constructive differential algebra and their representation in the diffalg package,” http://www-sop.inria.fr/ cafe/Evelyne.Hubert/diffalg/diffalg/ differential−algebra1.html, viewed April 17th, 2008.

    [8] Thomas E. Stern, Theory of Nonlinear Networks and Systems. An Introduction, Addison-Wesley, Reading, Massachusetts, 1965.

    [9] Eugen S. Philippow and Wolfgang G. Bu¨ ntig, Analyse nichtlinearer dynamischer Systeme der Elektrotechnik, Hanser-Verlag, Mu¨ nchen, 1992.

    [10] Leon O. Chua, “The Genesis of Chua's Circuit,” Int. J. Electron. Commun. (AEU¨ ), vol. 46, no. 4, pp. 250-257, 1992.

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