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Analytical Properties of Circuits with Memristors

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Scientific Computing in Electrical Engineering SCEE 2010

Part of the book series: Mathematics in Industry ((TECMI,volume 16))

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Abstract

The memristor is a new lumped circuit element defined by a nonlinear charge-flux characteristic. The recent design of such a device has motivated a lot of research on this topic. In this communication we address certain analytical properties of semistate models of memristive circuits formulated in terms of differential-algebraic equations (DAEs). Specifically, we focus on the characterization of the geometric index of the DAEs arising in so-called branch-oriented analysis methods, which cover in particular tree-based techniques. Some related results involving nodal models and non-passive problems are discussed in less detail.

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Acknowledgements

The author acknowledges support by Project MTM2007-62064, Ministerio de Educación y Ciencia, Spain.

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Authors and Affiliations

  1. Depto. Matemática Aplicada TTI, ETSI Telecomunicación, Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain

    Ricardo Riaza

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  1. Ricardo Riaza
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Correspondence to Ricardo Riaza .

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  1. ONERA, avenue Édouard Belin 2, Toulouse, 31055, France

    Bastiaan Michielsen

  2. LAPLACE-ENSEEIHT, rue Charles Camichel 2, Toulouse, 31071, France

    Jean-René Poirier

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Riaza, R. (2012). Analytical Properties of Circuits with Memristors. In: Michielsen, B., Poirier, JR. (eds) Scientific Computing in Electrical Engineering SCEE 2010. Mathematics in Industry(), vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22453-9_7

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