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Stability Analysis and Limit Cycles of High Order Sigma-Delta Modulators

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Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering

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

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Abstract

In this chapter we present an unified approach for study the stability and validation of potential limit cycles of one bit high order Sigma-Delta modulators. The approach is general because it uses the general form of a Sigma-Delta modulator. It is based on a parallel decomposition of the modulator and a direct nonlinear systems analysis. In this representation, the general N-th order modulator is transformed into a decomposition of low order, generally complex modulators, which interact only through the quantizer function. The developed conditions for stability and for validation of potential limit cycles are very easy for implementation and this procedure is very fast.

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Authors and Affiliations

  1. Dept of Theoretical Electrical Engineering, Technical University of Sofia, 8, Kliment Ohridski St., Sofia, Bulgaria

    Valeri Mladenov

Authors
  1. Valeri Mladenov
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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

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Mladenov, V. (2013). Stability Analysis and Limit Cycles of High Order Sigma-Delta Modulators. 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_17

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  • DOI: https://doi.org/10.1007/978-3-642-34560-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34559-3

  • Online ISBN: 978-3-642-34560-9

  • eBook Packages: EngineeringEngineering (R0)

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