Network Theorems for Fractional-Order Circuits

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    Abstract

    In this paper, we provide a circuit-theoretic analysis of linear fractional-order circuits based on the use of Tellegen's theorem. The advantages of the circuit-theoretic analysis over the more common control-theoretic one are illustrated with general theorems on the driving-point impedances and admittances of multi-type, fractional-order circuits made of an arbitrary, finite, connected mesh of fractional-order elements. The explicit use of Kirchhoff's circuit laws leads to sharp results on the stability and resonant behavior of such networks. In particular, it results in more intuitive conditions on the range of fractional orders needed to guarantee network stability or resonant behavior.

    Original languageBritish English
    Title of host publicationISCAS 2023 - 56th IEEE International Symposium on Circuits and Systems, Proceedings
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    ISBN (Electronic)9781665451093
    DOIs
    StatePublished - 2023
    Event56th IEEE International Symposium on Circuits and Systems, ISCAS 2023 - Monterey, United States
    Duration: 21 May 202325 May 2023

    Publication series

    NameProceedings - IEEE International Symposium on Circuits and Systems
    Volume2023-May
    ISSN (Print)0271-4310

    Conference

    Conference56th IEEE International Symposium on Circuits and Systems, ISCAS 2023
    Country/TerritoryUnited States
    CityMonterey
    Period21/05/2325/05/23

    Keywords

    • Circuit theory
    • Fractional-order circuits
    • Fractional-order impedance
    • Minimum phase
    • Stability
    • Tellegen's theorem

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