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Electrical Network Synthesis: A Survey of Recent Work

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Emerging Applications of Control and Systems Theory

Part of the book series: Lecture Notes in Control and Information Sciences - Proceedings ((LNCOINSPRO))

Abstract

The field of electrical network synthesis has a number of long-standing unanswered questions. The most perplexing concern minimality in the context of resistor, inductor and capacitor (RLC) network synthesis. In particular, the famous Bott–Duffin networks appear highly non-minimal from a system theoretic perspective. We survey some recent developments on this topic. These include results establishing the minimality of the Bott–Duffin networks and their simplifications for realising certain impedances; enumerative approaches to the analysis of RLC networks within given classes of restricted complexity; and new necessary and sufficient conditions for a (not necessarily controllable) system to be passive. Finally, some remaining open questions are discussed.

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Acknowledgements

T. H. Hughes is grateful for the support of the Cambridge Philosophical Society in funding his Henslow Research Fellowship at the University of Cambridge. A. Morelli is grateful to acknowledge the support of the MathWorks for their funding of the MathWorks studentship in Engineering at the University of Cambridge.

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Authors and Affiliations

  1. Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK

    Timothy H. Hughes, Alessandro Morelli & Malcolm C. Smith

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  1. Timothy H. Hughes
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  2. Alessandro Morelli
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  3. Malcolm C. Smith
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Correspondence to Malcolm C. Smith .

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Editors and Affiliations

  1. IEIIT—CNR, Politecnico di Torino, Turin, Italy

    Roberto Tempo

  2. Department of Systems Engineering, University of Texas at Dallas, Richardson, Texas, USA

    Stephen Yurkovich

  3. Russ Engineering Center, Wright State University, Dayton, Ohio, USA

    Pradeep Misra

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Hughes, T.H., Morelli, A., Smith, M.C. (2018). Electrical Network Synthesis: A Survey of Recent Work. In: Tempo, R., Yurkovich, S., Misra, P. (eds) Emerging Applications of Control and Systems Theory. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-67068-3_21

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  • DOI: https://doi.org/10.1007/978-3-319-67068-3_21

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  • Online ISBN: 978-3-319-67068-3

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