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Circuit Analyses with Nullors

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Pathological Elements in Analog Circuit Design

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 479))

Abstract

This chapter describes the nullor-based modelling of active devices from the circuit level of abstraction. After a brief overview on the nullor concept and its properties, the modelling of active devices not only at the voltage-mode but also at the current-mode and the mixed-mode of operation from two-port and four-terminal network point of view are described in details. The circuit analysis with nullors and the topological approach for transfer function generation by two-graph tree enumeration as well are presented. The generalized topological formula with homogeneous parameters is proved for all the circuit functions, and a simple representation of the four types of controlled sources by admittances is proposed, that allows a uniform treatment of the entire circuit in terms of admittances. In order to implement the procedure, the rules to automatically generate the two graphs and to enumerate the common spanning trees are presented. Some simplifications in the circuit and in the two graph structure before tree generation and a graph representation on levels, improve the efficiency of the tree enumeration procedure. The original approach, in which each edge is labelled with an admittance term, could handle only one type of active element, namely VCCS (voltage controlled current source), but the method was further developed by many researchers for general linear circuits to include virtually all active elements. Some techniques to convert the CCVSs (current controlled voltage sources), VCVSs (voltage controlled voltage sources) and CCCSs (current controlled current sources) in equivalent schemes containing only VCCSs together with admittances and the inductance modelling proposed in the literature are discussed.

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Authors and Affiliations

  1. POLITEHNICA University of Bucharest, Bucharest, Romania

    Mihai Iordache, Lucia Dumitriu, Dragos Niculae, Marilena Stanculescu, Victor Bucata & Georgiana Rezmerita

Authors
  1. Mihai Iordache
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  2. Lucia Dumitriu
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  3. Dragos Niculae
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  4. Marilena Stanculescu
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  5. Victor Bucata
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  6. Georgiana Rezmerita
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Correspondence to Mihai Iordache .

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Editors and Affiliations

  1. University of Sfax, Sfax, Tunisia

    Mourad Fakhfakh

  2. Wroclaw University of Technology, Wrocław, Poland

    Marian Pierzchala

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Iordache, M., Dumitriu, L., Niculae, D., Stanculescu, M., Bucata, V., Rezmerita, G. (2018). Circuit Analyses with Nullors. In: Fakhfakh, M., Pierzchala, M. (eds) Pathological Elements in Analog Circuit Design. Lecture Notes in Electrical Engineering, vol 479. Springer, Cham. https://doi.org/10.1007/978-3-319-75157-3_4

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  • DOI: https://doi.org/10.1007/978-3-319-75157-3_4

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  • Online ISBN: 978-3-319-75157-3

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