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Hybrid Analysis of Nonlinear Circuits: DAE Models with Indices Zero and One

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Abstract

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices.

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Acknowledgements

This work was supported by Research Projects MTM2010-15102 of Ministerio de Ciencia e Innovación and CCG10-UPM/ESP-5236 of Comunidad de Madrid/UPM, Spain.

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  1. Departamento de Matemática Aplicada a las Tecnologías de la Información, Escuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    Ignacio García de la Vega & Ricardo Riaza

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  1. Ignacio García de la Vega
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Correspondence to Ricardo Riaza.

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García de la Vega, I., Riaza, R. Hybrid Analysis of Nonlinear Circuits: DAE Models with Indices Zero and One. Circuits Syst Signal Process 32, 2065–2095 (2013). https://doi.org/10.1007/s00034-013-9570-y

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