Semistate models of electrical circuits including memristors |
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Authors: | Ricardo Riaza Caren Tischendorf |
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Affiliation: | 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;2. Mathematisches Institut, Universit?t zu K?ln, Weyertal 86‐90, 50931 K?ln, Germany |
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Abstract: | In this paper we present several semistate or differential‐algebraic models arising in nodal analysis of nonlinear circuits including memristors. The goal is to characterize the tractability index of these models under strict passivity assumptions, a key issue for the numerical simulation of circuit dynamics. We show that the main model, which combines memristors' fluxes and charges, is index two. From a technical point of view, this result is based on the use of a projector along the image of the leading matrix, in contrast to previous index analyses. For charge‐controlled memristors, the elimination of fluxes yields an index one system in topologically nondegenerate circuits, and an index two model otherwise. Analogous results are also proved to hold for flux‐controlled memristors. Our framework accommodates coupling effects among resistors, memristors, capacitors and inductors. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | memristor lumped circuit nodal analysis differential‐algebraic equation semistate model index |
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