DAEs in Circuit Modelling: A Survey
This paper surveys different analytical aspects of differential-algebraic models of electrical and electronic circuits. The use of DAEs in circuit modelling has increased in the last two decades, and differential-algebraic (or semistate) models play nowad
- PDF / 639,720 Bytes
- 40 Pages / 441 x 666 pts Page_size
- 103 Downloads / 218 Views
Abstract This paper surveys different analytical aspects of differential-algebraic models of electrical and electronic circuits. The use of DAEs in circuit modelling has increased in the last two decades, and differential-algebraic (or semistate) models play nowadays a key role in circuit simulation programs and also in the analysis of several aspects of nonlinear circuit dynamics. We discuss not only nodal systems, including MNA, but also branch-oriented and hybrid ones, as well as the models arising in other approaches to circuit analysis. Different results characterizing the index of DAE models, for both passive and active circuits, are reviewed in detail. We also present a detailed discussion of memristive devices (memristors, memcapacitors and meminductors), displaying a great potential impact in electronics in the near future, and address how to accommodate them in differential-algebraic models. Some dynamical aspects and other topics in circuit theory in which DAEs play a role, regarding e.g. model reduction, coupled problems or fault diagnosis, are discussed in less detail. Keywords Differential-algebraic equation · Electrical circuit · Electronic circuit · Semistate model · State equation · Index · Nodal analysis · Hybrid analysis · Loop analysis · Equilibrium · Bifurcation · Memristor · Memcapacitor · Meminductor Mathematics Subject Classification 05C50 · 34A09 · 94C05 · 94C15
1 Introduction Circuit modelling, analysis and simulation in the nonlinear setting have greatly benefited from the use of the DAE formalism in the last three decades. The ubiquitous presence of nonlinear devices in modern electronic circuits naturally leads to time-domain models; the differential-algebraic form of circuit equations emanates R. Riaza (B) Departamento de Matemática Aplicada a las Tecnologías de la Información, Escuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politécnica de Madrid, 28040 Madrid, Spain e-mail: [email protected] A. Ilchmann, T. Reis (eds.), Surveys in Differential-Algebraic Equations I, Differential-Algebraic Equations Forum, DOI 10.1007/978-3-642-34928-7_3, © Springer-Verlag Berlin Heidelberg 2013
97
98
R. Riaza
from the combination of differential equations coming from reactive elements with algebraic (non-differential) relations modelling Kirchhoff laws and device characteristics. In the opposite direction, a considerable amount of research on analytical and numerical aspects of differential-algebraic equations has been motivated by applications in circuit theory. The term ‘algebraic-differential system’ was already used in the circuit context by Brown in 1963 [25]. Actually, the work of Bashkow, Brown, Bryant and others in the late 1950s and in the 1960s [10, 15, 29, 30, 48, 49, 105, 128, 181] on the formulation of state space models defines an important precedent of the use of DAEs in circuit modelling. A nice compilation of the state-of-the-art of state space modelling of nonlinear circuits up to 1980 can be found in Chua’s paper [35]. The state space approach to cir
Data Loading...
