The DAE-index in electric circuit simulation

Günther, Michael; Feldmann, U.

doi:10.1016/0378-4754(95)00120-0

Cited by 48 publications

(35 citation statements)

References 8 publications

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“…In the following, we compare the Meyer model with a charge model that can be considered as an extension to this capacitance model [7,8,111. In both models, the nonlinear capacitances CGD, CGB and CGS resp.…”

Section: Two Models For the Intrinsic Charge Flowmentioning

confidence: 99%

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Modelling and simulating charge sensitive mos circuits

Günther¹,

Denk²,

Feldmann³

1996

Mathematical Modelling of Systems

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We show how charge distribution effects in MOS transistors are reflected only correctly by models based on the physical properties of the device. Hence one has to consider carefully the impact of modelling to obtain correct results for MOS circuits by numerical simulation. Additionally, the choice of an appropriate integration scheme is essential for both reliable and efficient simulation results. To spotlight these influences, we use a charge pump as an instructive test circuit and discuss a variety of modelling approaches.

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Section: Two Models For the Intrinsic Charge Flowmentioning

confidence: 99%

“…To lower the index, regularization techniques may be used already at the level of model development [8]. …”

Section: The Impact Of the Modelling Levelmentioning

confidence: 99%

Modelling and simulating charge sensitive mos circuits

Günther¹,

Denk²,

Feldmann³

1996

Mathematical Modelling of Systems

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“…For this reason, our approach necessarily involves a reformulation of Sotomayor conditions in DAE terms. General background on DAE theory can be found in [Brenan et al, 1996;Kunkel and Mehrmann, 2006;Lamour et al, 2013;Rabier and Rheinboldt, 2002;Riaza, 2008], and DAE-based circuit modelling is extensively discussed in [Estévez-Schwarz and Tischendorf, 2000;Giinther and Feldmann, 1995;Günther and Rentrop, 1996;Lamour et al, 2013;Riaza, 2008;Tischendorf, 1999Tischendorf, , 2003. DAEs are nowadays pervasive in circuit simulation programs, such as SPICE, which set up the circuit equations using Modified Nodal Analysis (MNA) techniques.…”

Section: Introductionmentioning

confidence: 99%

“…and the topological properties of the digraph underlying the circuit. The origin of this graph-theoretic or topological approach can be traced back to the state-space formulation problem in the 1960s and 1970s [Brown, 1963;Bryant and Tow, 1972], and has been successfully applied to qualitative analyses of nonlinear circuits [Chua, 1980;Fosséprez, 1992;Bryant, 1984, 1986] and to the characterization of the index of DAE circuit models [Estévez-Schwarz and Tischendorf, 2000;Giinther and Feldmann, 1995;Günther and Rentrop, 1996;Riaza, 2008;Tischendorf, 1999Tischendorf, , 2003]. …”

Section: Introductionmentioning

confidence: 99%

Saddle-Node Bifurcations in Classical and Memristive Circuits

Vega

Riaza

2016

Int. J. Bifurcation Chaos

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This paper addresses a systematic characterization of saddle-node bifurcations in nonlinear electrical and electronic circuits. Our approach is a circuit-theoretic one, meaning that the bifurcation is analyzed in terms of the devices' characteristics and the graph-theoretic properties of the digraph underlying the circuit. The analysis is based on a reformulation of independent interest of the saddle-node theorem of Sotomayor for semiexplicit index one differential-algebraic equations (DAEs), which define the natural context to set up nonlinear circuit models. The bifurcation is addressed not only for classical circuits, but also for circuits with memristors. The presence of this device systematically leads to non-isolated equilibria, and in this context the saddle-node bifurcation is shown to yield a bifurcation of manifolds of equilibria; in cases with a single memristor, this phenomenon describes the splitting of a line of equilibria into two, with different stability properties.

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“…Especially they are encountered in multi-body and mechatronical system descriptions [19], [9]. Also in electronics [13] and even in economics [17] descriptor systems are encountered.…”

Section: Introductionmentioning

confidence: 99%

H//sub∞/ control of descriptor systems in a differential inclusion setting

Rehm

Allgöwer

Proceedings of the 2005, American Control Conference, 2005.

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Based on a differential inclusion approach, the notion of quadratic H∞ performance is introduced for a rather general class of nonlinear descriptor systems. The approach is specialized to the performance analysis and controller synthesis of descriptor systems with norm bounded uncertainties. In this case quadratic H∞ performance can be characterized by means of parameterized linear matrix inequalities (LMIs).

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The DAE-index in electric circuit simulation

Cited by 48 publications

References 8 publications

Modelling and simulating charge sensitive mos circuits

Modelling and simulating charge sensitive mos circuits

Saddle-Node Bifurcations in Classical and Memristive Circuits

H//sub∞/ control of descriptor systems in a differential inclusion setting

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