Non-linear circuit modelling via nodal methods

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SUMMARYIn 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.

“…[18,22,23,31]. However, the following result of Griepentrog and Marz [44,Theorem 9] will turn out to be useful in our analysis.…”

Section: Lemmamentioning

confidence: 95%

Section: Semistate Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Semistate models of electrical circuits including memristors

Riaza

Tischendorf

2011

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“…Augmented node analysis (ANA) [9,15] provides di erential-algebraic circuit models which capture explicitly the circuit topology. When compared with modiÿed node analysis (MNA) [4-6, 10, 30], which can be formulated as a reduction of ANA, augmented systems keep capacitive branch variables in the model; of course, this may be a drawback from a computational point of view, but makes it possible to discuss conditions directly leading to a state equation in terms of capacitor voltages and inductor currents, in contrast to MNA which expresses the former in terms of node voltages.…”

Section: Augmented Node Analysismentioning

confidence: 99%

“…The focus will be placed on augmented node analysis (ANA) models [9,15] which, capturing explicitly the circuit topology, additionally allow for the derivation of state-space reductions. Within this semistate context, singular conÿgurations (V -C loops, I -L cutsets) are formally characterized by a nilpotency index greater than one in the matrix pencil describing the linearized problem.…”

Section: Introductionmentioning

confidence: 99%

Time‐domain properties of reactive dual circuits

Riaza

2006

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SUMMARYThe present work explores some e ects of the replacement of capacitors by inductors and vice versa in state and semistate models of lumped circuits. Such a replacement, when performed together with an inversion of the capacitance and inductance matrices, yields a transformation of the form → −1 in the system spectra. In the semistate context, this covers in particular extremal cases in which null eigenvalues or inÿnite ones with higher index appear in the matrix pencil associated with the model; these cases describe certain pathological circuit conÿgurations. This approach leads to a discussion of new properties of strictly passive circuits; speciÿcally, from the known fact that the index of strictly passive circuits does not exceed two, we derive that the index of null eigenvalues in this setting cannot exceed one. This precludes in particular Takens-Bogdanov degeneracies, deÿned by an index-two doublezero eigenvalue, in strictly passive circuits. Although the results are addressed in a linear context, they can be extended via linearization to non-linear problems, as it is the case in the transformation of singularity-induced bifurcation phenomena into steady bifurcations discussed at the end of the paper.

Dynamic behavioral modeling of nonlinear circuits using a novel recurrent neural network technique

Naghibi

Sadrossadat

2019

In this paper, a new method called local-global feedback recurrent neural network (LGFRNN) is proposed for dynamic behavioral modeling of nonlinear circuits. The structure of the proposed method is based on recurrent neural network and constructed by time-delayed local and global feedbacks. Adding time-delayed feedbacks has a great impact on the learning capability of previous neural network-based methods. Moreover, time-delayed local feedbacks alleviate the problem of slow convergency of the conventional neural network-based methods in the training phase. The proposed LGFRNN can be trained only by having sampled input-output waveforms of the original circuit without knowing the internal details of the circuit. A training algorithm based on real-time recurrent learning (RTRL) is used to train LGFRNN. After the training phase, the proposed LGFRNN provides accurate macromodel of a nonlinear circuit.The proposed method is more accurate compared with the conventional neural-based models (which do not benefit from time-delayed local-global feedbacks) and also significantly reduces the training time of the conventional models. Moreover, proposed LGFRNN is faster than the existing models in simulation tools. The validity of the proposed method is verified by time-domain modeling of three nonlinear devices including commercial TI's SN74AHCT540 device, five-stage complementary metal-oxide-semiconductor (CMOS) receiver, and commercial TI's LM324 power amplifier.