The Art of Finding Accurate Memristor Model Solutions

Ascoli, Alon; Tetzlaff, Ronald; Biolek, Zdeněk; Kolka, Zdenek; Biolková, Viera; Biolek, Dalibor

doi:10.1109/jetcas.2015.2426493

Cited by 69 publications

(66 citation statements)

References 25 publications

(60 reference statements)

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“…It may be directly used in LTspice version IV to investigate the full potential of the Hewlett Packard nanostructure in electronics. This work complements other important contributions on techniques for robust numerical simulation of memristor models [28]- [29].…”

Section: Discussionsupporting

confidence: 57%

Robust Simulation of a TaO Memristor Model

Ascoli¹,

Tetzlaff²,

Chua³

2015

RADIOENGINEERING

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Abstract. This work presents a continuous and differentiable approximation of a Tantalum oxide memristor model which is suited for robust numerical simulations in software. The original model was recently developed at Hewlett Packard labs on the basis of experiments carried out on a memristor manufactured in house. The Hewlett Packard model of the nano-scale device is accurate and may be taken as reference for a deep investigation of the capabilities of the memristor based on Tantalum oxide. However, the model contains discontinuous and piecewise differentiable functions respectively in state equation and Ohm's based law. Numerical integration of the differential algebraic equation set may be significantly facilitated under substitution of these functions with appropriate continuous and differentiable approximations. A detailed investigation of classes of possible continuous and differentiable kernels for the approximation of the discontinuous and piecewise differentiable functions in the original model led to the choice of near optimal candidates. The resulting continuous and differentiable DAE set captures accurately the dynamics of the original model, delivers well-behaved numerical solutions in software, and may be integrated into a commercially-available circuit simulator.

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Section: Discussionsupporting

confidence: 57%

Robust Simulation of a TaO Memristor Model

Ascoli¹,

Tetzlaff²,

Chua³

2015

RADIOENGINEERING

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“…After this flash, many scientific papers associated with memristors and memristive devices have been published and several basic memristor models have been proposed [2][3][4][5][6][7][8][9][10]. Each of the basic memristor models-the linear drift model proposed by Strukov and Williams [2] and the nonlinear drift models made by Joglekar [3], Pickett [4,5], and Biolek [6]-is appropriate for specific electrical modes for the operation of the memristor elements.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Drift Memristor Model with a Modified Biolek Window Function and Activation Threshold

Mladenov

Kirilov

2017

Electronics

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Abstract:The main idea of the present research is to propose a new memristor model with a highly nonlinear ionic drift suitable for computer simulations of titanium dioxide memristors for a large region of memristor voltages. For this purpose, a combination of the original Biolek window function and a weighted sinusoidal window function is applied. The new memristor model is based both on the Generalized Boundary Condition Memristor (GBCM) Model and on the Biolek model, but it has an improved property-an increased extent of nonlinearity of the ionic drift due to the additional weighted sinusoidal window function. The modified memristor model proposed here is compared with the Pickett memristor model, which is used here as a reference model. After that, the modified Biolek model is adjusted so that its basic relationships are made almost identical with these of the Pickett model. After several simulations of our new model, it is established that its behavior is similar to the realistic Pickett model but it operates without convergence problems and due to this, it is also appropriate for computer simulations. The modified memristor model proposed here is also compared with the Joglekar memristor model and several advantages of the new model are established.

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“…Finding a general model for pinched hysteresis behavior was attempted in [4] for specific devices labeled as memristors [5]. In [6] and from a simplified mathematical point of view, the following model was proposed and shown to exhibit a pinched hysteresis behavior which can fit both chargecontrolled and flux-controlled memristance definitions:…”

Section: Introductionmentioning

confidence: 99%

CMOS Realization of All-Positive Pinched Hysteresis Loops

2017

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Two novel nonlinear circuits that exhibit an all-positive pinched hysteresis loop are proposed. These circuits employ two NMOS transistors, one of which operates in its triode region, in addition to two first-order filter sections. We show the equivalency to a charge-controlled resistance (memristance) in a decremental state via detailed analysis. Simulation and experimental results verify the proposed theory. IntroductionPinched hysteresis was proposed to be a signature of memristive devices [1,2], yet it can also be observed in several other nonlinear devices such as nonlinear inductors (capacitors) with quadratic-type current (voltage) dependence [3]. Finding a general model for pinched hysteresis behavior was attempted in [4] for specific devices labeled as memristors [5]. In [6] and from a simplified mathematical point of view, the following model was proposed and shown to exhibit a pinched hysteresis behavior which can fit both chargecontrolled and flux-controlled memristance definitions:where if ( ) = V( ) and ( ) = ( ), the chargecontrolled memristance is obtained, while for the alternative setting ( ) = ( ) and ( ) = V( ), the flux-controlled memristance is obtained. In (1), the constants and are scaling and integration time constants, respectively. Note that circuit realization of this model for the purpose of emulating its pinched hysteresis behavior in non-solid-state devices requires a multiplier block, an integrator block, and an adder [6]. Several other emulator circuits have recently been proposed in the literature [7][8][9][10][11][12][13]. It is important to note that (1) is nonlinear due to the multiplication term and that pinched hysteresis cannot appear in a linear system. It is also possible to include other forms of nonlinearity that apply to the shaping of the loop as a result of shaping the applied excitation. This means replacing ( ) in (1) more generally with ( ( )). Pinched hysteresis loop is generally observed as a result of applying a bipolar sinusoidal voltage or current excitation signal and is thus symmetrical around the origin. Nonsymmetrical loops can also be obtained when the pinch point is shifted away from the origin. However, an all-positive pinched loop, to the best of our knowledge, has not been demonstrated before. It is the purpose of this work to introduce two simple circuits where this behavior is observed. We rely on the inherent nonlinearity of a MOS transistor to perform the multiplication operation required by (1) in order to obtain a charge-controlled memristance. Recall that a MOS transistor current-voltage relation can be described by

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The Art of Finding Accurate Memristor Model Solutions

Cited by 69 publications

References 25 publications

Robust Simulation of a TaO Memristor Model

Robust Simulation of a TaO Memristor Model

A Nonlinear Drift Memristor Model with a Modified Biolek Window Function and Activation Threshold

CMOS Realization of All-Positive Pinched Hysteresis Loops

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