Elsevier

Microelectronics Journal

Volume 46, Issue 9, September 2015, Pages 834-838
Microelectronics Journal

Pinched hysteresis with inverse-memristor frequency characteristics in some nonlinear circuit elements

https://doi.org/10.1016/j.mejo.2015.06.019Get rights and content

Abstract

Pinched hysteresis is considered to be a signature of the existence of memristance. However, here we report on a model that exhibits pinched hysteresis yet it may represent a nonlinear inductor or a nonlinear capacitor (both with quadratic nonlinearity) or a derivative-controlled nonlinear resistor/transconductor. Further, the lobe area of the pinched hysteresis loop in these devices has inverse-memristor characteristics; i.e. it is observed to widen rather than decline with increased operating frequency. Experimental results are provided to validate the model.

Introduction

In the past few years, a significant number of publications related to memristors; their modeling and their applications have been published [1], [2], [3], [4], [5], [6], [7], [8]. Due to the fact that memristors are nonlinear devices which exhibit pinched hysteresis in the (vi) plane, simple models that can capture this behavior are necessary. One such mathematical model was recently proposed by the authors in [9] where memristance was linked to the existence of a nonlinear term of the form x(t)×0tx(τ)dτ resulting in a pinched-hysteresis that declines with increased frequency [10]. The state variable x(t) may represent the voltage v(t) in a voltage-controlled memristor or the current i(t) in a current-controlled memristor. In [10], the self-crossing (pinched) hysteresis loop was shown to be a necessary characteristic of all memristive devices. However, [11] added two more conditions on memristive devices which are

  • (i)

    starting from some critical frequency, the hysteresis lobe area should decrease monotonically as the excitation frequency increases and

  • (ii)

    the pinched hysteresis loop should shrink to a single-valued function when the frequency tends to infinity. This means that the lobe area declines with increased frequency.

In this work, however, we propose a system that represents a nonlinear inductor or a nonlinear capacitor (with quadratic nonlinearity) that exhibits self-crossing pinched hysteresis. The same system may also represent a nonlinear derivative-controlled transconductor; which we verify experimentally and observe inverse-memristor frequency characteristics in the form of widening (rather than shrinking) in the lobe area with increased frequency. These observations lead to the conclusion that self-crossing pinched hysteresis can be obtained from other nonlinear elements. This observation is in line with the observations of other researchers as well [12].

Section snippets

System with pinched hysteresis

Consider the following model:y=ax+(b+cx)dxdtwhere y is a normalized output, x is a normalized input signal, and (a,b,c) are scaling constants. Under sinusoidal excitation where x(t)=k·sin(ωt+ϕ) we obtaindxdt=kωcos(ωt+ϕ)=±ωk2x2Using trigonometric identities, one obtainsy=ax±ω(b+cx)k2x2

This equation has the following properties:

  • (i)

    There exists a line of symmetry given by the first order equation:y=axEvidently, for a=0, the y-axis is the line of symmetry.

  • (ii)

    A pinched double-loop hysteresis behavior is

Circuit identification

From an electrical circuit point of view, Eq. (1) can represent different types of circuits based on the nature of x and y. Restricting ourselves to the vi plane, the possible choices of x(t) and y(t) are either a voltage v(t) or a current i(t). When x(t)=i(t) and y(t)=v(t) then (1) can be translated into series connected components. Alternatively, if x(t)=v(t) and y(t)=i(t) then (1) can be translated into parallel connected components. These components are identified as follows.

Experimental validation

The design principle to validate (12) is shown in Fig. 3(a) where an applied voltage V is differentiated using a floating differentiator circuit and then used to control a voltage-controlled transconductance Gm through its control voltage Vc. Gm is implemented using an LM13700 chip [13] where Gm is proportional to a bias voltage Vc given by [13]Gm=0.64×RARB×Vc+8.6885×RARBmΩ1where RA and RB are external biasing resistors. If the control voltage Vc is forced to be equal to the derivative of the

Conclusion

In this work, we have demonstrated the fact that the existence of pinched hysteresis is not a sufficient condition to identify a memristor since it can be observed from other nonlinear devices; particularly with quadratic-type nonlinearity. The authors in [12] have also recently demonstrated pinched hysteresis from circuits with standard components. In our proposed model of (1), we were also able to identify an equivalent standard component to each term in the model. In view of recent

References (14)

  • Z. Biolek et al.

    Specification of one classical fingerprint of ideal memristor

    Microelectron. J.

    (2015)
  • A. Mosad et al.

    Improved memristor-based relaxation oscillator

    Microelectron. J.

    (2013)
  • A.G. Radwan et al.

    On the Mathematical Modeling of Memristor, Memcapacitor, and Meminductor

    (2015)
  • W. Guang-Yi et al.

    Dynamical behaviors of a TiO2 memristor oscillator

    Chin. Phys. Lett.

    (2013)
  • R. Kozma et al.

    Advances in Neuromorphic Memristor Science and Applications

    (2012)
  • A. Adamatzky et al.

    Memristor Networks

    (2014)
  • R. Tetzlaff

    Memristors and Memristive Systems

    (2014)
There are more references available in the full text version of this article.

Cited by (46)

  • Multilevel resistive switching and synaptic plasticity of nanoparticulated cobaltite oxide memristive device

    2021, Journal of Materials Science and Technology
    Citation Excerpt :

    This kind of behavior is contradictory to the ideal definition of the memristor. However, the extended version of the memristor, which has few properties or is unable to mimic all properties, is termed a memristive device [44,45]. Because of this, the proposed Pt/Co3O4/Pt device is regarded as a memristive device rather than an ideal memristor.

  • On the mechanism of creating pinched hysteresis loops using a commercial memristor device

    2019, AEU - International Journal of Electronics and Communications
    Citation Excerpt :

    The memristor’s characteristic behavior is a pinched loop in the current-voltage plane [9]. Although this behavior has been shown to exist in other nonlinear devices and circuits such as a non-linear inductor or a non-linear capacitor [10,11], and that its appearance is linked to satisfying the conditions of the theory of Lissajous figures [12,13], it is still mistakenly attributed only to memristive device [14]. Despite the fact that there are growing doubts about the uniqueness of the memristor as a fundamental device [15], there is no doubt it is a dynamic and nonlinear device [16,17].

  • Revisiting memristor properties

    2020, International Journal of Bifurcation and Chaos
View all citing articles on Scopus
1

The author is also with the Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt.

View full text