Memristor and Inverse Memristor: Modeling, Implementation and Experiments

Pinched hysteresis is considered to be a signature of the existence of memristive behavior. However, this is not completely accurate. In this chapter, we are discussing a general equation taking into consideration all possible cases to model all known elements including memristor. Based on this equation, it is found that an opposite behavior to the memristor can exist in a nonlinear inductor or a nonlinear capacitor (both with quadratic nonlinearity) or a derivative-controlled nonlinear resistor/transconductor which we refer to as the inverse memristor. We discuss the behavior of this new element and introduce an emulation circuit to mimic its behavior. Connecting the conventional elements with the memristor and/or with inverse memeristor either in series or parallel affects the pinched hysteresis lobes where the pinch point moves from the origin and lobes’ area shrinks or widens. Different cases of connecting different elements are discussed clearly especially connecting the memristor and the inverse memristor together either in series or in parallel. New observations and conditions on the memristive behavior are introduced and discussed in detail with different illustrative examples based on numerical, and circuit simulations.

[1]  Khaled N. Salama,et al.  Generalized model for Memristor-based Wien family oscillators , 2011, Microelectron. J..

[2]  Mohammed Affan Zidan,et al.  HP Memristor mathematical model for periodic signals and DC , 2010, 2010 53rd IEEE International Midwest Symposium on Circuits and Systems.

[3]  Ahmed Gomaa Radwan,et al.  Stability and non-standard finite difference method of the generalized Chua's circuit , 2011, Comput. Math. Appl..

[4]  Masud H. Chowdhury,et al.  Memristor emulator based on practical current controlled model , 2015, 2015 IEEE 58th International Midwest Symposium on Circuits and Systems (MWSCAS).

[5]  Masud H. Chowdhury,et al.  A novel memristor emulator based only on an exponential amplifier and CCII+ , 2015, 2015 IEEE International Conference on Electronics, Circuits, and Systems (ICECS).

[6]  Khaled N. Salama,et al.  Memristor-based reactance-less oscillator , 2011 .

[7]  Masud H. Chowdhury,et al.  Memristor emulator based on single CCII , 2015, 2015 27th International Conference on Microelectronics (ICM).

[8]  Mohammed E. Fouda,et al.  On the Mathematical Modeling of Memristor, Memcapacitor, and Meminductor , 2015 .

[9]  Luigi Fortuna,et al.  Experimental Evidence of Chaos from Memristors , 2015, Int. J. Bifurc. Chaos.

[10]  Robert Kozma,et al.  Advances in Neuromorphic Memristor Science and Applications , 2012, Springer Series in Cognitive and Neural Systems.

[11]  Stephen J. Wolf,et al.  The elusive memristor: properties of basic electrical circuits , 2008, 0807.3994.

[12]  D. Biolek,et al.  Pinched hysteretic loops of ideal memristors, memcapacitors and meminductors must be 'self-crossing' , 2011 .

[13]  Leon O. Chua,et al.  Three Fingerprints of Memristor , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  K. N. Salama,et al.  Memristor-based relaxation oscillators using digital gates , 2012, 2012 Seventh International Conference on Computer Engineering & Systems (ICCES).

[15]  Ahmed Gomaa Radwan,et al.  Generalized Analysis of Symmetric and Asymmetric Memristive Two-Gate Relaxation Oscillators , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Ahmed S. Elwakil,et al.  A Simple Model of Double-Loop Hysteresis Behavior in Memristive Elements , 2013, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  Leon O. Chua,et al.  Memristor Networks , 2014, Springer International Publishing.

[18]  K.N. Salama,et al.  Non linear dynamics of memristor based 3rd order oscillatory system , 2012, Microelectron. J..

[19]  Dalibor Biolek,et al.  Specification of one classical fingerprint of ideal memristor , 2015, Microelectron. J..

[20]  Sundarapandian Vaidyanathan,et al.  Advances and Applications in Nonlinear Control Systems , 2016 .

[21]  Ahmed Gomaa Radwan,et al.  Resistive-less memcapacitor-based relaxation oscillator , 2015, Int. J. Circuit Theory Appl..

[22]  J. Yang,et al.  Switching dynamics in titanium dioxide memristive devices , 2009 .

[23]  Ahmed G. Radwan,et al.  Simple Floating Voltage-Controlled Memductor Emulator for Analog Applications , 2014 .

[24]  Khaled N. Salama,et al.  A memristor-based third-order oscillator: beyond oscillation , 2011 .

[25]  Ahmed Gomaa Radwan,et al.  Fractional-order Memristor Response Under DC and Periodic Signals , 2015, Circuits Syst. Signal Process..

[26]  A. Radwan,et al.  Power Dissipation of Memristor-Based Relaxation Oscillators , 2015 .

[27]  L. Chua.  Memristor-The missing circuit element , 1971 .

[28]  Ahmed S. Elwakil,et al.  Pinched hysteresis with inverse-memristor frequency characteristics in some nonlinear circuit elements , 2015, Microelectron. J..

[29]  Sundarapandian Vaidyanathan,et al.  Advances and Applications in Chaotic Systems , 2016, Studies in Computational Intelligence.

[30]  Khaled N. Salama,et al.  A family of memristor‐based reactance‐less oscillators , 2014, Int. J. Circuit Theory Appl..

[31]  Mohamed E. Fouda,et al.  A simple MOS realization of current controlled memristor emulator , 2013, 2013 25th International Conference on Microelectronics (ICM).

[32]  Mohammed Affan Zidan,et al.  On the mathematical modeling of memristors , 2010, 2010 International Conference on Microelectronics.

[33]  Ahmed Gomaa Radwan,et al.  Memristor based N-bits redundant binary adder , 2015, Microelectron. J..