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Analysis of memristors with nonlinear memristance versus state maps
Author(s) -
Biolek Zdeněk,
Biolek Dalibor,
Biolková Viera,
Kolka Zdeněk,
Ascoli Alon,
Tetzlaff Ronald
Publication year - 2017
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2314
Subject(s) - memristor , nonlinear system , resistor , exponential function , state variable , waveform , mathematics , voltage , topology (electrical circuits) , control theory (sociology) , mathematical analysis , physics , computer science , quantum mechanics , artificial intelligence , control (management) , combinatorics , thermodynamics
Summary According to the axiomatic definition of the memristor from 1971, its properties are unambiguously determined by the memristance versus charge (or flux) map. The original model of the ‘HP memristor’ introduces this map via a linear function that represents this memristor as a variable resistor whose resistance is linearly dependent on the amount of charge flowing through. However, some analog applications require nonlinear, frequently exponential or logarithmic dependence of the resistance on an external controlling variable. The memristor with nonlinear memristance versus charge map is analyzed in the paper. The results are specified for the exponential type of this nonlinearity, which may be useful for future applications. Analytic formulae of the area of the pinched hysteresis loop of such a memristor are derived for harmonic excitation. It is also shown that the current flowing through such a memristor, which is driven by a voltage of arbitrary waveform, conforms to the Abel differential equation, and its closed‐form solution is found. Copyright © 2017 John Wiley & Sons, Ltd.