Fractional‐Order Memristor Emulator Circuits

Abstract

This brief leads the synthesis of fractional-order memristor (FOM) emulator circuits. To do so, a novel fractional-order integrator (FOI) topology based on current-feedback operational amplifier and integer-order capacitors is proposed. Then, the FOI is substituting the integer-order integrator inside flux- or charge-controlled memristor emulator circuits previously reported in the literature and in both versions: floating and grounded. This demonstrates that FOM emulator circuits can also be configured at incremental or decremental mode and the main fingerprints of an integer-order memristor are also holding up for FOMs. Theoretical results are validated through HSPICE simulations and the synthesized FOM emulator circuits can easily be reproducible. Moreover, the FOM emulator circuits can be used for improving future applications such as cellular neural networks, modulators, sensors, chaotic systems, relaxation oscillators, nonvolatile memory devices, and programmable analog circuits.

Tunable flux‐controlled floating memristor emulator circuits

“…Memristor emulators can be divided into two types according to their structures: floating memristors [3][4][5][6][7][8][9][10][11][12][13] and grounded memristors [14][15][16][17][18][19][20][21][22][23][24], with only certain memristor emulator circuits being suitable for high frequencies in the order of megahertz (MHz) [4,5,7,10,16,17,23,24]. Some of them can operate with a variable configuration, as one of the solutions proposed here, meaning that it is possible to emulate grounded or floating type of memristor with the same circuits [25][26][27]. If the memristor emulator circuits are of a grounded type, its application areas are limited in circuit designs, rendering it unsuitable for use as a twoterminal device in more complicated circuits since the grounded restriction places a substantial obstacle on their connectivity with other circuit elements.…”

“…Activecircuit elements provide advantages in designing complex and nonlinear circuit-element patterns. For this reason, various activecircuit-element-based memristor circuits can be found in the literature based on operational amplifier (OpAmp) [3], secondgeneration current conveyor (CCII) [6,8,12,14,21,22], differential difference CCs (DDCC) [5], current backward transconductance amplifier (CBTA) [18], operational transconductance amplifier (OTA) [9,11,15,19,25] differential voltage-CC transconductance amplifier (DVCCTA) [17], currentfeedback OpAmp (CFOA) [13,20,26]. Floating memristor emulators using one CCTA, one CCII and few passive elements have been proposed in [4], while the circuits [27] are based on only one CCTA.…”

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

“…Here, they presented interesting controller parameters for the 4D memristive circuit including Lyapunov exponents, phase portrait, bifurcation diagram, and Poincaré maps. The dynamical illustrations can be continued on memristors, and we include here few latest attempts subject to chaos analysis 9–11 …”

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

“…The past history of the memristor current such as the time integral of the current is effective on the memristance. Due to the fractional interaction between flux and charge, many memristors cannot be treated as ideal ones [27], [28]. It is nearly impossible to understand the physical behavior of the circuit with memristors without the use of a properly modelled non-ideal memristor.…”