Nonlinear circuits with parallel‐/series‐connected HP‐type memory elements and their characteristic analysis

Liu, Yue; Guo, Zhang; Chau, Tat Kei; Iu, Herbert Ho Ching; Si, Gangquan

doi:10.1002/cta.2915

Cited by 8 publications

(12 citation statements)

References 29 publications

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“…In 2020, Guo Z et al introduced a phasor analysis method for memory elements to help with the understanding of complex non-linear phenomena in circuits with a memristor, memcapacitor, meminductor, and secondorder memristor [31]. In 2021, the expression of equivalent admittance and impedance connected in parallel and series memristive circuits were derived [32], which are still in their infancy. Also, these existing researches have opened new realms for non-linear circuit investigations.…”

Section: Open Accessmentioning

confidence: 99%

AC power analysis for second-order memory elements

Liu

Liu²,

Luo³

et al. 2023

Front. Phys.

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As the product of a circuit’s voltage and current, apparent power (S) is of paramount necessity and importance in electrical utilities, electronics, communication, and neural network systems. Based on the existing AC power analysis on the two-terminal passive elements (i.e., R, L, and C), some in-depth research on AC apparent power calculations for second-order memory elements and memristive systems is introduced to help with revealing their complex and unique non-linear phenomena. This paper derives the forms of real power, reactive power, and apparent power for the proposed second-order memory elements (i.e., MR, MC, and ML) and reveals the difference between ideal memory elements and traditional passive ones (i.e., R, C, and L). For all involved memory elements, harmonic values and an extra term occur in the expression of powers to represent their memory characteristics. Especially, the real power is a function of a circuit’s dissipative elements (usually resistances R), but not exactly the memristor (MR). Then, the corresponding curves could be depicted, which demonstrate the differences between R/C/L and MR/MC/ML and verified that harmonic values existed in SMR/SMC/SML, meaning that it would perpetually supply energy when operated with an alternating current.

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Section: Open Accessmentioning

confidence: 99%

AC power analysis for second-order memory elements

Liu

Liu²,

Luo³

et al. 2023

Front. Phys.

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“…Various memelements models in IO and FO have since captured the attention of researchers. 3,[9][10][11] They have also been used as nonlinear components in studies like neuromorphic and multi-level memory systems, 12,13 memristorbased Neural-Networks, 14 chaotic and oscillator circuits, [15][16][17][18] logic and combinatoral circuits, [19][20][21] and even as nonlinear loads in DC-DC converters in literature. 22,23 It is thus important to fully understand their underlying properties.…”

Section: Introductionmentioning

confidence: 99%

Conditions for realization of multiple pinch‐off points in generalized fractional‐order memory elements

et al. 2023

Circuit Theory & Apps

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SummaryMemelements (memristor, meminductor, and memcapacitor) have gained wide interests due to their useful hysteresis and nonlinear properties. In this work, fractional‐order current‐controlled memelements are modeled using an ‐order polynomial. By decomposing the ‐order polynomial into some sets of current‐controlled functions, we were able to theoretically analyze and establish the general conditions necessary for all memelements' voltage‐current dynamics to create up to number of lobes and hence pinch‐off points in their hysteresis. The exact coordinate locations of the pinch‐off points on the ‐axis and ‐axis are calculated in all cases. The observations made in this work are novel and contributes to how all multiple‐lobed memory elements are analyzed. A general emulator circuit is then designed to verify the theoretical deductions, the emulator output agrees with the numerical results.

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“…19,20 By applying the fractional calculus concept, the modeling and analysis attempts of memelement with fractional order kinetic have been proposed in many previous works. [21][22][23][24] Since a novel circuit element with memory, namely, the inverse memristor, has been recently proposed [25][26][27] and often cited [28][29][30][31] where its behavior can be found/emulated in practice, [32][33][34][35] similarly to the memristor, it is worthy to introduce the fractional order kinetic to this new element and performing the modeling/analysis. By this motivation, the analytical model of inverse memelement which is a super set of inverse memristor, with fractional order kinetic, has been derived in this work.…”

Section: Introductionmentioning

confidence: 99%

Analytical model of inverse memelement with fractional order kinetic

Banchuin

2022

Circuit Theory & Apps

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In this work, the analytical model of inverse memelement with fractional order kinetic has been proposed. The classical yet noncontroversial Caputo fractional derivative has been adopted for modeling such fractional order kinetic due to its simplicity yet accuracy. Based on the proposed model, the analysis of fractional order kinetic inverse memristor has been thoroughly performed where both nonperiodic and periodic excitations have been considered. Analytical formulations of the related parameters, for example, the rate of changes of inverse memristance, area of inverse memristance loop, and area of pinched hysteresis loop, and so on, have been performed. The extension of the proposed model to the fractional inverse memelement has been performed where the fractional inverse memristor has been analyzed. We have found that the inverse memristor still behaves in an opposite manner to the memristor even with the fractional order kinetic. All obtained results have been found to be intuitively applicable to any inverse memelement. The equivalent circuit models of both fractional inverse memristor and fractional inverse memelement have also been presented. This work provides a comprehensive understanding on both inverse memelement with fractional order kinetic and fractional inverse memelement. The realization of the emulator of such inverse memelement with fractional order kinetic and the fractional inverse memelement emulator has been found to be interesting opened research questions.

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Nonlinear circuits with parallel‐/series‐connected HP‐type memory elements and their characteristic analysis

Cited by 8 publications

References 29 publications

AC power analysis for second-order memory elements

AC power analysis for second-order memory elements

Conditions for realization of multiple pinch‐off points in generalized fractional‐order memory elements

Analytical model of inverse memelement with fractional order kinetic

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