Emulation circuits of fractional-order memelements with multiple pinched points and their applications

Khalil, Nariman A.; Said, Lobna A.; Radwan, Ahmed G.; Soliman, Ahmed M.

doi:10.1016/j.chaos.2020.109882

Cited by 23 publications

(17 citation statements)

References 44 publications

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“…Regarding the ability to realize different types of FOMEs, only single FOMR emulators are proposed in [41] and [42]. In addition, FOMI emulator cannot be realized in [44]. However, the proposed FOME emulators have the ability to flexibly realize three types of FOMEs, which is more functional.…”

Section: Fractional-order Meminductor Circuit Responsementioning

confidence: 99%

“…A limitation of these approaches are that the constructed FOMC and FOMI emulators depend on the characteristics of the memristor emulators they are originally based upon, and the circuit structure thus becomes unnecessarily complex and difficult to simplify. Generalized grounded and floating FOMEs emulators that can emulate FOMR and FOMC are proposed by using different impedance combinations in [44], but these emulators cannot implement FOMI emulation, and are limited to the functionality of FOMR and FOMC. In [45], a fractional higher-order FOMR, FOMC and FOMI emulator was implemented by using a current conveyor (CCII) and analog voltage multiplier (AVM), but these FOMEs only have one free port, which does not enable flexible usage.…”

Section: Introductionmentioning

confidence: 99%

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Modeling and Dynamics Analysis of a Universal Interface for Constructing Floating Fractional Order Mem-Elements

Xie

Zheng

et al. 2021

Preprint

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Fractional-order systems generalize classical differential systems and have empirically shown to achieve fine-grain modeling of the temporal dynamics and frequency responses of certain real-world phenomena. Although the study of integer-order memory element (mem-element) emulators has persisted for several years, the study of fractional-order memory elements (FOMEs) has received little attention. To promote the study of the characteristics and applications of mem-element systems in fractional calculus (FC) and memory systems, in this paper, we propose a novel universal interface for constructing floating FOMEs. When the topological structure of the interface remains unchanged, the floating fractional-order memristor (FOMR), fractional-order memcapacitor (FOMC) and fractional-order meminductor (FOMI) emulators can be realized by using the impedance combinations of different passive elements, without any mem-element emulators and mutators. When compared with previously proposed FOMEs, the proposed fractional-order mem-element emulators based on a universal interface not only feature the characteristics of floating terminals and simpler circuit structures, but can also realize all three different types of FOMEs. To explore the dynamical relationships between the mem-elements and the fractional order, we mathematically derive and analyze the maximum and minimum possible values of memductance, memcapacitance and inverse meminductance which accounts for practical design considerations when building FO systems. The memory characteristics of FOMEs are analyzed by varying their orders and stimuli frequencies. The consistency of theoretical analysis, numerical calculation and simulation results validates the correctness of our proposed emulators.

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Section: Fractional-order Meminductor Circuit Responsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling and Dynamics Analysis of a Universal Interface for Constructing Floating Fractional Order Mem-Elements

Xie

Zheng

et al. 2021

Preprint

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“…We can thus classify the g½Á relation for all ideal u-controlled memelements (IO and FO models) modeled in literature: as linear functions g½Á ¼ λ 0 þ λ 1 D Àζ t uðtÞ in previous works [22][23][24] (ζ is another arbitrary FO index); as quadratic, cubic, or just generally as a polynomial functions g½Á ¼ P n r¼0 λ r D Àζ t uðtÞ r in previous studies. [25][26][27][28][29][30][31] In a case where the memristor becomes linear and its flux-charge…”

Section: Introductionmentioning

confidence: 99%

“…While previous works [16][17][18][19][20][21] have presented several analytical and practical studies on CPEs, only recently did Fouda et al 32 looked into the energy relations of CPEs (supercapacitors and fractional-order coils). Also, memelements in integer an fractional orders have been analyzed in notable works, 5,22,25,26,31,[33][34][35][36] and previous studies 23,24,[27][28][29][30]37 even focused on designing different forms of memelement emulator circuits. In this work, however, we generalize the relation of these ideal memelements and the CPEs using a single mathematical model with three different FO indexes, which enables more comparative studies.…”

Section: Introductionmentioning

confidence: 99%

A unified modeling approach for characterization of fractional‐order memory elements

Oresanya

et al. 2023

Circuit Theory & Apps

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SummaryA generalized mathematical model for current‐controlled fractional‐order memory elements is introduced in this work. The model characterizes constant‐phase elements (CPEs) when its nonlinearity parameter is zero (); otherwise (), it characterizes three main types of fractional‐order memory elements (memristor, meminductor, and memcapacitor). Time‐domain analyses of the voltage and energy relations of the model are derived and verified via numerical and circuit simulations. Some new deductions on the effects of the respective fractional‐order values are recorded: Each fractional‐order element transposes into their corresponding resistive or memristive properties as their fractional‐order values are varied; the meminductor's voltage response have undesired initial trails due to the fractional differentiator; the hysteresis loop of the meminductor is only pinched when its fractional‐order values are unequal. A new CPE emulator circuit is designed, and a generalized memelement emulator is also designed and verified in PSpice circuit simulator: Circuit simulation results confirm the numerical analysis in all cases.

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“…In this manner, and as already demonstrated in [2], the CMOS operational transconductance amplifier (OTA) is helpful to reduce the silicon area when designing chaotic systems. Other CMOS amplifiers that are useful to design chaotic oscillators are summarized in [16], and others include the following: voltage differencing transconductance amplifier (VDTA) [17], current backward transconductance amplifier (CBTA) [18], operational trans-resistance amplifier (OTRA) [19], secondgeneration current conveyor (CCII), differential-input double-output transconductance amplifier (DOTA+), and differential voltage current conveyor (DVCC) [20]. Among them, the OTA shows advantages to develop cryptographic applications [21].…”

Section: Introductionmentioning

confidence: 99%

CMOS OTA-Based Filters for Designing Fractional-Order Chaotic Oscillators

et al. 2021

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Fractional-order chaotic oscillators (FOCOs) have shown more complexity than integer-order chaotic ones. However, the majority of electronic implementations were performed using embedded systems; compared to analog implementations, they require huge hardware resources to approximate the solution of the fractional-order derivatives. In this manner, we propose the design of FOCOs using fractional-order integrators based on operational transconductance amplifiers (OTAs). The case study shows the implementation of FOCOs by cascading first-order OTA-based filters designed with complementary metal-oxide-semiconductor (CMOS) technology. The OTAs have programmable transconductance, and the robustness of the fractional-order integrator is verified by performing process, voltage and temperature variations as well as Monte Carlo analyses for a CMOS technology of 180 nm from the United Microelectronics Corporation. Finally, it is highlighted that post-layout simulations are in good agreement with the simulations of the mathematical model of the FOCO.

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Emulation circuits of fractional-order memelements with multiple pinched points and their applications

Cited by 23 publications

References 44 publications

Modeling and Dynamics Analysis of a Universal Interface for Constructing Floating Fractional Order Mem-Elements

Modeling and Dynamics Analysis of a Universal Interface for Constructing Floating Fractional Order Mem-Elements

A unified modeling approach for characterization of fractional‐order memory elements

CMOS OTA-Based Filters for Designing Fractional-Order Chaotic Oscillators

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