Nonlinear Fractional-Order Circuits and Systems: Motivation, A Brief Overview, and Some Future Directions

Tavazoei, Mohammad Saleh; Tavakoli-Kakhki, Mahsan; Bizzarri, Federico

doi:10.1109/ojcas.2020.3029254

Cited by 14 publications

(6 citation statements)

References 143 publications

(148 reference statements)

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“…Nowadays, fractional calculus is widely applied in many engineering areas; one of them was highlighted in the topic of fractional-order circuits and systems [3,9], where the main goal is the approximation of the fractional-order differentiator and integrator operators [10][11][12]. As emphasized in [29], the main advantage of fractional calculus is to extend the differential operators such that they exhibit non-integers orders. For instance, according to the Riemann-Liouville approach, the notion of a fractional integral of order α(α > 0) is a natural consequence of the Cauchy formula defined in (1) for repeated integrals [30], where the gamma function is given in (2).…”

Section: Fractional-order Chaotic Oscillatorsmentioning

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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Section: Fractional-order Chaotic Oscillatorsmentioning

confidence: 99%

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

et al. 2021

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“…The theoretical concepts of fractional calculus [1][2][3], which generalized differ-integral operators, have led to significant developments in circuit theory, signal processing, control theory, bio-impedance modeling, etc. [4][5][6][7][8]. Fractional-order (FO) filters are considered as the generalization of the traditional filters [9].…”

Section: Introductionmentioning

confidence: 99%

On the Design of Power Law Filters and Their Inverse Counterparts

2021

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This paper presents the optimal modeling of Power Law Filters (PLFs) with the low-pass (LP), high-pass (HP), band-pass (BP), and band-stop (BS) responses by means of rational approximants. The optimization is performed for three different objective functions and second-order filter mother functions. The formulated design constraints help avoid placement of the zeros and poles on the right-half s-plane, thus, yielding stable PLF and inverse PLF (IPLF) models. The performances of the approximants exhibiting the fractional-step magnitude and phase responses are evaluated using various statistical indices. At the cost of higher computational complexity, the proposed approach achieved improved accuracy with guaranteed stability when compared to the published literature. The four types of optimal PLFs and IPLFs with an exponent α of 0.5 are implemented using the follow-the-leader feedback topology employing AD844AN current feedback operational amplifiers. The experimental results demonstrate that the Total Harmonic Distortion achieved for all the practical PLF and IPLF circuits was equal or lower than 0.21%, whereas the Spurious-Free Dynamic Range also exceeded 57.23 and 54.72 dBc, respectively.

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“…Fractional-order systems have found their application in diverse industry branches such as medicine [1,2], modeling and measurement of various signals [3][4][5], agriculture [6], car industry [7], etc. In case of the electrical engineering, the utilization of FO calculus covers circuits filtering the spectrum [8][9][10][11][12][13][14][15][16][17], FO oscillators [18][19][20][21][22][23] and other circuits with fractional-order characteristics [24][25][26][27][28][29], which then can be implemented and find their purpose in applications of above-mentioned industry areas.…”

Section: Introductionmentioning

confidence: 99%

Reconnection–less Reconfigurable Fractional–Order Current–Mode Integrator Design With Simple Control

Langhammer¹,

Šotner

Dvořák

et al. 2021

IEEE Access

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A design of a fractional-order (FO) integrator is introduced for operation of resulting solution in the current mode (CM). The solution of the integrator is based on the utilization of RC structures, but in comparison to other RC structure based FO designs, the proposed integrator offers the electronic control of the order. Moreover, the control of the proposed integrator does not require multiple specific and accurate values of the control voltages/currents in comparison to the topologies based on the approximation of the FO Laplacian operator. The electronic control of a gain level (gain adjustment) of the proposed integrator is available. The paper offers the results of Cadence IC6 (spectre) simulations and more importantly experimental measurements to support the presented design. The proposed integrator can be used to build various FO circuits as demonstrated by the utilization of the integrator into a structure of a frequency filter in order to provide FO characteristics.

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Nonlinear Fractional-Order Circuits and Systems: Motivation, A Brief Overview, and Some Future Directions

Cited by 14 publications

References 143 publications

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

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

On the Design of Power Law Filters and Their Inverse Counterparts

Reconnection–less Reconfigurable Fractional–Order Current–Mode Integrator Design With Simple Control

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