A note on applications of time-domain solution of Cole permittivity models

Alagöz, Barış Baykant; Alisoy, G.T.; Alagoz, Serkan; Alisoy, H.Z.

doi:10.1016/j.ijleo.2017.04.010

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…In TDR simulation measurement, the Cole impedance parameter is chosen as R 1 ¼ 10:231 kΩ, R 2 ¼ 424:38 Ω, C α ¼ 208:5 nF Á s À0:36 , estimated from a plumb. 1 The current excitation xðtÞ is set as a sinusoidal signal defined in (19), and its initial phase ϕ or (angular) frequency f is changed in simulation verification. The resulting TDR is then calculated in (26), where the discretization parameters of λ ¼ 1:01 and f max ¼ ω max =2π ¼ 10 9 Hz are applied to approximate the transfer function.…”

Section: Simulation Verificationmentioning

confidence: 99%

“…Besides the above‐mentioned TDR analysis of fractance devices and series fractional‐order circuits, the TDR analysis of series‐parallel fractional‐order circuits (SPFOC) is also significant, especially in modeling biological tissues, batteries, and supercapacitors. However, the direct TDR solution to such circuits is particularly challenging, because it can only be accurately derived in the Mittag–Leffler function to some specific excitations, such as the impulse signal 19 or the step signal, 20,21 while cannot be applied to more general harmonic electromotive force, such as the sinusoidal signal. Instead, a great research effort has been made to synthesize the TDR of SPFOC by accurately approximating the transfer function of

s^{α}

as the sum of integer‐order expressions.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of time‐domain response of series‐parallel fractional‐order RC_α and RL_β circuits based on Cole distribution function

Zhang

Chen

Lin

et al. 2023

Circuit Theory & Apps

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Summary Fractional‐order circuits, which contain fractance devices ( Lβ and Cα) described by fractional‐order differential equations, are widely used in interdisciplinary engineering research. The application of time‐domain response (TDR) measurement increases rapidly in analyzing the characteristics of fractance devices and fractional‐order circuits. However, the previous methods are mainly focused on deducing TDR expressions of a single fractance device or series fractional‐order circuits in some specific input signals, while overlook the TDR analysis of series‐parallel fractional‐order circuits (SPFOC) that are commonly applied in modeling electrochemical impedance or electrical bioimpedance. This paper proposes a novel method to derive TDR expressions of SPFOC in an arbitrary periodic signal. First, a discretization method to represent the SPFOC as the sum of first‐order circuits is proposed in Cole distribution function, which could approximate the transfer function of fractional‐order impedance/admittance. Second, the TDR expression of SPFOC in sinusoidal input signals is deduced in inverse Laplace transform, which can be applied as the components of a general TDR expression of SPFOC in an arbitrary periodic signal based on the Fourier series theory. Finally, both TDR simulations and experiments on Cole impedance model (a basic SPFOC) are conducted to verify the proposed method, which shows excellent agreement compared to theorical analysis. This paper presents a TDR solution to SPFOC that consist of a RCα or RLβ element. In future, the theoretical and application extension of the proposed TDR analysis method is still necessary on analysis of more general fractional‐order circuits.

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Section: Simulation Verificationmentioning

confidence: 99%

s^{α}

as the sum of integer‐order expressions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of time‐domain response of series‐parallel fractional‐order RC_α and RL_β circuits based on Cole distribution function

Zhang

Chen

Lin

et al. 2023

Circuit Theory & Apps

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“…As a result, different fractional derivatives describe the effect of past state, that is, memory effect, of an arbitrary system in different manners. The applications of fractional calculus concept and fractional derivatives can be found in many research areas, for example, biomedical engineering, 10,11 control system, [12][13][14] electrical/electronic engineering, [15][16][17][18] and plasma physics. 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.…”

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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“…As a result, different fractional derivatives describe the effect of the past state, i.e., memory effect, of an arbitrary system in different manners. e applications of the fractional calculus concept and fractional derivatives can be found in many research areas, e.g., biomedical engineering [11,12], control system [13][14][15], electrical/electronic engineering [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], and plasma physics [31,32].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Memreactance with Fractional Kinetics

Banchuin

2020

Mathematical Problems in Engineering

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In this work, the analysis of the memreactance, i.e., meminductor and memcapacitor, with fractional-order kinetics has been proposed. The meminductances, memcapacitances, and related parameters due to both DC and periodic input waveforms have been derived. The behavioral analysis has been thoroughly performed with the aid of numerical simulation. The effects of fractional-order kinetics have been explored where both linear and nonlinear dopant drift scenarios have been considered. Moreover, the emulation of memreactance with fractional-order kinetics by using the memristor and the effect of the fractional-order kinetics on the memreactance-based circuits have also been mentioned along with the extension of our results to the fractional-order memreactance.

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A note on applications of time-domain solution of Cole permittivity models

Cited by 8 publications

References 18 publications

Analysis of time‐domain response of series‐parallel fractional‐order RC_α and RL_β circuits based on Cole distribution function

Analysis of time‐domain response of series‐parallel fractional‐order RC_α and RL_β circuits based on Cole distribution function

Analytical model of inverse memelement with fractional order kinetic

Analysis of Memreactance with Fractional Kinetics

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A note on applications of time-domain solution of Cole permittivity models

Cited by 8 publications

References 18 publications

Analysis of time‐domain response of series‐parallel fractional‐order RCα and RLβ circuits based on Cole distribution function

Analysis of time‐domain response of series‐parallel fractional‐order RCα and RLβ circuits based on Cole distribution function

Analytical model of inverse memelement with fractional order kinetic

Analysis of Memreactance with Fractional Kinetics

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Analysis of time‐domain response of series‐parallel fractional‐order RC_α and RL_β circuits based on Cole distribution function

Analysis of time‐domain response of series‐parallel fractional‐order RC_α and RL_β circuits based on Cole distribution function