Fractional‐order mutual inductance: analysis and design

Soltan, Ahmed; Radwan, Ahmed G.; Soliman, Ahmed M.

doi:10.1002/cta.2064

Cited by 55 publications

(42 citation statements)

References 38 publications

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“…The fractional mutual inductor can be viewed as the generalization of traditional integer‐order mutual inductor considering that the order is limited as 1 in integer case while varies arbitrarily in fractional case. The reciprocal commensurate fractional‐order mutual inductor is expressed as follows, and its circuit notation is depicted in Figure .

([], \begin{array}{c} U_{1} ((), s) \\ U_{2} ((), s) \end{array}) = s^{α} ([], \begin{array}{c} L_{11} & M \\ M & L_{22} \end{array}) ([], \begin{array}{c} I_{1} ((), s) \\ I_{2} ((), s) \end{array})

…”

Section: Passivity Of Fractional‐order Elementsmentioning

confidence: 99%

“…As the base of the fractional‐order circuit theory, the fractional‐order elements, also known as constant phase elements, have been deeply explored, and many ingenious methods were reported to realize them, including the self‐similar RC tree circuit and grid‐type RC ladder circuit for 0.5‐order approximation, the PMMA film‐coated capacitive probe, and the fractal structure on silicon . Besides, many other novel fractional‐order elements have also been proposed, such as fractional‐order mutual inductor, fractional‐order 2‐port, and fractional memristor . At the same time, researchers have also investigated many fractional‐order circuits and systems of new types, which can not only provide extra design freedoms but also enhance the circuit performance.…”

Section: Introductionmentioning

confidence: 99%

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Multivariate theory‐based passivity criteria for linear fractional networks

Liang

2018

Circuit Theory & Apps

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Summary In traditional linear network theory, the positive‐real (PR) criteria are widely used to judge the passivity of elements and networks in the light of the fact that there exists an equivalent relationship between the passivity and the PR property of their immittance functions (matrices). However, the equivalence will no longer hold when the fractional elements are introduced into the network, and the PR criteria are not suitable in complex frequency domain anymore. On the other hand, the rapid development of fractional‐order circuits and systems and the corresponding study in fractional circuit analysis and designs put forward an urgent requirement for the passivity criterion, which can tackle linear fractional networks. Hence, in this paper, we propose new passivity criteria for linear fractional networks by aid of generalized Tellegen's theorem and multivariable PR theory. By using the proposed criteria, the passivity of linear fractional networks can be judged, and the steps of the proposed criterion are illustrated by examples.

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([], \begin{array}{c} U_{1} ((), s) \\ U_{2} ((), s) \end{array}) = s^{α} ([], \begin{array}{c} L_{11} & M \\ M & L_{22} \end{array}) ([], \begin{array}{c} I_{1} ((), s) \\ I_{2} ((), s) \end{array})

…”

Section: Passivity Of Fractional‐order Elementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multivariate theory‐based passivity criteria for linear fractional networks

Liang

2018

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

“…A few years later, results of researches on the frequency characteristics of coils with soft ferromagnetic cores proved that fractional-order models have been adequate for them either [37,38] . Moreover, fractional calculus has been used for a description of other, previously known from classic circuit theory, elements and systems, like magnetically-coupled coils [40] or memristors and circuits and systems with memristors [22,26] . Still supercapacitors C α and lossy coils L β with ferromagnetic cores are most common fractional-order elements.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the transient state in a parallel circuit of the class RLC

Jakubowska-Ciszek

Walczak

2018

Applied Mathematics and Computation

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“…[1][2][3][4][5][6][7][8][9] The fractional derivatives are nonlocal operators, because they are defined using integrals. During the last 30 years, FC has attracted much attention because of its powerful and widely used tool for better modelling and control of processes in many areas of science and engineering.…”

Section: Introductionmentioning

confidence: 99%

Electrical circuits described by fractional conformable derivative

López-Martínez

Rosales

Carreño

et al. 2018

Circuit Theory & Apps

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Summary In the last 3 years, the fractional conformable derivative and its properties have been introduced. Unlike other definitions, this new fractional derivative is based on the basic limit definition of the derivative and satisfies the same formulas of derivation, such as product and quotient of 2 functions and the chain rule. Using this new derivative, we obtain a new class of linear ordinary differential equations with noninteger power variable coefficients for the Resistance Capacitance (RC), Inductance Capacitance (LC), and Resistance, Inductance Capacitance (RLC) electric circuits. The numerical solutions are solved through the Matlab software. Solutions depend on time and on the fractional order parameter 0 < γ ≤ 1. The computing using this new derivative is much easier than using other definitions of fractional derivative. It has been shown that in the particular case γ = 1, these solutions become the ordinary ones. Also, a comparison has been made with the Caputo fractional derivative for the case of the RC circuit with constant source.

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Fractional‐order mutual inductance: analysis and design

Cited by 55 publications

References 38 publications

Multivariate theory‐based passivity criteria for linear fractional networks

Multivariate theory‐based passivity criteria for linear fractional networks

Analysis of the transient state in a parallel circuit of the class RLC

Electrical circuits described by fractional conformable derivative

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