Realization of a fractional-order RLC circuit via constant phase element

Caponetto, Riccardo; Graziani, S.; Murgano, Emanuele

doi:10.1007/s40435-021-00778-4

Cited by 13 publications

(9 citation statements)

References 37 publications

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“…Constitutive equations of dissipative and generative capacitor (1) and ( 2), along with the constitutive models (3) and (4) corresponding to the dissipative and generative inductor are employed to model: dissipative-dissipative fractional series RLC circuit, consisting of dissipative electric elements, by the governing equation ( 5); generative-generative circuit, consisting of generative elements, using the governing equation (6); as well as to model dissipative-generative and generative-dissipative circuits, consisting of dissipative capacitor and generative inductor for the former and generative capacitor and dissipative inductor for the latter, by the governing equations ( 7) and (8).…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, the constitutive equation of fractional capacitor may also involve fractional differentiation orders higher than one, as in [20]. The experimental work includes testing of supercapacitors at various frequencies and comparison of obtained results with the theoretical models, see [1,22], or even manufacturing electric elements of fractional order, see [21,24,28], as well as their realizations by the use of constant phase element, as demonstrated in [5,6]. The modeling of electrochemical double-layer capacitors also includes the fractional calculus, that is investigated in [19] through the frequency characteristics, in [26,35] through the time domain analysis, and in [27] by the analysis of capacitor's quality properties.…”

Section: Introductionmentioning

confidence: 99%

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Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Haška

Zorica

Cvetićanin

2022

Circuits Syst Signal Process

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Equations governing the transient and steady-state regimes of the fractional series RLC circuits containing dissipative and/or generative capacitor and inductor are posed by considering the electric current as a response to electromotive force. Further, fractional RLC circuits are analyzed in the steady-state regime and their energy consumption/production properties are established depending on the angular frequency of electromotive force. Frequency characteristics of the modulus and argument of transfer function, i.e., of circuit's equivalent admittance, are analyzed through the Bode diagrams for the whole frequency range, as well as for low and high frequencies as the asymptotic expansions of transfer function modulus and argument.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Haška

Zorica

Cvetićanin

2022

Circuits Syst Signal Process

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“…where α is the order of the fractional inductance denoted L α and d α /dt α is the fractional order derivative operator [56]. In general, the fractional order inductor of the α order is in the range of 0 < α < 2, and the voltage leads the current by (1/2) πα degrees.…”

Section: Impedance Spectroscopy Of the Qcm Sensor Based On The Fracti...mentioning

confidence: 99%

Assessing Impedance Analyzer Data Quality by Fractional Order Calculus: A QCM Sensor Case Study

Burda

2023

Electronics

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The paper presents the theoretical, simulation, and experimental results on the QCM sensor based on the Butterworth van Dyke (BVD) model with lumped reactive motional circuit elements of fractional order. The equation of the fractional order BVD model of the QCM sensor has been derived based on Caputo definitions and its behavior around the resonant frequencies has been simulated. The simulations confirm the ability of fractional order calculus to cover a wide range of behaviors beyond those found in experimental practice. The fractional order BVD model of the QCM sensor is considered from the perspective of impedance spectroscopy to give an idea of the advantages that fractional order calculus brings to its modeling. For the true values of the electrical parameters of the QCM sensor based on the standard BVD model, the experimental investigations confirm the equivalence of the measurements after the standard compensation of the virtual impedance analyzer (VIA) and the measurements without compensation by fitting with the fractional order BVD model. From an experimental point of view, using fractional order calculus brings a new dimension to impedance analyzer compensation procedures, as well as a new method for validating the compensation.

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“…There are interesting realizations of differintegrators and applications to circuits [74], [75], [44], [48], [76], [77]. An interesting generalization of the Kramers-Krönig relations was presented in [21].…”

Section: The Differintegratormentioning

confidence: 99%

The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models

Ortigueira

Machado

2022

IEEE Circuits Syst. Mag.

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This paper presents the continuous-time fractional linear systems and their main properties. Two particular classes of models are introduced: the fractional autoregresive-moving average type and the tempered linear system. For both classes, the computations of the impulse response, transfer function, and frequency response are discussed. It is shown that such systems can have integer and fractional components. From the integer component we deduce the stability. The fractional order component is always stable. The initial-condition problem is analysed and it is verified that it depends on the structure of the system. For a correct definition and backward compatibility with classic systems, suitable fractional derivatives are also introduced. The Gr ünwald-Letnikov and Liouville derivatives, as well as the corresponding tempered versions, are formulated.

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Realization of a fractional-order RLC circuit via constant phase element

Cited by 13 publications

References 37 publications

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Assessing Impedance Analyzer Data Quality by Fractional Order Calculus: A QCM Sensor Case Study

The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models

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