Analysis of electrical circuits including fractional order elements

Bošković, Marko; Šekara, Tomislav B.; Lutovac, Budimir; Daković, Miloš; Mandić, Petar; Lazarević, Mihailo P.

doi:10.1109/meco.2017.7977226

Cited by 21 publications

(8 citation statements)

References 10 publications

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“…The equations describing time domain behavior of RLC and RC circuits are generalized in [12,13] by the simple replacement of the integer order derivatives by the fractional ones, while the transient response investigations of the series RC α circuit, as well of the series and parallel RL β C α are conducted in [16,17,18], where the fractional models of capacitor and inductor are taken into account. The analytical tools in obtaining the time domain response of electrical circuits containing fractional capacitor and inductor are applied in [4], while [7,44,45] use numerical tools for the same purpose. The analysis of RL β C α and fractional RC, RL, and LC circuits in the frequency domain is performed in [37,38,39], while [9,40] investigate the Wien bridge oscillators.…”

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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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: Introductionmentioning

confidence: 99%

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Haška

Zorica

Cvetićanin

2022

Circuits Syst Signal Process

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“…There are many other applications of FO models in the literature, including those in the digital domain [26]. A time and frequency analysis of electrical circuits with FO elements is presented in [27]. The application of FO derivatives in system theory and their relevance in representation of dynamical systems is shown in [28].…”

Section: Introductionmentioning

confidence: 99%

Analog Modeling of Fractional-Order Elements: A Classical Circuit Theory Approach

2021

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In this paper a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) is presented. Unlike most already proposed techniques, a standard approach from classical circuit theory is applied. It includes the realization of a system function by a mathematical approximation of the desired phase response, and the synthesis procedure for the realization of basic fractional-order (FO) one-port models as passive RC Cauer-and Foster-form canonical circuits. Based on the presented oneports, simple realizations of two-port differentiator and integrator models are derived. Beside the description of the design procedure, illustrative examples, circuit diagrams, simulation results and practical realizations are presented.

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“…Using analytical tools and by considering the series connection of resistor and fractional capacitor as a generalized capacitor, the transient regime analysis of the series RC α circuit is performed in [15], while by considering the series connection of resistor and fractional inductor as a generalized inductor, the transient regime analysis of the parallel RL β C α is performed in [16,17]. Simple RC and an example of a more complex circuit containing fractional capacitor and inductor is considered in [5] for the transient regime using analytical approach, while in [6,37,38] numerical tools are used to solve governing equations of fractionally generalized electric circuits in the time domain.…”

Section: Introductionmentioning

confidence: 99%

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Haška

Cvetićanin

Zorica

2021

Preprint

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Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

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Analysis of electrical circuits including fractional order elements

Cited by 21 publications

References 10 publications

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Analog Modeling of Fractional-Order Elements: A Classical Circuit Theory Approach

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

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Analysis of electrical circuits including fractional order elements

Cited by 21 publications

References 10 publications

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Analog Modeling of Fractional-Order Elements: A Classical Circuit Theory Approach

Dissipative and Generative Fractional Electric Elements in Modeling RC&nbsp;and RL&nbsp;Circuits

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Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits