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Open AccessArticle

Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements

Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska Street 45D, 15-351 Bialystok, Poland
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Academic Editor: Dominik Sierociuk
Electronics 2021, 10(4), 475; https://doi.org/10.3390/electronics10040475
Received: 31 December 2020 / Revised: 5 February 2021 / Accepted: 15 February 2021 / Published: 17 February 2021
(This article belongs to the Special Issue Fractional-Order Circuits & Systems Design and Applications)
The paper is devoted to the theoretical and experimental analysis of an electric circuit consisting of two elements that are described by fractional derivatives of different orders. These elements are designed and performed as RC ladders with properly selected values of resistances and capacitances. Different orders of differentiation lead to the state-space system model, in which each state variable has a different order of fractional derivative. Solutions for such models are presented for three cases of derivative operators: Classical (first-order differentiation), Caputo definition, and Conformable Fractional Derivative (CFD). Using theoretical models, the step responses of the fractional electrical circuit were computed and compared with the measurements of a real electrical system. View Full-Text
Keywords: ladder element; fractional derivatives; fractional electric circuit; Conformable Fractional Derivative (CFD) definition; Caputo definition; different orders ladder element; fractional derivatives; fractional electric circuit; Conformable Fractional Derivative (CFD) definition; Caputo definition; different orders
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MDPI and ACS Style

Piotrowska, E.; Rogowski, K. Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements. Electronics 2021, 10, 475. https://doi.org/10.3390/electronics10040475

AMA Style

Piotrowska E, Rogowski K. Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements. Electronics. 2021; 10(4):475. https://doi.org/10.3390/electronics10040475

Chicago/Turabian Style

Piotrowska, Ewa; Rogowski, Krzysztof. 2021. "Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements" Electronics 10, no. 4: 475. https://doi.org/10.3390/electronics10040475

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