On Applications of Fractional Derivatives in Circuit Theory

In this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equ...

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Bibliographic Details
Published in2020 27th International Conference on Mixed Design of Integrated Circuits and System (MIXDES) pp. 160 - 163
Main Authors Gulgowski, Jacek, Stefanski, Tomasz P., Trofimowicz, Damian
Format Conference Proceeding
LanguageEnglish
Published Department of Microelectronics & Computer Science 01.06.2020
Subjects
circuit simulation
Circuit theory
fractional calculus
Frequency-domain analysis
Integrated circuit modeling
Laplace equations
Mathematical model
Power transmission lines
Transmission line measurements
transmission lines
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Summary:In this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited applicability in the circuit theory. That is, the Riemann-Liouville and Caputo derivatives with finite base point have a limited applicability whereas the Grünwald-Letnikov and Marchaud derivatives lead to reasonable results of the circuit-level modelling.
DOI:10.23919/MIXDES49814.2020.9155559