On Applications of Fractional Derivatives in Circuit Theory

• Published in: 2020 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
• Language: English
• 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
• DOI: 10.23919/MIXDES49814.2020.9155559

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.