Experimental Study of Fractional-Order RC Circuit Model Using the Caputo and Caputo-Fabrizio Derivatives

Da Lin, Xiaozhong Liao, Lei Dong, Ruocen Yang, Samson S. Yu, Herbert Ho Ching Iu, Tyrone Fernando, Zhen Li

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


This study employs the Caputo-Fabrizio fractional derivative to determine the model of fractional-order RC circuits with arbitrary voltage input which can be widely used in a variety of electrical systems. Analog circuit implementation of fractional-order RC circuits defined by Caputo-Fabrizio fractional derivative is presented and verified by comparing with the model proposed in this work. For the purpose of judging whether the fractional-order model defined by the Caputo-Fabrizio derivative is practical, the comparison experiments are carried out. By using Laplace transform, the analytical solutions of fractional-order RC circuits based on the Caputo-Fabrizio derivatives with constant and periodic voltage sources are deduced. Fractional-order model of RC circuits with arbitrary input are also calculated using the convolution formula. The correctness of the derivation of the model using the Caputo-Fabrizio derivative is verified. Through discussing the impedance model of capacitor in frequency domain, the analog realization of fractional capacitor based on the Caputo-Fabrizio derivative is derived. The fractional-orders of the RC circuits models defined by the Caputo and Caputo-Fabrizio fractional derivatives are fitted respectively through repeated charging and discharging experiment data. The fractional-order models based on the Caputo and Caputo-Fabrizio derivatives, and the integer-order model are all compared with the experiment data.

Original languageEnglish
Article number9323030
Pages (from-to)1034-1044
Number of pages11
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number3
Publication statusPublished - Mar 2021


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