Theoretical analysis and experimental verification of fractional-order RC cobweb circuit network

• Published in: Chaos, solitons and fractals solitons and fractals, 2023-07, Vol.172, p.113541, Article 113541
• Main Authors: Liu, Yang, Chen, Liping, Wu, Xiaobo, Lopes, António M., Cui, Fengqi, Chen, YangQuan
• Format: Article
• Language: English
• Subjects: Fractional-order circuit network; Impedance; Magnitude characteristic; Phase characteristics
• ISSN: 0960-0779
• DOI: 10.1016/j.chaos.2023.113541

Recent research has shown that ideal capacitors and inductors do not physically exist, and that the dynamics of real devices can be accurately described by fractional-order (FO) mathematical models. This paper investigates a class of 2×n order RC cobweb FO circuit network with central node. Based on the Kirchhoff’s laws, the impedance magnitude and phase between two points of the network are derived using difference equations and matrix transformations. Three impedance expressions are deduced, and their correctness is verified numerically and by simulations. The influence of various parameters of the electrical network, namely the resistance, capacitance, number of circuit units, frequency and fractional order, on the impedance is studied. Additionally, for the first time, physical experiments are presented to compare the effectiveness of FO and integer-order circuit networks for describing the impedance of actual physical circuits. These experiments confirm that FO circuit network models perform better than the integer-order ones for representing the characteristics of the impedance magnitude and phase. •The mathematical model of a class of 2×n RC cobweb FO circuit network with central node is given.•The effect of five system parameters on the characteristics of the impedance is systematically studied.•It is proved that the FO circuit network model represents the actual circuit better than the integer-order one.