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

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 x 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.

Automated summary

Recent research has found that ideal capacitors and inductors do not exist in reality, and that the behavior of real devices can be accurately described using fractional-order mathematical models. This study focuses on a class of 2 x n order RC cobweb fractional-order circuit network with a central node. Using Kirchhoff's laws, impedance magnitude and phase between two points in the network are derived using difference equations and matrix transformations. Three impedance expressions are deduced and their accuracy is verified through numerical analysis and simulations. The study also investigates the impact of various parameters such as resistance, capacitance, number of circuit units, frequency, and fractional order on the impedance. Furthermore, physical experiments are conducted for the first time to compare the performance of fractional-order and integer-order circuit networks in describing the impedance of actual physical circuits. These experiments confirm that fractional-order circuit network models outperform integer-order models in representing the characteristics of impedance magnitude and phase.