Analysis of Fractional-Order 2xn RLC Networks by Transmission Matrices

Abstract

In this study, a new method is devised and presented for the dynamic analysis of a 2xn RLC circuit network modeled with the fractional-order circuit elements. The analysis method is based on the principles of dynamic analysis with transfer function approximation. Firstly, the fractional-order 2xn RLC circuit network of interest which is divided into n equal cells connected in cascaded form, then related transmission matrices are individually calculated for each cell correspondingly, Secondly. the transmission matrix of the whole circuit network is calculated based on the properties of the cascaded connection. By means of this transmission matrix and the two-part connection, diagram circuit functions, such as transfer function and the equivalent input impedance of the whole circuit network, are obtained depending on the number of cells (n) and the fractional-order values.Finally, essential dynamic system analysis, such as frequency, step and pulse responses, and the impedance characteristics of the network, are simulated using necessary MATLAB programs depending on cell number n and the fractional-order values.