Analysis of fractional-order 2×n RLC networks by transmission matrices

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