Fractional-Order 2 × n RLC Circuit Network

This paper introduces new fundamentals of the 2 × n RLC circuit network in the fractional-order domain. First, we derive the three general formulae of the equivalent impedances of the circuit network by using the matrix transform methods and constructing the differential equation models in three different cases. Moreover, we systematically study the effects of the system parameters on the impedence characteristics in the three different cases. Specifically, the new phenomena and laws are presented by the results of the numerical simulations, which are impossible in the conventional cases. Finally, a comparative sensitivity analysis about the three cases with respect to the fractional orders for the fractional-order circuit network is carried out in detail. Mathematical analyses and numerical simulations are included to validate the study.

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