Fractional-order L_βC_α filter circuit network

In this paper we introduce the new fundamentals of the conventional LC filter circuit network in the fractional domain. First, we derive the general formulae of the impedances for the conventional and fractional-order filter circuit network. Based on this, the impedance characteristics and phase characteristics with respect to the system variables of the filter circuit network are studied in detail, which shows the greater flexibility of the fractional-order filter circuit network in design. Moreover, from the point of view of the filtering property, we systematically study the effects of the filter units and fractional orders on the amplitude–frequency characteristics and phase–frequency characteristics. In addition, numerical tables of the cut-off frequency are presented. Finally, two typical examples are presented to promote the industrial applications of the fractional-order filter circuit network. Numerical simulations are presented to verify the theoretical results introduced in this paper.