Passive Realization of Fractional-Order Impedances by a Fractional Element and RLC Components: Conditions and Procedure

In this paper, conditions for checking the realizability of fractional-order impedance functions by passive networks composed of a fractional element (either a fractional capacitor or a fractional inductor) and some RLC components are derived. To this end, at first the newly obtained conditions for realizability of fractional-order impedance functions by a passive network composed of a fractional capacitor and some RLC components are extended to include the case that the polynomials involving in the impedance function can have roots on the imaginary axis. Then, the necessary and sufficient conditions are found on a fractional-order impedance function to be realized by a passive network composed of a fractional element and some RLC components. Furthermore, a procedure for finding the realization in the realizable cases is proposed. Finally, the realizability conditions for a special class of fractional-order impedance functions are simplified.