Fractional-Order Inductor: Design, Simulation, and Implementation

Fractional calculus has tremendous potential in modeling the evolution of complex systems including those with memory. Indeed, fractional-order models are more accurate approximating non-locally distributed dynamics short- or long-term memory effects. However, realization fractional is often hindered by lack robust energy storage devices, particularly inductors (FOIs). Inherent eddy currents, hysteresis losses, suitable materials, and a systematic design procedure among challenges FOI synthesis. In this work, straightforward approach realizing FOIs coaxial structure proposed. This relies on fact that wave impedance transverse electromagnetic (TEM) mode scales ( j ?) 0.5 , where =?{(-1)} ? angular frequency when filling material highly conductive. experimental characterization realized device shows it half-order inductive response (corresponding to 45° phase angle) stable range 18 MHz - 1 GHz angle deviation not exceeding 5°. Furthermore, effects geometry permeability, permittivity, conductivity investigated.