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

Automated summary

Fractional calculus is powerful for modeling complex systems with memory effects. The lack of robust fractional-order energy storage devices, particularly FOIs, hinders the realization of fractional systems. A straightforward approach using a coaxial structure to realize FOIs is proposed in this work, and experimental results show stable response with half-order inductive behavior. The effects of device geometry and filling material properties on device response are also investigated.