Fractional-Order Inductor: Design, Simulation, and Implementation
IEEE Access, vol.9, pp.73695-73702, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 9
- Publication Date: 2021
- Doi Number: 10.1109/access.2021.3077561
- Journal Name: IEEE Access
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
- Page Numbers: pp.73695-73702
- Keywords: Coaxial cable, coil, electromagnetic fields, fractional-order circuits, fractional-order inductor, fractional-order resonator
- Yıldız Technical University Affiliated: No
Abstract
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 (TEM) mode on the coaxial structure scales with (\mathit {j}\omega)^{0.5} , where \mathit {j}=\sqrt {(-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° phase angle) that is stable in the frequency range 18 MHz - 1 GHz with a phase angle deviation not exceeding 5°. Furthermore, the effects of the device geometry and the permeability, the permittivity, the conductivity of the filling material on device response are investigated.