Fractional-Order Inductor: Design, Simulation, and Implementation
Li Zhang, Aslıhan Kartcı, Ahmed S. Elwakil, Hakan Bağcı, K. Saláma
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 ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</i> ω) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</sup> , where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</i> =√{(-1)} and ω 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.