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Fractional-Order Inductor: Design, Simulation, and Implementation
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DOI：10.1109/ACCESS.2021.3077561.png)
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Abstract
En 中文
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.
Keywords:
Coaxial cable
coil
electromagnetic fields
fractional-order circuits
fractional-order inductor
fractional-order resonator
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