Analog Realization of Fractional-Order Capacitor and Inductor via the Caputo–Fabrizio Derivative

Capacitors and inductors have been proven to exhibit fractional-order characteristics. Therefore, the establishment of fractional-order models for circuits containing such components is of great significance in practical circuit analysis. This study establishes the impedance models of fractional-order capacitors and inductors based on the Caputo–Fabrizio derivative and performs the analog realization of fractional-order electronic components. The mathematical models of fractional RC, RL, and RLC electrical circuits are deduced and verified via a comparison between the numerical simulation and the corresponding circuit simulation. The electrical characteristics of the fractional circuits are analyzed. This study not only enriches the models of fractional capacitors and inductors, but can also be applied to the description of circuit characteristics to obtain more accurate results.

电容器和电感器已被证明具有分数阶特性。因此，建立包含此类元件的电路的分数阶模型在实际电路分析中具有重要意义。本研究基于卡普托 - 法布里齐奥导数建立了分数阶电容器和电感器的阻抗模型，并对分数阶电子元件进行了模拟实现。推导了分数阶RC、RL和RLC电路的数学模型，并通过数值模拟和相应的电路模拟之间的比较进行了验证。分析了分数阶电路的电气特性。本研究不仅丰富了分数阶电容器和电感器的模型，还可应用于电路特性的描述以获得更准确的结果。