This research realizes fractional-order devices or constant phase element (CPE) using continued fraction expansion (CFE) and rational function approximation methods. An RC ladder network prototype was realized using CFE based on the Cauer network principle. The RC ladder network and signal flow graph (SFG) were employed to realize the proposed CPE. Voltage gain circuits and voltage-mode integrators were realized by using operational transconductance amplifiers (OTA) and grounded capacitors. The proposed CPE was subsequently synthesized using voltage gain circuits and voltage-mode integrators based on SFG. The proposed CPE could function as fractional-order capacitor and fractional-order inductor. Besides, the CPE could be constructed in arbitrary fractional-orders. The impedance and operation frequency are independently tunable by manipulating OTA bias current. To validate, the proposed fractional-order device was applied to six types of electrical Cole models of skull tissues, and simulation results were compared with the approximation function and theory. The electrical characteristics of the Cole models based on the proposed CPE are comparable to the theoretical characteristics of the Cole model.

这项研究使用连续分数展开（CFE）和有理函数逼近方法来实现分数阶设备或恒定相元素（CPE）。基于Cauer网络原理，使用CFE实现了RC梯形网络原型。利用RC梯形图网络和信号流图（SFG）来实现所提出的CPE。电压增益电路和电压模式积分器通过使用运算跨导放大器（OTA）和接地电容器来实现。随后，使用电压增益电路和基于SFG的电压模式积分器合成了所提出的CPE。所提出的CPE可以用作分数阶电容器和分数阶电感器。此外，CPE可以任意分数阶构造。阻抗和工作频率可通过调节OTA偏置电流来独立调节。为了进行验证，将提出的分数阶设备应用于六种类型的颅骨组织电Cole模型，并将仿真结果与逼近函数和理论进行了比较。基于提出的CPE的Cole模型的电气特性与Cole模型的理论特性相当。