论文|Qiu-Yan He, Yi-Fei Pu, Bo Yu, Xiao Yuan. Scaling Fractal-Chuan Fractance Approximation Circuits of Arbitrary Order

本文原载Circuits, Systems, and Signal Processing，由四川大学计算机学院蒲亦非教授、电子信息学院袁晓副教授等科研人员创作，系四川大学“智慧法治”超前部署学科系列学术成果。后续会持续分享四川大学“智慧法治”超前部署学科系列学术成果，欢迎大家阅读。

Abstract: The scaling fractal-chuan fractance approximation circuit (SFCFAC), which can realize the rational approximation of arbitrary-order fractances and has an excellent approximation performance, is presented in this paper. For an original SFCFAC, the progression ratios of resistance and capacitance are limited to the range 0–1. However, it is possible for the values of both progression ratios to be greater than one. The impedance function of an SFCFAC can be represented by an irregular scaling equation. By solving the scaling equation approximately, the operational order of an SFCFAC can be obtained using both progression ratios as μ =−lgα/lg(αβ). Therefore, the SFCFAC has fractional operational characteristics, which is explained in theory. Oscillation phenomena are inherent to the SFCFAC. It is necessary to learn about these oscillation characteristics. The approximation performance can be improved by adding a series resistor and a series capacitor to the SFCFAC. The corresponding resistance and capacitance are determined by both progression ratios. The optimization has the advantages of simple operation, evident influence, and good practicality, which will make the SFCFAC competitive in future studies. Moreover, the values of the operational order of SFCFACs are extended from−1 <μ<0 to 0< |μ| < 2 without using inductors, which is feasible for practical applications.

Keywords: Fractance; Fractor; Fractional-order circuits and systems; Fractional calculus; Scaling extension

Qiu-Yan He, Yi-Fei Pu, Bo Yu, Xiao Yuan. Scaling Fractal-Chuan Fractance Approximation Circuits of Arbitrary Order[J]. Circuits, Systems, and Signal Processing, 2019, 11(38): 4933–4958. (SCI IF: 1.998)（论文下载）