|Table of Contents|

Design of simulator for fractional order capacitor and inductor(PDF)


Research Field:
Publishing date:


Design of simulator for fractional order capacitor and inductor
He Qingping Liu Zuolian and Yang Ru
electronic circuit; fractional order circuit; LC serial circuit; inductive simulator; capacitive simulator; impedance conversion
electronic circuit fractional order circuit LC serial circuit inductive simulator capacitive simulator impedance conversion
TN 721.2
A fractional order simulant capacitor is designed based on the Potter frequency domain approximation algorithm and the impedance capacitance division circuit.By using a generalized impedance transformation circuit, the α (0<α<1) order simulant capacitor is converted to an α order simulant inductor. The order of the fractional order simulant capacitor is extended from zero to second. The fractional order simulant inductance and fractional order LC series circuit are simulated by using Multisim software, and the results are in good agreement with the theoretical analysis ones.


[1] 王发强,马西奎.电感电流连续模式下 Boost 变换器的分数阶建模与仿真分析[J].物理学报,2011,60(7):89-96.
Wang Faqiang, Ma Xikui. Fractional order modeling and simulation analysis of Boost converter in continuous conduction mode operation[J]. Acta Physica Sinica, 2011, 60(7): 89-96.(in Chinese)
[2] Westerlund S, Ekstam L. Capacitor theory[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 1994, 1(5): 826-839.
[3] Jesus I S, Machado J A T. Development of fractional order capacitors based on electrolyte processes[J]. Nonlinear Dynamics, 2009, 56(1): 45-55.
[4] Machado J A T, Galhano A M S F. Fractional order inductive phenomena based on the skin effect[J]. Nonlinear Dynamics, 2011, 68(1/2): 107-115.
[5] 王发强,刘崇新.分数阶临界混沌系统及电路实验的研究[J].物理学报,2006,55(8):3922-3927.
Wang Faqiang, Liu Chongxin. Study on the critical chaotic system with fractional order and circuit experiment[J]. Acta Physica Sinica, 2006, 55(8): 3922-3927.(in Chinese)
[6] 刘崇新.分数阶混沌电路理论及应用[M].西安:西安交通大学出版社,2011:118-128.
Liu Chongxin. Theory and application of Fractional order chaotic circuit[M]. Xi’an: Xi’an Jiaotong University Press, 2011: 118-128.(in Chinese)
[7] 贾红艳,陈增强,薛薇.分数阶Lorenz系统的分析及电路实现[J].物理学报,2013,62(14):140503.
Jia Hongyan, Chen Zengqiang, Xue Wei. Analysis and circuit implementation for the fractional order Lorenz system[J]. Acta Physica Sinica, 2013, 62(14): 140503.(in Chinese)
[8] 陈恒,雷腾飞,王震,等.分数阶Chen混沌系统的动力学分析与电路实现[J].河北师范大学学报自然科学版,2015,39(3):208-215.
Chen Heng, Lei Tengfei, Wang Zhen, et al. Dynamics analysis and circuit implementation for the fractional order Chen chaotic system[J]. Journal of Hebei Normal University Natural Science Edition, 2015, 39(3): 208-215.(in Chinese)
[9] 陈向荣,刘崇新,王发强,等.分数阶Liu混沌系统及其电路实验的研究与控制[J].物理学报,2008,57(3):1416-1422.
Chen Xiangrong, Liu Chongxin, Wang Faqiang, et al. Study on the fractional order Liu chaotic system with circuit experiment and its control[J]. Acta Physica Sinica, 2008, 57(3): 1416-1422.(in Chinese)
[10] 杨志宏,张彩霞,屈双惠,等.异分数阶 chen 系统的动力学特性及其多元电路实现[J].江西师范大学学报自然科学版,2017,41(2):133-139.
Yang Zhihong, Zhang Caixia, Qu Shuanghui, et al. The dynamic properties of the heterogeneous fractional order Chen system and its plural circuit implementation[J]. Journal of Jiangxi Normal University Natural Science, 2017, 41(2): 133-139. (in Chinese)
[11] 贾红艳,王庆合.异结构分数阶四翼混沌系统的同步及电路实现[J]. 天津科技大学学报,2017,32(1):62-67.
Jia Hongyan,Wang Qinghe.Synchronization of four-wing fractional-order chaotic system with different structures and its circuit implementation[J]. Journal of Tianjin University of Science & Technology, 2017, 32(1): 62-67.(in Chinese)
[12] Radwan A G, Salama K N. Passive and active elements using fractional circuit[J]. IEEE Transactions on Circuit and Systems, 2011, 58(10): 2388-2397.
[13] 刁利杰,张小飞,陈帝伊.分数阶并联RLαCβ电路[J].物理学报,2014,63(3):038401.
Diao Lijie, Zhang Xiaofei, Chen Diyi. Fractional-order multiple RLαCβ circuit[J]. Acta Physica Sinica, 2014, 63(3): 038401.(in Chinese)
[14] 余战波.分数阶T型LαCβ电路仿真研究[J].西南大学学报自然科学版,2015,37(2):141-147.
Yu Zhanbo. Numerical simulation of a T-shaped fractional LαCβ circuit[J]. Journal of Southwest University Natural Science Edition, 2015, 37(2): 141-147.(in Chinese)
[15] Zhou Rui,Zhang Runfan,Chen Diyi. Fractional-order LβCα low-pass filter circuit[J]. Journal of Electrical Engineering & Technology, 2015, 10(4): 1598-1610.
[16] Ahmadi P , Maundy B , Elwakil A S , et al. High-quality factor asymmetric-slope band-pass filters: a fractional-order capacitor approach[J]. IET Circuits Devices & Systems, 2012, 6(3): 187-197.
[17] Podlubny I. Fractional differential equations[M]. New York, USA: Academic Press, 1999: 79-106
[18] Charef A, Sun H H, Tsao Y Y, et al. Fractal system as represented by singularity function[J]. IEEE Transactions on Automatic Control, 1992, 37(9): 1465-1470.
[19] Ahmad W M, Sprott J C. Chaos in fractional-order autonomous nonlinear systems[J]. Chaos Solitons & Fractals, 2003, 16(2): 339-351.
[20] 燕奎臣,王晓辉,李硕.回转器及其应用[J].仪表技术与传感器,2000(5):36-39.
Yan Kuichen, Wang Xiaohui, Li Shuo. Gyrator and its application[J]. Journal of Instrument Technique and Sensor, 2000(5): 36-39.(in Chinese)


Last Update: 2017-09-11