Attempt to generalize fractional-order electric elements to complex-order ones
The complex derivative D^α±jβ, with α, β ∈ R＋ is a generalization of the concept of integer derivative, where α = 1,β = 0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complexorder electric elements concept is proposed for the first time,...
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| Published in | Chinese physics B Vol. 26; no. 6; pp. 87 - 92 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Chinese Physical Society and IOP Publishing Ltd
01.06.2017
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-1056 2058-3834 |
| DOI | 10.1088/1674-1056/26/6/060503 |
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| Summary: | The complex derivative D^α±jβ, with α, β ∈ R＋ is a generalization of the concept of integer derivative, where α = 1,β = 0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complexorder electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed.Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system. |
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| Bibliography: | complex derivative, fractional-order elements, imaginary and real part, memristor 11-5639/O4 Gangquan Si, Lijie Diao, Jianwei Zhu, Yuhang Lei,Yanbin Zhang（ State Key Laboratory of Electrical Insulation and Power Equipment, Xi＇ an Jiaotong University, Xi＇ an 710049, China） The complex derivative D^α±jβ, with α, β ∈ R＋ is a generalization of the concept of integer derivative, where α = 1,β = 0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complexorder electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed.Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system. |
| ISSN: | 1674-1056 2058-3834 |
| DOI: | 10.1088/1674-1056/26/6/060503 |