Fractional-order L<sub>β</sub>C<sub>α</sub>Low-Pass Filter Circuit

Zhou, Rui; Zhang, Run-Fan; Chen, Diyi

doi:10.5370/jeet.2015.10.4.1597

Cited by 4 publications

(2 citation statements)

References 29 publications

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“…system, [25,26] and filter circuit. [27,28] In this paper, a complexorder derivative is introduced to circuit elements, and many interesting phenomena are found. The real part of the order affects the phase of the output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor.…”

Section: Introductionmentioning

confidence: 99%

Attempt to generalize fractional-order electric elements to complex-order ones

Diao

Zhu

et al. 2017

Chinese Phys. B

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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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Section: Introductionmentioning

confidence: 99%

Attempt to generalize fractional-order electric elements to complex-order ones

Diao

Zhu

et al. 2017

Chinese Phys. B

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“…Motivated by the above analyses, circuit designers will face new challenges on the new phenomena and laws owing to the applications of the fractional-order components. Recently, researchers have been concentrating on the study of the fractional-order circuits [22][23][24] and fractional-order circuit networks [25,26], while there are few papers about the fractional-order infinite rectangle circuit networks, though the fractional calculus can better describe the physical phenomena.…”

Section: Introductionmentioning

confidence: 99%

Fractional‐order LβCα infinite rectangle circuit network

Zhou

Chen

et al. 2016

IET Circuits, Devices & Systems

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This study is a step forward to introduce the new fundamentals of LC infinite rectangle circuit network in the fractional domain. The authors first derive the general formula of the impedance between two arbitrary nodes of the fractional-order infinite rectangle circuit network by using Fourier transform in a coordinate system. Then, two properties (relevance and symmetry) of the fractional-order circuit network are systematically discussed. On the basis of these findings, the impedance can also be derived. Moreover, a comparative analysis is carried out to show an excellent agreement between the results obtained here and the results of the previous studies. Furthermore, the effects of the system parameters on the impedance characteristics and phase characteristics are systematically discussed. Finally, four potential application cases are presented. Numerical simulations are presented to verify the theoretical results introduced.

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