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Analysis and Passive Synthesis of Immittance for Fractional-Order Two-Element-Kind Circuit

  • Guishu Liang
  • Jiawei HaoEmail author
Article
  • 31 Downloads

Abstract

Fractional circuits have attracted an extensive attention of scholars and researchers for their superior performance and potential applications. The passive realization of the fractional-order immittance function plays an important role in fractional circuits theory, which is useful in fractional circuits design and modeling. This paper deals with the analysis and passive synthesis of fractional two-element-kind network. Firstly, the time-domain response of fractional two-element-kind network is analyzed based on its immittance function expressions, and the response shows oscillation only in fractional \( L_{\beta } C_{\alpha } \) circuits. Then, necessary and sufficient conditions to realize the fractional-order immittance functions by a passive network with only two kinds of elements are obtained in view of impedance scaling. A procedure is also proposed to realize such immittance functions using two-element-kind network. Finally, three examples are given to illustrate the proposed method.

Keywords

Fractional circuits Fractional-order impedance Network synthesis Analysis Impedance scaling 

Notes

Acknowledgements

This research was supported in part by Natural Science Foundation of Beijing Municipality under Grant No. 3192039 and the Natural Science Foundation of Hebei Province under Grant No. E2018502121.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electric EngineeringNorth China Electric Power UniversityBaodingChina

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