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Sensitivity Analysis of Networks with Fractional Elements

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Abstract

Fractional circuits have attracted the extensive attention of scholars and researchers all around the world in view of their superior performance and extra design freedom compared with conventional circuits. On the one hand, conventional circuit theory could be extended with the development of fractional circuits; on the other hand, the newly developed fractional circuits constitute a new challenge for the analysis and synthesis methods of conventional theory. As is known to all, almost no physical circuit can perform exactly in accordance with the design in view of the practical considerations such as the tolerance of circuit elements, environmental effects and aging problems. Therefore, the analysis of the effects of element parameter variations on circuit performance is of interest and should be considered during the design stage. Hence, it is necessary to conduct a sensitivity analysis for networks with fractional elements. In this paper, the adjoint network method is generalized to analyze the sensitivity of networks with fractional elements. The sensitivity formulae for the multi-port fractional elements are derived with the help of Tellegen’s theorem, and the time domain formulae are also derived. Some linear circuits and nonlinear circuits that contain nonlinear resistors are taken as examples to demonstrate the validity and accuracy of the formulae.

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Acknowledgements

This research was supported in part by the National Natural Science Foundation of China under Grant Nos. 51177048 and 51407073, the Natural Science Foundation of Hebei Province under Grant No. E2012502009, the Fundamental Research Funds for the Central Universities under Grant No. 11MG36, and the Fundamental Research Funds for the Hebei Province Universities under Grant No. Z2011220.

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  1. School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, 071003, China

    Guishu Liang & Long Ma

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  1. Guishu Liang
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  2. Long Ma
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Correspondence to Long Ma.

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Liang, G., Ma, L. Sensitivity Analysis of Networks with Fractional Elements. Circuits Syst Signal Process 36, 4227–4241 (2017). https://doi.org/10.1007/s00034-017-0504-y

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