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Fractional Order Sallen–Key and KHN Filters: Stability and Poles Allocation

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Abstract

This paper presents the analysis for allocating the system poles and hence controlling the system stability for KHN and Sallen–Key fractional order filters. The stability analysis and stability contours for two different fractional order transfer functions with two different fractional order elements are presented. The effect of the transfer function parameters on the singularities of the system is demonstrated where the number of poles becomes dependent on the transfer function parameters as well as the fractional orders. Numerical, circuit simulation, and experimental work are used in the design to test the proposed stability contours.

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Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne, UK

    Ahmed Soltan

  2. Department of Engineering Mathematics and Physics, Cairo University, Cairo, Egypt

    Ahmed G. Radwan

  3. Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza, Egypt

    Ahmed G. Radwan

  4. Department of Electronics and Communications Engineering, Cairo University, Cairo, Egypt

    Ahmed M. Soliman

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  1. Ahmed Soltan
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  2. Ahmed G. Radwan
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  3. Ahmed M. Soliman
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Correspondence to Ahmed G. Radwan.

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Soltan, A., Radwan, A.G. & Soliman, A.M. Fractional Order Sallen–Key and KHN Filters: Stability and Poles Allocation. Circuits Syst Signal Process 34, 1461–1480 (2015). https://doi.org/10.1007/s00034-014-9925-z

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