Circuits, Systems, and Signal Processing

, Volume 34, Issue 5, pp 1461–1480 | Cite as

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

  • Ahmed Soltan
  • Ahmed G. Radwan
  • Ahmed M. Soliman


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.


Stability, LTI system Fractional-order system Filters Oscillators Control 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Ahmed Soltan
    • 1
  • Ahmed G. Radwan
    • 2
    • 3
  • Ahmed M. Soliman
    • 4
  1. 1.School of Electrical and Electronic EngineeringNewcastle UniversityNewcastle upon TyneUK
  2. 2.Department of Engineering Mathematics and PhysicsCairo UniversityCairoEgypt
  3. 3.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityGizaEgypt
  4. 4.Department of Electronics and Communications EngineeringCairo UniversityCairoEgypt

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