Circuits, Systems, and Signal Processing

, Volume 35, Issue 6, pp 2017–2039 | Cite as

On The Optimization of Fractional Order Low-Pass Filters

  • Lobna A. Said
  • Samar M. Ismail
  • Ahmed G. Radwan
  • Ahmed H. Madian
  • Mohamed F. Abu El-Yazeed
  • Ahmed M. Soliman
Article

Abstract

This paper presents three different optimization cases for normalized fractional order low-pass filters (LPFs) with numerical, circuit and experimental results. A multi-objective optimization technique is used for controlling some filter specifications, which are the transition bandwidth, the stop band frequency gain and the maximum allowable peak in the filter pass band. The extra degree of freedom provided by the fractional order parameter allows the full manipulation of the filter specifications to obtain the desired response required by any application. The proposed mathematical model is further applied to a case study of a practical second- generation current conveyor (CCII)-based fractional low-pass filter. Circuit simulations are performed for two different fractional order filters, with orders 1.6 and 3.6, with cutoff frequencies 200 and 500 Hz, respectively. Experimental results are also presented for LPF of 4.46 kHz cutoff frequency using a fabricated fractional capacitor of order 0.8, proving the validity of the proposed design approach.

Keywords

Fractional order element Low-pass filter Optimization CCII 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Lobna A. Said
    • 1
  • Samar M. Ismail
    • 1
  • Ahmed G. Radwan
    • 2
    • 3
  • Ahmed H. Madian
    • 3
    • 4
  • Mohamed F. Abu El-Yazeed
    • 5
  • Ahmed M. Soliman
    • 5
  1. 1.Faculty of IETGerman University in Cairo (GUC)CairoEgypt
  2. 2.Department of Engineering Mathematics and PhysicsCairo UniversityGizaEgypt
  3. 3.NISC Research CenterNile UniversityCairoEgypt
  4. 4.Radiation Engineering DepartmentNCRRT, Egyptian Atomic Energy, AuthorityCairoEgypt
  5. 5.Electronics and Communications Engineering DepartmentCairo UniversityCairoEgypt

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