Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 2–29 | Cite as

On the Approximations of CFOA-Based Fractional-Order Inverse Filters

  • Esraa M. Hamed
  • Lobna A. SaidEmail author
  • Ahmed H. Madian
  • Ahmed G. Radwan


In this paper, three novel fractional-order CFOA-based inverse filters are introduced. The inverse low-pass, high-pass and band-pass responses are investigated using different approximation techniques. The studied approximations for the fractional-order Laplacian operator are the continued fraction expansion and Matsuda approximations. A comparison is held between the ideal filter characteristic and the realized ones from each approximation. A comparative study is summarized between the proposed circuits with some of the released inverse filters introduced in the literature. Foster-I realization is employed to transform the obtained fractional-order capacitor (FOC) from the investigated approximations into an RC parallel–series circuit topology. Additionally, to discuss the sensitivity of the FOC to component tolerances, Monte Carlo simulations are carried out which shows immunity to the component tolerances. Numerical examples, as well as SPICE circuit simulations, have been introduced to validate the theoretical discussions. Finally, the three CFOA inverse filters are tested experimentally.


Fractional order circuits Inverse filters Fractance Approximations Matsuda CFE Foster-I 



Authors would like to thank Science and Technology Development Fund (STDF) for funding the project \(\#\) 25977 and Nile University for facilitating all procedures required to complete this study.


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

Authors and Affiliations

  1. 1.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityGizaEgypt
  2. 2.Radiation Engineering Department, NCRRTEgyptian Atomic Energy AuthorityCairoEgypt
  3. 3.Engineering Mathematics and Physics Department, Faculty of EngineeringCairo UniversityGizaEgypt
  4. 4.Faculty of Engineering and Basic SciencesNile UniversitySheikh Zayed CityEgypt

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