Circuits, Systems, and Signal Processing

, Volume 35, Issue 6, pp 1973–1982 | Cite as

Approximated Fractional-Order Inverse Chebyshev Lowpass Filters

  • Todd J. Freeborn
  • Ahmed S. ElwakilEmail author
  • Brent Maundy


In this paper we use a least-squares fitting routine to approximate the stopband ripple characteristics of fractional-order inverse Chebyshev lowpass filters which have fractional-order zeros and poles. MATLAB simulations of \((1+\alpha )\)-order lowpass filters with fractional steps from \(\alpha =0.1\) to \(\alpha =0.9\) are given as examples. SPICE simulations of 1.2-, 1.5-, and 1.8-order lowpass filters and experimental results of a 1.5-order filter using approximated fractional-order capacitors in a Multiple-Input Biquad circuit validate the implementation of these circuits.


Fractional-order circuits Fractional-order filters  Analog filter circuits Fractional calculus 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Todd J. Freeborn
    • 1
  • Ahmed S. Elwakil
    • 2
    Email author
  • Brent Maundy
    • 3
  1. 1.Department of Electrical and Computer EngineeringUniversity of AlabamaTuscaloosaUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of SharjahSharjahUnited Arab Emirates
  3. 3.Department of Electrical and Computer EngineeringUniversity of CalgaryCalgaryCanada

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