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Mathematical Problems in Engineering
Volume 2013, Article ID 726721, 10 pages
Research Article

Fractional Resonance-Based Filters

1Department of Electrical and Computer Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4
2Department of Electrical and Computer Engineering, University of Sharjah, P.O. Box 27272, Sharjah, UAE

Received 17 September 2012; Accepted 20 December 2012

Academic Editor: József Kázmér Tar

Copyright © 2013 Todd J. Freeborn et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose the use of a fractional order capacitor and fractional order inductor with orders ,   , respectively, in a fractional series circuit to realize fractional-step lowpass, highpass, bandpass, and bandreject filters. MATLAB simulations of lowpass and highpass responses having orders of , 1.5, and 1.9 and bandpass and bandreject responses having orders of 1.5 and 1.9 are given as examples. PSPICE simulations of 1.1, 1.5, and 1.9 order lowpass and 1.0 and 1.4 order bandreject filters using approximated fractional order capacitors and fractional order inductors verify the implementations.