Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters

Abstract
In this paper, a new two-steps design strategy is introduced for the optimal rational approximation of the fractional-order Butterworth filter. At first, the weighting factors of the summation between the nth -order and the (n+1)th -order Butterworth filters are optimally determined. Subsequently, this model is employed as an initial point for another optimization routine, which minimizes the magnitude-frequency error relative to the (n+)th -order, where (0,1) , Butterworth filter. The proposed approximant demonstrates improved performance about the magnitude mean squared error compared to the state-of-the-art design for six decades of bandwidth, but the introduced approach does not require a fractional-order transfer function model and the approximant of the s operator. The proposed strategy also avoids the use of the cascading technique to yield higher-order fractional-order Butterworth filter models. The performance of the proposed 1.5th-order Butterworth filter in follow-the-leader feedback topology is verified through SPICE simulations and its hardware implementation based on Analog Devices AD844AN-type current feedback operational amplifier.
Description
Citation
IEEE Access. 2021, vol. 9, issue 1, p. 81097-81114.
https://ieeexplore.ieee.org/document/9445054
Document type
Peer-reviewed
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Published version
Date of access to the full text
Language of document
en
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Comittee
Date of acceptance
Defence
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Document licence
Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
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