Approximation of Fractional-Order Butterworth Filter Using Pole-Placement in W-Plane

This work presents a new technique to approximate the fractional-order Butterworth filter using the pole-placement in the W-plane. Initially, poles of the fractional-order Butterworth transfer function are obtained by replacing the complex frequency s with a new variable (\boldsymbol {s}')^{2N...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Express briefs, 2021-10, Vol.68 (10), p.3229-3233
Main Authors: Mishra, Shalabh K., Upadhyay, Dharmendra K., Gupta, Maneesha
Format: Article
Language:English
Subjects:
Butterworth filters
Circuits
Circuits and systems
Eigenvalues
Eigenvectors
Filtering algorithms
fractional-order
Information filters
Matched filters
Passband
Placement
pole-placement technique
Poles
Sallen-Key
SPICE
stability
Transfer functions
W-plane
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Summary:This work presents a new technique to approximate the fractional-order Butterworth filter using the pole-placement in the W-plane. Initially, poles of the fractional-order Butterworth transfer function are obtained by replacing the complex frequency s with a new variable (\boldsymbol {s}')^{2N/\alpha } . These poles and their complex-conjugate counterparts are plotted in {W} -plane. Half of these poles, lying in the stable regions, are chosen to derive the characteristic equation of the fractional Butterworth filter. Therefore, the proposed fractional-order filters are inherently stable. Further, a 1.5 th order Butterworth filter is designed using the proposed technique, and realized using the fractional-order Sallen-Key circuit. Additionally, several other higher order fractional Butterworth filters are realized using the proposed pole-placement technique. Finally, PSpice and MATLAB based simulations have been done to see the accuracy and effectiveness of the proposed design technique.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2021.3074076