Design of Fractional-order Transitional Filters of the Butterworth-Sync-Tuned, Butterworth-Chebyshev, and Chebyshev-Sync-Tuned Types: Optimization, Simulation, and Experimental Verification

Abstract

This paper presents the optimal and generalized design of three different fractional-order (FO) transitional filters for the first time in the literature. The transitional filters considered are of the FO Butterworth-sync-tuned, the FO Butterworth-Chebyshev, and the FO Chebyshev-sync-tuned types. A metaheuristic swarm intelligence optimizer, namely the Crow Search Algorithm (CSA), helps to achieve the optimal FO filter model that minimizes the magnitude error with the theoretical function. The accuracy of the proposed approximants is examined for 19 different combinations of orders of the constituent filters for each of the three types of FO transitional filters. Comparisons with the modified stability boundary locus-based second-, third-, and fourth-order filter approximants demonstrate the compactness and superior accuracy of the proposed models. The average performance regarding the approximation accuracy, computational time, and convergence of CSA for solving the proposed filter design problems is investigated. Circuit simulations conducted on the OrCAD PSPICE platform for the proposed filter using the current feedback operational amplifier as an active element highlight good matching between the proposed model and theoretical filter function. Experimental validation is also carried out to justify the practical feasibility of the proposed filter with printed circuit board fabricated FO capacitor emulators.