Optimal Design of (α + β)-Order Butterworth Filter and Its Realization Using RLβCα Circuit

This paper presents the implementation of an optimal fractional-order Butterworth filter (FBF) using the RLβCα, where 0 < α, β < 1, series circuit. Improved Particle Swarm Optimization algorithm is used to determine the coefficients of three s-domain based fractional-order transfer functions that approximate the FBF characteristics, such that the condition of 0 dB gain at DC is satisfied. Stability, roll-off, accuracy, and algorithm convergence for the proposed FBFs are evaluated. The proposed designs achieve significantly lower error as compared to the recent literature. The Bruton transformation, generalized to the fractional domain, is employed to realize inductor-less FBF circuits. Simulations are carried out in OrCAD PSPICE to verify the design feasibility.