| Summary: | 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 <inline-formula> <tex-math notation="LaTeX">${n}^{\text {th}}$ </tex-math></inline-formula>-order and the <inline-formula> <tex-math notation="LaTeX">$(n + 1)^{\text {th}}$ </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">$(n+\alpha)^{\text {th}}$ </tex-math></inline-formula>-order, where <inline-formula> <tex-math notation="LaTeX">$\alpha \in (0, 1)$ </tex-math></inline-formula>, 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 <inline-formula> <tex-math notation="LaTeX">$s^\alpha $ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$1.5^{\text {th}}$ </tex-math></inline-formula>-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.
|
|---|