Realization of optimized fractional-order symmetric-slope bandpass filter using switched-capacitors

Here, the design, simulation, and modelling of a symmetric-slope fractional-order bandpass filter (FOBPF) using four fractional capacitors of orders α0,β0,α1,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _0, \beta _0, \alpha _1,$$\end{document} and β1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1$$\end{document} has been explored. The characteristics of cascaded integer order bandpass filters (IOBPF) are well established. However, this is not so far for a FOBPF. Different issues in frequency and time response as obtained from different combinations of fractional orders with a stepping value of 0.1 have been elaborated in this work. The genetic algorithm optimization technique has been used here to determine the fractional orders of each fractional capacitors (FC1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${FC_1}$$\end{document} and FC2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${FC_2}$$\end{document}) providing the maximum quality factor of the filter. The proposed FOBPF has achieved a quality factor of 11.47 as comapred to the quality factor of 0.44 in case of an integer order filter. The parameters of the proposed filter were derived analytically and then compared with the experimental observations using an RC-Symmetric approximated fractional capacitor and general impedance converter (GIC). The second phase of the work deals with the application of switched-capacitors in the proposed filter circuit. It has also been observed in simualtion as well as experimental analysis that incorporation of switched-capacitor in place of resistors reduces settling time and hence increases the speed of response.