Modelling of Inverse Fractional-Order Band-pass and Band-stop Filters using Fractional-Elements

Abstract

This paper discusses the analysis of inverse fractional-order band-pass and band-stop filter in frequency domain. The control models of the proposed fractional-order filters are examined using fractional-capacitor and fractional-inductors bearing impedances ${z_c} = \frac{1}{{{s^\alpha }}}$ and z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> = Ls <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</sup> respectively with orders varying as 0.1<α<1.0 and 0.1<β1.0. The mathematical models of both the filters are obtained and the magnitude as well as the phase equations are derived. The design parameters are compared with its classical order counterpart and the dependencies of fractional-orders (α, β) are resulted with the center frequency, bandwidth, selectivity and roll-off-rates using MATLAB/Simulink. Here, a higher selectivity bandpass response is obtained using fractional-order inverse band-stop filter topology. Whereas, a higher bandwidth band-stop filter is realized using fractional-order inverse bandpass topology.