Fractional-order band-pass filter design using fractional-characteristic specimen functions

摘要

Two (alpha + beta)-order transfer functions realizing fractional-order band-pass filter responses are presented and analysed, where 0 alpha = 1 and 0 beta = 1. Generalizing the transfer functions from integer to fractional order offers continuous and independent control of the magnitude characteristic slopes both below and above the filter center frequency. The transfer function coefficients that minimize the magnitude error between the discussed fractional-order transfer functions and proposed fractional-characteristic specimen functions in a specified frequency band are determined using a numerical least squares optimization search routine. The relations for computing the transfer function coefficients as functions of alpha and beta are given. The simulations show that the magnitude frequency characteristics of the transfer functions with the new coefficients are very well matched with the specimen functions. Further verification of these results was carried out using the Tow-Thomas filter topology with RC approximations of fractional-order capacitors. The computation of filter element parameters is demonstrated for selected values of alpha and beta and the simulated and measured frequency characteristics of the filter are included to validate the fractional-order responses.