One active element implementation of fractional-order Butterworth and Chebyshev filters

Abstract

Fractional-order low-pass and high-pass Butterworth and Chebyshev filters with cut-off frequencies determined independently of their order are approximated in this work. The already available schemes in the literature have a cut-off frequency pre-determined by the pole frequency value, and hence the filter’s order. The derivation of rational integer-order approximation functions, which approximate the frequency behavior of the filters, is performed through the utilization of a magnitude curve-fitting based method. The form of the transfer function is common for all filter functions, providing design versatility. Implementation is performed using just one active element, leading to a structure with minimized active component count. The evaluation of the accuracy of the employed approximation method is performed through numerical and experimental results, while the evaluation of the behavior of the active circuit topology is done using circuit simulations.