(3 + α)-Order Transfer Functions for Approximating Butterworth-Type Flat Passband Characteristics

In this work, the design and implementation of (3+α) order transfer functions to approximate the flat-passband characteristics of Butterworth type low-pass filters are presented. A numerical optimization approach is adopted to identify the transfer function coefficients necessary for the flat-pass band characteristics. The transfer function with the least error (compared to the ideal Butterworth response) is implemented in simulation and realized experimentally to validate the performance of the proposed (3 + α) = 3.75 order design. The physical circuits are implemented using Analog Devices AD844 current-feedback operational amplifiers and an approximated fractional-order capacitor realized using a 7-th order RC ladder design. Experimental magnitude and phase from 1 Hz to 100 kHz validate the proposed design.