(N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response

The formula of the all-pole low-pass frequency filter transfer function fractional order (N + α) designated for implementation by non-cascade multiple-feedback analogue structures is presented. aim to determine coefficients this and its possible variants depending on distribution fractional-order terms in function. Optimization algorithm used approximate target Butterworth magnitude response, whereas approximation errors are evaluated. interpolated equations computing provided. An example transformation high-pass also results verified simulation with operational transconductance amplifiers element.