Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE Framework

Abstract

This paper presents the optimal rational approximation of (1+α) order Butterworth filter, where α ∊ (0,1) under the continued fraction expansion framework, by employing a new cost function. Two simple techniques based on the constrained optimization and the optimal pole-zero placements are proposed to model the magnitude-frequency response of the fractional-order lowpass Butterworth filter (FOLBF). The third-order FOLBF approximants achieve good agreement to the ideal characteristic for six decades of design bandwidth. Circuit realization using the current feedback operational amplifier is presented, and the modelling efficacy is validated in the OrCAD PSPICE platform.

Keywords

• biquadratic approximation
• Butterworth filter
• continued fraction expansion
• current feedback operational amplifier
• fractional-order filter design
• optimization