Analysis and Design of Fractional-order Low-pass Filter with Three Elements of Independent Orders

Abstract

This paper studies a new fractional-order form for the active low-pass filter. The form was mainly generated from generalizing an active second-order low-pass filter with three capacitors to the fractional-order domain with three independent orders. The transfer function introduced an extra term in the denominator comprising the third fractional order. The effect of the third fractional-order alongside the other transfer function coefficients on the critical frequencies had been studied numerically. For simulation purposes, Foster I realization had been utilized to synthesis the fractional-order capacitors approximated by using Matsuda technique. The simulation had been carried out on OrCAD showing matching results to the theoretical analysis with subtle error for the half-power frequency. Experimental work had been conducted on ELVIS II kit using off-the-shelf components and the results showed a match to the simulation profile with low error. Aside from that, complete design flow for active fractional-order filters had been followed in this work.