Design & Analysis of CPE Based Fractional Filters

In this paper, a design and analysis of a constant phase element (CPE) based fractional-order filter (FOF) is presented. This paper leverages a voltage differencing transconductance amplifier (VDTA) to design a current-mode fractional-order filter, capable of realizing four types: low-pass, high-pass, band-pass, and band-reject, all with just two VDTAs. The circuit utilizes both a standard integer-order capacitor and a novel fractional-order capacitor. The proposed filter is resistor-less and electronically tunable. Mathematical formulations are outlined for the transfer functions of FOF. All the filter responses are obtained at varying value of
$\alpha=0.5,0.6$
, 0.7, 0.8 and 0.9. All the simulations are carried out using Cadence Virtuoso at 45nm CMOS technology node.