Electronically Tunable Fractional Order Filter

Abstract

In this paper, an electronically tunable resistorless fractional order filter (FOF) based on operational transconductance amplifier (OTA) is presented. It uses two fractional capacitors (FC) of same order and provides fractional order low-pass filter and fractional order band-pass filter responses simultaneously. Mathematical formulations are outlined for various critical frequencies and transfer function sensitivities for presented FOF. The FCs of orders 0.5 and 0.9 are considered for illustrating the proposal. The FCs are realized using the fourth-order continued fraction expansion-based RC ladder and are characterized using SPICE simulations. Functional verification of presented FOF with FC of orders 0.5 and 0.9 is exhibited through SPICE simulations. The OTA is implemented using $$0.5\,\upmu \hbox {m}$$ CMOS technology model parameters. Electronic tunability of half power and right-phase frequencies of presented FOF is achieved through bias current variation of OTA. The transfer functions’ sensitivity with respect to various circuit parameters is also examined through simulations, and it is found that the values remain well within unity for most of the circuit parameters. Furthermore, the presented FOF is attractive from integration viewpoint as it achieves tunability via bias current variation in contrast to tuning through resistor variation in existing FOFs.