FRACTIONAL ORDER OSCILLATORS USING OTAs

Abstract

Fractional order harmonic oscillators are sinusoidal oscillators in which, the reactive element, instead of being an integer order capacitor/inductor, is a fractional order reactive element, also referred as a constant phase element (CPE). The interest in these fractional order oscillators have stemmed from the fact that, unlike a conventional RC oscillator, the frequency and phase relationships in a fractional order oscillator are functions of the fractional order parameters α, β, γ… defining the CPE. Though the concept of a fractional order oscillator was introduced in the context of an FM demodulation system long back, it could not gather much attention till the early 2000s. The detailed theoretical framework for the general fractional order oscillators, however, was developed during the early years of the last decade, when wherein the design equations for CO and FO of fractional order oscillators were presented. Since then, many fractional order oscillator circuits employing different types of amplifiers and other active building blocks have been presented. Out of the fractional order oscillators reported, those oscillators which employ the OTA, are of special interest, as the control over the FO, CO and phase in these oscillator circuits can be implemented very easily by changing the bias currents of the OTAs. Very little work is available in open literature, wherein, fractional order oscillators have been realized with OTAs. In this work, we have presented OTA based fractional order oscillators, which employ two/three fractional order capacitors and five OTAs, providing two/three output voltages with electronically controllable phase difference between them. The dependence of FO, CO and phase difference between the output voltages on α, β and γ has been investigated in detail.