Compact design of four-phase fractional-order oscillator with independent phase and frequency control

This article presents a compact design of four-phase fractional-order sinusoidal oscillator employing three fractional capacitors and three differential voltage–current conveyors. The presented fractional oscillator enjoys the freedom of independent phase and frequency control. In the beginning of this work, the condition of oscillation and the frequency of oscillation have been derived since the traditional Barkhausen criterion does not guarantee the sustained oscillation in the fractional-order oscillator. Further, the dependencies of oscillation condition, frequency and phase on various circuit parameters have been studied explicitly. Stability analysis has also been performed by analysing pole-zero plots in fractional W-plane. Besides this, non-ideal characteristics and their effects on the oscillation frequency have also been studied by Monte Carlo analysis. At the end, the proposed oscillator has been simulated in PSpice environment using 0.5-μm CMOS model, to see the practical aspects of the presented design.