Design and implementation of DDCC-based fractional-order oscillator

Abstract

A differential difference current conveyor (DDCC)-based fractional-order sinusoidal oscillator is presented. In this work, the condition of oscillation and the oscillation frequency are derived initially, and then the variation in its phase and frequency for different orders are studied. Stability of the proposed fractional oscillator is analysed using its pole-zero and root-locus plots in fractional W-plane. The dependence of oscillation frequency on its various circuit parameters is investigated and depicted in 3−D plots. Variation in the oscillation frequency due to the tracking error of DDCCs is analysed using Monte Carlo analysis. Moreover, a simple technique is also introduced to approximate a fractance device (FD) suitable for fractional oscillators by a single R−C parallel pair, in place of the existing complex and bulky semi-infinite tree or ladder circuits. Then, a fractional-order capacitor is realized using this technique to simulate the proposed fractional-order oscillator in PSpice environment. Finally, the proposed fractional oscillator is implemented practically to see the effectiveness of the proposed design.