Performance and Stability Improvement of Fractional Order RC-Phase Shift Oscillator

Abstract

The work presented, describes the design of a RC-Phase shift oscillator in fractional domain is illustrated using Foster-1 approximated fractional-capacitor. Here the simulated analysis is carried out using three fractional-capacitors $FC_{1}, \ FC_{2}$, and $FC_{3}$ bearing different non-dependent fractional-orders $\alpha,\ \beta$, and $\gamma$. respectively in the Fractional-order RC-phase shift oscillator. The phase shifting section of the proposed fractional-order oscillator has been investigated by simulating time and frequency-domain responses in MATLAB. In frequency-domain, it is envisaged that maximum phase-shift depends on varying the fractional-orders, which enhances the degree of design freedom. Later, in this paper simulation studies for stability analysis have been performed to explore the dependence of different parameters (rise-time, peak-overshoot, settling-time) of the proposed oscillators on the fractional-exponents.