Fractional-order Wien-bridge oscillator

The classical Wien-bridge sinusoidal oscillator is studied, when both of the capacitors of the oscillator acquire a fractional order. Accordingly, the Wien oscillator is described by a set of fractional-order nonlinear differential equations. It is shown that sinusoidal oscillations are preserved but the phase-shift between the waveforms of the two state variables and the frequency of oscillation both depend on the fractional-order, leading to a significant advantage over the integer-type Wien oscillator. Findings are validated via numerical simulations.