Sinusoidal oscillators are known to be realized using dynamical systems of second-order or higher. Here we derive the Barhkausen condition for a linear noninteger-order (fractional-order) dynamical system to oscillate. We show that the oscillation condition and oscillation frequency of some famous integer-order sinusoidal oscillators can be obtained as special cases from general equations governing their fractional-order counterparts. Examples including fractional-order Wien oscillators, Colpitts oscillator, phase-shift oscillator and LC tank resonator are given supported by numerical and PSpice simulations. © 2008 IEEE.
Radwan A.G., Elwakil A.S., Soliman A.M.
Fractional-order circuits; Noninteger order systems; Oscillators
IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 55, PP. 2051 to 2063, Doi: 10.1109/TCSI.2008.918196