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Fractional-Order Sinusoidal Oscillators: Design Procedure and Practical Examples

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3 Author(s)
Radwan, A.G. ; Dept. of Eng. Math., Cairo Univ., Cairo ; Elwakil, A.S. ; Soliman, Ahmed M.

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.

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:55 ,  Issue: 7 )