Design equations for fractional-order sinusoidal oscillators: Four practical circuit examples


Four practical sinusoidal oscillators are studied in the general form where fractional-order energy storage elements are considered. A fractional-order element is one whose complex impedance is given by Z = a(j?) ±?, where ? is a constant and a is not necessarily an integer. As a result, these oscillators are described by sets of fractional-order differential equations. The integer-order oscillation condition and oscillation frequency formulae are verified as special cases. Numerical and PSpice simulation results are given. Experimental results are also reported for a selected Wien-bridge oscillator. Copyright © 2007 John Wiley & Sons, Ltd.


Radwan A.G., Soliman A.M., Elwakil A.S.


Circuit theory; Fractional calculus; Fractional-order oscillators; Oscillators

Document Type



International Journal of Circuit Theory and Applications, Vol. 36, PP. 473 to 492, Doi: 10.1002/cta.453

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