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(jω)±α, where a is a constant and α is not necessarily an integer. As a result, these oscill...

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Bibliographic Details
Published in:International journal of circuit theory and applications 2008-06, Vol.36 (4), p.473-492
Main Authors: Radwan, A. G., Soliman, A. M., Elwakil, A. S.
Format: Article
Language:English
Subjects:
circuit theory
fractional calculus
fractional-order oscillators
oscillators
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Summary: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(jω)±α, where a is a constant and α 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.
ISSN:0098-9886
1097-007X
DOI:10.1002/cta.453