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Design equations for fractional‐order sinusoidal oscillators: Four practical circuit examples
Author(s) -
Radwan A. G.,
Soliman A. M.,
Elwakil A. S.
Publication year - 2008
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.453
Subject(s) - oscillation (cell signaling) , integer (computer science) , order (exchange) , mathematics , fractional calculus , bridge (graph theory) , differential equation , mathematical analysis , computer science , medicine , genetics , finance , economics , biology , programming language
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.