Fractional-order sinusoidal oscillators: Design procedure and practical examples

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 i...

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Veröffentlicht in:IEEE transactions on circuits and systems. I, Regular papers Jg. 55; H. 7; S. 2051 - 2063
Hauptverfasser: Radwan, A.G., Elwakil, A.S., Soliman, A.M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.08.2008
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Capacitors
Circuit simulation
Circuits
Computer simulation
Design engineering
Differential equations
Dynamical systems
Finite element methods
Fractional-order circuits
Frequency
Inductors
Laplace equations
Mathematical analysis
noninteger order systems
Oscillations
Oscillators
Probes
Resistors
Tanks
ISSN:1549-8328, 1558-0806
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Zusammenfassung: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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ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2008.918196