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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Abstract 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.
AbstractList 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 @@iLC@ tank resonator are given supported by numerical and PSpice simulations.
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.
Author Soliman, A.M.
Radwan, A.G.
Elwakil, A.S.
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  givenname: A.M.
  surname: Soliman
  fullname: Soliman, A.M.
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Cites_doi 10.1002/cta.453
10.1016/S0167-6911(00)00050-5
10.1142/S0218126608004162
10.1109/TCSII.2006.879102
10.1080/00207210210126952
10.1134/1.1448634
10.1006/jmaa.2000.7194
10.1016/j.chaos.2007.10.033
10.1016/j.sna.2004.11.025
10.1049/el:20010756
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References ref13
hartley (ref4) 1998
ref15
ref14
saito (ref9) 1993; e76
carlson (ref5) 1964; cas 11
ref17
ref18
matignon (ref16) 1996; 2
nakagawa (ref8) 1992; e75
samko (ref2) 1987
ref23
miller (ref3) 1993
ref25
ref20
abbisso (ref11) 2001; 3
ref22
ref21
steiglitz (ref7) 1964; 11
arena (ref12) 2002; 38
oldham (ref1) 1974
el-khazali (ref19) 2003; 12
budak (ref24) 1991
roy (ref6) 1967; cas 14
sugi (ref10) 1999; e82
References_xml – volume: 12
  start-page: 73
  year: 2003
  ident: ref19
  article-title: stability analysis of composite fractional systems
  publication-title: Int J Appl Math
– ident: ref22
  doi: 10.1002/cta.453
– volume: e76
  start-page: 205
  year: 1993
  ident: ref9
  article-title: simulation of power-law relaxations by analog circuits: fractal distribution of relaxation times and noninteger exponents
  publication-title: IEICE Trans Fundam Electron Commun Comput Sci
– ident: ref17
  doi: 10.1016/S0167-6911(00)00050-5
– year: 1974
  ident: ref1
  publication-title: Fractional calculus
– year: 1998
  ident: ref4
  article-title: initialization, conceptualization, and application in the generalized fractional calculus
  publication-title: National Aeronautics and Space Administration (NASA/TP-1998-208415)
– ident: ref25
  doi: 10.1142/S0218126608004162
– volume: cas 11
  start-page: 210
  year: 1964
  ident: ref5
  article-title: approximation of fractional capacitors by a regular newton process
  publication-title: IEEE Trans Circuits Syst
– year: 1993
  ident: ref3
  publication-title: An Introduction to the Fractional Calculus and Fractional Differential Equations
– ident: ref14
  doi: 10.1109/TCSII.2006.879102
– volume: 3
  start-page: 688
  year: 2001
  ident: ref11
  article-title: noninteger-order integration by using neural networks
  publication-title: Proc IEEE Int Symp Circuits Systems ISCAS 01
– volume: cas 14
  start-page: 264
  year: 1967
  ident: ref6
  article-title: on the realization of a constant-argument immitance or fractional operator
  publication-title: IEEE Trans Circuits Syst
– ident: ref15
  doi: 10.1080/00207210210126952
– volume: 11
  start-page: 160
  year: 1964
  ident: ref7
  article-title: an impedance approximation to
  publication-title: IEEE Trans Circuits Syst
– year: 1987
  ident: ref2
  publication-title: Fractional Integrals and Derivatives Theory and Applications
– year: 1991
  ident: ref24
  publication-title: Passive and Active Network Analysis And Synthesis
– volume: e82
  start-page: 1627
  year: 1999
  ident: ref10
  article-title: simulation of fractal immittance by analog circuits: an approach to the optimized circuits
  publication-title: IEICE Trans Fundam Electron Commun Comput Sci
– volume: e75
  start-page: 1814
  year: 1992
  ident: ref8
  article-title: basic characteristics of a fractance device
  publication-title: IEICE Trans Fundam Electron Commun Comput Sci
– ident: ref21
  doi: 10.1134/1.1448634
– volume: 38
  year: 2002
  ident: ref12
  article-title: nonlinear noninteger order circuits and systems
  publication-title: World Scientific Ser Nonlinear Sci
– volume: 2
  start-page: 963
  year: 1996
  ident: ref16
  article-title: stability results in fractional differential equations with applications to control processing
  publication-title: Proc IEEE-SMC Multiconf Comput Eng Syst Appl
– ident: ref18
  doi: 10.1006/jmaa.2000.7194
– ident: ref23
  doi: 10.1016/j.chaos.2007.10.033
– ident: ref13
  doi: 10.1016/j.sna.2004.11.025
– ident: ref20
  doi: 10.1049/el:20010756
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Snippet Sinusoidal oscillators are known to be realized using dynamical systems of second-order or higher. Here we derive the Barhkausen condition for a linear...
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SubjectTerms 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
Title Fractional-order sinusoidal oscillators: Design procedure and practical examples
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