Editing Relaxation oscillator (section)

{{Short description|Oscillator that produces a nonsinusoidal repetitive waveform}}

[[File:Animated schmitt-trigger-oscillator.gif|thumb|Simple relaxation oscillator made by [[Feedback|feeding back]] an inverting [[Schmitt trigger]]'s output voltage through a [[RC network]] to its input.]]

In [[electronics]], a '''relaxation oscillator''' is a [[linear circuit|nonlinear]] [[electronic oscillator]] circuit that produces a [[Non-sinusoidal waveform|nonsinusoidal]] repetitive output signal, such as a [[triangle wave]] or [[Square wave (waveform)|square wave]].<ref name="Graf">{{cite book   
  | last = Graf
  | first = Rudolf F. 
  | title = Modern Dictionary of Electronics
  | publisher = Newnes
  | date = 1999
  | pages = 638
  | url = https://books.google.com/books?id=uah1PkxWeKYC&pg=PA638
  | isbn = 0750698667}}</ref><ref name="Edson">{{cite book   
  | last = Edson
  | first = William A.
  | title = Vacuum Tube Oscillators
  | publisher = John Wiley and Sons
  | date = 1953
  | location = New York
  | pages = 3
  | url = http://www.tubebooks.org/Books/vto.pdf
  }} on Peter Millet's [http://www.tubebooks.org Tubebooks] website</ref><ref name=" Morris">{{cite book   
  | last =  Morris
  | first = Christopher G. Morris
  | title = Academic Press Dictionary of Science and Technology
  | publisher = Gulf Professional Publishing
  | date = 1992
  | pages = 1829
  | url = https://books.google.com/books?id=nauWlPTBcjIC&pg=PA1829
  | isbn = 0122004000 }}</ref><ref name="Du">{{cite book   
  | last = Du
  | first = Ke-Lin
  |author2=M. N. S. Swamy 
  | title = Wireless Communication Systems: From RF Subsystems to 4G Enabling Technologies
  | publisher = Cambridge Univ. Press
  | date = 2010
  | pages = 443
  | url = https://books.google.com/books?id=5dGjKLawsTkC&q=%22relaxation+oscillator&pg=PA443
  | isbn = 978-1139485760}}</ref> The circuit consists of a [[feedback loop]] containing a switching device such as a [[transistor]], [[comparator]], [[relay]],<ref name="Varigonda">{{cite journal
  | last = Varigonda
  | first = Subbarao 
  |author2=Tryphon T. Georgiou
   | title = Dynamics of Relay Relaxation Oscillators
  | journal = IEEE Transactions on Automatic Control
  | volume = 46
  | issue = 1
  | pages = 65
  | publisher = Inst. of Electrical and Electronic Engineers
  | date = January 2001
  | url = http://www.ece.umn.edu/~georgiou/papers/DynamicsOfRelay.pdf
  | doi = 10.1109/9.898696
  | accessdate = February 22, 2014}}</ref> [[op amp]],  or a [[negative resistance]] device like a [[tunnel diode]],  that repetitively charges a [[capacitor]] or [[inductor]] through a resistance until it reaches a threshold level, then discharges it again.<ref name="Du" /><ref name="HyperPhysics">{{cite web
  | last = Nave
  | first = Carl R.
  | title = Relaxation Oscillator Concept
  | work = [[HyperPhysics]]
  | publisher = Dept. of Physics and Astronomy, Georgia State Univ.
  | date = 2014
  | url = http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/relaxo.html
  | accessdate = February 22, 2014}}</ref> The [[frequency|period]] of the oscillator depends on the [[time constant]] of the capacitor or inductor circuit.<ref name="Edson" /> The active device switches abruptly between charging and discharging modes, and thus produces a discontinuously changing repetitive waveform.<ref name="Edson" /><ref name="Du" /> This contrasts with the other type of electronic oscillator, the harmonic or [[electronic oscillator#linear oscillator|linear oscillator]], which uses an [[amplifier]] with feedback to excite [[resonant]] oscillations in a [[resonator]], producing a [[sine wave]].<ref name="Oliveira">{{cite book   
  | last = Oliveira
  | first = Luis B. 
  | title = Analysis and Design of Quadrature Oscillators
  | publisher = Springer
  | date = 2008
  | pages = 24
  | url = https://books.google.com/books?id=e5Yck9AWiPkC&pg=PA24
  | isbn = 978-1402085161|display-authors=etal}}</ref>

[[Image:Turnsignals On.jpg|thumb|upright=0.7|The blinking [[turn signal]] on some motor vehicles is generated by a simple relaxation oscillator powering a [[relay]].]]

Relaxation oscillators may be used for a wide range of frequencies, but as they are one of the oscillator types suited to low frequencies, below audio, they are typically used for applications such as blinking lights ([[Automotive lighting|turn signals]]) and [[Buzzer|electronic beepers]], as well as [[voltage controlled oscillator]]s (VCOs), [[inverter]]s, [[Switching power supply|switching power supplies]], [[dual-slope ADC|dual-slope analog to digital converter]]s, and [[function generator]]s.

The term ''relaxation oscillator'', though often used in electronics engineering, is also applied to [[dynamical system]]s in many diverse areas of science that produce nonlinear oscillations and can be analyzed using the same mathematical model as electronic relaxation oscillators.<ref name="Wang">{{cite conference
  | first = Wang
  | last = DeLiang
  | title = Relaxation oscillators and networks
  | book-title = Wiley Encyclopedia of Electrical and Electronics Engineering, Vol. 18
  | pages = 396–405
  | publisher = Wiley & Sons
  | date = 1999
  | url = http://www.cse.ohio-state.edu/~dwang/papers/Wang99.pdf
  | accessdate = February 2, 2014}}</ref><ref name="Sauro">{{cite web
  | last = Sauro
  | first = Herbert M.
  | title = Oscillatory Circuits 
  | work = Class notes on oscillators: Systems and Synthetic Biology
  | publisher = Sauro Lab, Center for Synthetic Biology, University of Washington
  | date = 2009
  | url = https://digital.lib.washington.edu/researchworks/bitstream/handle/1773/44940/OscillatoryCircuits_Sauro_2019.pdf?sequence=1&isAllowed=y
  | accessdate = November 12, 2019}},</ref><ref name="Letellier1">{{cite book   
  | last = Letellier
  | first = Christopher 
  | title = Chaos in Nature
  | publisher = World Scientific
  | date = 2013
  | pages = 132–133
  | url = https://books.google.com/books?id=Lpc0KhOaioIC&pg=PA132
  | isbn = 978-9814374422}}</ref><ref name="Ginoux1">{{cite journal
  | last1  = Ginoux
  | first1 = Jean-Marc
  | last2  = Letellier
  | first2 = Christophe 
  | title = Van der Pol and the history of relaxation oscillations: toward the emergence of a concept
  | journal = Chaos
  | volume = 22
  | issue = 2
  | pages = 023120
  | date = June 2012
  | url = https://hal.archives-ouvertes.fr/hal-01056923/document
  | doi = 10.1063/1.3670008
  | accessdate = December 24, 2014| arxiv = 1408.4890
  | bibcode = 2012Chaos..22b3120G
  | pmid = 22757527
 | s2cid = 293369
 }}</ref> For example, geothermal [[geyser]]s,<ref name="Enns">{{cite book   
  | last = Enns
  | first = Richard H.
  |author2=George C. McGuire
   | title = Nonlinear Physics with Mathematica for Scientists and Engineers
  | publisher = Springer
  | date = 2001
  | pages = 277
  | url = https://books.google.com/books?id=TPyUQ1xnjBoC&q=%22relaxation+oscillator&pg=PA277
  | isbn = 0817642234}}</ref><ref name="Pippard">{{cite book   
  | last = Pippard
  | first = A. B. 
  | title = The Physics of Vibration
  | publisher = Cambridge Univ. Press
  | date = 2007
  | pages = 359–361
  | url = https://books.google.com/books?id=F8-9UNvsCBoC&pg=PA360
  | isbn = 978-0521033336}}</ref> networks of firing [[nerve cell]]s,<ref name="Ginoux1" /> [[thermostat]] controlled heating systems,<ref name="Pippard1">[https://books.google.com/books?id=F8-9UNvsCBoC&pg=PA41    Pippard, The Physics of Vibration, p. 41-42]</ref> coupled chemical reactions,<ref name="Sauro" /> the beating human heart,<ref name="Ginoux1" /><ref name="Pippard1" /> earthquakes,<ref name="Enns" /> the squeaking of chalk on a blackboard,<ref name="Pippard1" /> the cyclic populations of predator and prey animals, and [[gene activation]] systems<ref name="Sauro" /> have been modeled as relaxation oscillators.  Relaxation oscillations are characterized by two alternating processes on different time scales: a long [[relaxation (physics)|relaxation]] period during which the system approaches an [[equilibrium point]], alternating with a short impulsive period in which the equilibrium point shifts.<ref name="Ginoux1" /><ref name="Enns" /><ref name="Pippard" /><ref name="Kinoshita">{{cite conference
  | first = Shuichi
  | last = Kinoshita
  | title = Introduction to Nonequilibrium Phenomena
  | book-title = Pattern Formations and Oscillatory Phenomena
  | pages = 17
  | publisher = Newnes
  | date = 2013
  | url = https://books.google.com/books?id=geQWCKsFhcUC&pg=PA17
  | isbn = 978-0123972996
  | accessdate = February 24, 2014}}</ref>  The [[frequency|period]] of a relaxation oscillator is mainly determined by the [[relaxation time]] constant.<ref name="Ginoux1" />  Relaxation oscillations are a type of [[limit cycle]] and are studied in [[nonlinear control]] theory.<ref name="Leigh">see Ch. 9, "Limit cycles and relaxation oscillations" in {{cite book   
  | last =  Leigh
  | first = James R.
  | title = Essentials of Nonlinear Control Theory
  | publisher = Institute of Electrical Engineers
  | date = 1983
  | pages = 66–70
  | url = https://books.google.com/books?id=oejayuS7ZB8C&q=%22relaxation+oscillations&pg=PA70
  | isbn = 0906048966}}</ref>