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==Relaxation oscillator== {{Main|Relaxation oscillator}} [[File:OpAmpHystereticOscillator.svg|thumb|A popular [[op-amp]] [[Relaxation oscillator#Comparator–based electronic relaxation oscillator|relaxation oscillator]].]] A '''nonlinear''' or '''[[relaxation oscillator]]''' produces a non-sinusoidal output, such as a [[Square wave (waveform)|square]], [[sawtooth wave|sawtooth]] or [[triangle wave]].<ref name="Garg" /><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=" 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> It consists of an energy-storing element (a [[capacitor]] or, more rarely, an [[inductor]]) and a nonlinear switching device (a [[Latch (electronics)|latch]], [[Schmitt trigger]], or [[negative resistance]] element) connected in a [[feedback loop]].{{sfn|Gottlieb|1997|p=69-73}}<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 switching device periodically charges the storage element with energy and when its voltage or current reaches a threshold discharges it again, thus causing abrupt changes in the output waveform.<ref name="van der Tang">{{cite book | last1 = van der Tang | first1 = J. | last2 = Kasperkovitz | first2 = Dieter | last3 = van Roermund | first3 = Arthur H.M. | title = High-Frequency Oscillator Design for Integrated Transceivers | publisher = Springer Science and Business Media | date = 2006 | location = | pages = 20 | language = | url = https://books.google.com/books?id=0rniokw7bLkC&dq=%22ring+oscillator%22+oscillator+relaxation&pg=PA20 | archive-url= | archive-date= | doi = | id = | isbn = 0306487160 | mr = | zbl = | jfm =}}</ref>{{rp|p.20}} Although in the past negative resistance devices like the [[unijunction transistor]], [[thyratron]] tube or [[neon lamp]] were used,{{sfn|Gottlieb|1997|p=69-73}} today relaxation oscillators are mainly built with [[integrated circuits]] like the [[555 timer IC]]. Square-wave relaxation oscillators are used to provide the [[clock signal]] for [[sequential logic]] circuits such as timers and [[digital counter|counters]], although [[crystal oscillator]]s are often preferred for their greater stability.<ref name="Patrick">{{cite book | last1 = Patrick | first1 = Dale R. | last2 = Fardo | first2 = Stephen W. | last3 = Richardson | first3 = Ray E. | title = Electronic Devices and Circuit Fundamentals | publisher = CRC Press | date = 2023 | language = | url = https://books.google.com/books?id=tZK4EAAAQBAJ&pg=PT767 | doi = | id = | isbn = 9781000879773 | mr = | zbl = | jfm =}}</ref>{{rp|p.20.1}} Triangle-wave or sawtooth oscillators are used in the timebase circuits that generate the horizontal deflection signals for [[cathode-ray tube]]s in analogue [[oscilloscope]]s and [[television]] sets.<ref name="Patrick" />{{rp|p.20.1}} They are also used in [[voltage-controlled oscillator]]s (VCOs), [[inverter]]s and [[switching power supply|switching power supplies]], [[dual-slope ADC|dual-slope analog to digital converter]]s (ADCs), and in [[function generator]]s to generate square and triangle waves for testing equipment. In general, relaxation oscillators are used at lower frequencies and have poorer frequency stability than linear oscillators. [[Ring oscillator]]s are built of a ring of active delay stages, such as [[inverter (logic gate)|inverter]]s.<ref name="van der Tang" />{{rp|p.20}} Generally the ring has an odd number of inverting stages, so that there is no single stable state for the internal ring voltages. Instead, a single transition propagates endlessly around the ring. Some of the more common relaxation oscillator circuits are listed below: *[[Multivibrator]] *[[Pearson–Anson effect|Pearson–Anson oscillator]] *[[Ring oscillator]] *[[Delay-line oscillator]] *[[Royer oscillator]]
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