Editing Relaxation oscillator (section)

==Electronic relaxation oscillators==
[[Image:Vacuum tube multivibrator calibrating wavemeter 1920.jpg|thumb|upright=1.4|A vacuum tube Abraham-Bloch multivibrator relaxation oscillator, France, 1920 ''(small box, left)''.  Its harmonics are being used to calibrate a wavemeter ''(center)''.]]
[[Image:Original Abraham-Bloch multivibrator circuit.png|thumb|Original [[vacuum tube]] Abraham-Bloch multivibrator oscillator, from their 1919 paper]]

The first relaxation oscillator circuit, the [[astable multivibrator]], was invented by [[Henri Abraham]] and [[Eugene Bloch]] using [[vacuum tube]]s during [[World War I]].<ref name="Abraham">{{cite journal
  | last = Abraham
  | first = H.
  |author2=E. Bloch
   | title = Mesure en valeur absolue des périodes des oscillations électriques de haute fréquence (Measurement of the periods of high frequency electrical oscillations)
  | journal = Annales de Physique
  | volume = 9
  | issue = 1
  | pages = 237–302
  | publisher = Société Française de Physique
  | location = Paris
  | date = 1919
  | url = http://hal.archives-ouvertes.fr/docs/00/24/20/12/PDF/ajp-jphystap_1919_9_211_0.pdf
  | doi = 10.1051/jphystap:019190090021100
  }}</ref><ref name="Ginoux">{{cite journal   
  | last = Ginoux
  | first = Jean-Marc 
  | title = Van der Pol and the history of relaxation oscillations: Toward the emergence of a concepts 
  | journal = Chaos: An Interdisciplinary Journal of Nonlinear Science 
 | publisher = Chaos 22 (2012) 023120
  | date = 2012
  | volume = 22 
 | issue = 2 
 | page = 023120 
 | doi = 10.1063/1.3670008
  | pmid = 22757527 
 | arxiv =1408.4890| bibcode =2012Chaos..22b3120G| s2cid = 293369 
 }}</ref>  [[Balthasar van der Pol]] first distinguished relaxation oscillations from harmonic oscillations, originated the term "relaxation oscillator", and derived the first mathematical model of a relaxation oscillator, the influential [[Van der Pol oscillator]] model, in 1920.<ref name="Ginoux" /><ref name="van der Pol1">{{cite journal
  | last = van der Pol
  | first = B.
  | title = A theory of the amplitude of free and forced triode vibrations 
  | journal = Radio Review
  | volume = 1
  | pages = 701–710, 754–762
  | date = 1920
  }}</ref><ref name="Van der Pol">{{cite journal
 | last = Van der Pol
 | first = Balthazar
 | title = On relaxation-oscillations
 | journal = The London, Edinburgh and Dublin Philosophical Magazine
 | volume = 2
 | issue = 7
 | pages = 978–992
 | year = 1927
 | url = http://audiophile.tam.cornell.edu/randdocs/classics/vanderpol.pdf
 | doi = 10.1080/14786442608564127
 }}</ref>  Van der Pol borrowed the term ''[[relaxation (physics)|relaxation]]'' from mechanics; the discharge of the capacitor is analogous to the process of ''[[stress relaxation]]'', the gradual disappearance of deformation and return to equilibrium in an [[inelastic]] medium.<ref name="Shukla">{{cite journal
  | first = Jai Karan N.
  | last =  Shukla
  | title = Discontinuous Theory of Relaxation Oscillators
  | version = Master of Science thesis
  | publisher = Dept. of Electrical Engineering, Kansas State Univ.
  | date = 1965
  | url = https://archive.org/stream/discontinuousthe00shuk#page/n1/mode/2up
  | accessdate = February 23, 2014}}</ref>   
Relaxation oscillators can be divided into two classes<ref name="Pippard" />
*'''''Sawtooth, sweep, or flyback oscillator''''':  In this type the energy storage capacitor is charged slowly but discharged rapidly, essentially instantly, by a short circuit through the switching device.  Thus there is only one "ramp" in the output waveform which takes up virtually the entire period.  The voltage across the capacitor approximates a [[sawtooth wave]], while the current through the switching device is a sequence of short pulses.
*'''''[[Astable multivibrator]]''''': In this type the capacitor is both charged and discharged slowly through a resistor, so the output waveform consists of two parts, an increasing ramp and a decreasing ramp.  The voltage across the capacitor approximates a [[triangle wave]]form, while the current through the switching device approximates a square wave.
Before the advent of microelectronics, simple relaxation oscillators often used a [[negative resistance]] device with [[hysteresis]] such as a [[thyratron]] tube,<ref name="Puckle" /> [[neon lamp]],<ref name="Puckle" /> or [[unijunction transistor]], however today they are more often built with dedicated integrated circuits such as the [[555 timer IC|555 timer]] chip.

===Applications===
Relaxation oscillators are generally used to produce low [[frequency]] signals for such applications as blinking lights and electronic beepers. During the vacuum tube era they were used as oscillators in electronic organs and horizontal deflection circuits and time bases for [[Cathode-ray tube|CRT]] [[oscilloscope]]s; one of the most common was the Miller integrator circuit invented by [[Alan Blumlein]], which used vacuum tubes as a constant current source to produce a very linear ramp.<ref name="Puckle">{{cite book
 | last1  = Puckle
 | first1 = O. S.
 | title  = Time Bases (Scanning Generators), 2nd Ed.
 | publisher = Chapman and Hall, Ltd.
 | date   = 1951
 | location = London
 | pages  = [https://archive.org/details/TimeBasesTheirDesignDevelopment/page/n96 15]–27
 | url    = https://archive.org/details/TimeBasesTheirDesignDevelopment
 }}</ref>  They are also used in [[voltage controlled oscillator]]s (VCOs),<ref name="Abidi">{{cite conference
  | first = Assad A.
  | last = Abidi
  |author2=Robert J. Meyer
   | title = Noise in Relaxation Oscillators
  | book-title = Monolithic Phase-Locked Loops and Clock Recovery Circuits: Theory and Design
  | pages = 182
  | publisher = John Wiley and Sons
  | date = 1996
  | isbn = 9780780311497
 | url = https://books.google.com/books?id=nyxGjjF-cHIC&pg=PA182
  | accessdate = 2015-09-22}}</ref> [[inverter (electrical)|inverter]]s and [[switching power supply|switching power supplies]], [[dual-slope ADC|dual-slope analog to digital converters]], and in [[function generator]]s to produce square and triangle waves.   Relaxation oscillators are widely used because they are easier to design than linear oscillators, are easier to fabricate on [[integrated circuit]] chips because they do not require inductors like LC oscillators,<ref name="Abidi" /><ref name="van der Tang" />  and can be tuned over a wide frequency range.<ref name="van der Tang">{{cite book   
  | last1 = van der Tang
  | first1 = J. 
  | first2 =  Dieter
  | last2 = Kasperkovitz
  | first3 = Arthur H.M. 
  | last3 = van Roermund
  | title = High-Frequency Oscillator Design for Integrated Transceivers
  | publisher = Springer
  | date = 2006
  | pages = 12
  | url = https://books.google.com/books?id=0rniokw7bLkC&pg=PT21
  | isbn = 0306487160}}</ref>  However they have more [[phase noise]]<ref name="Abidi" /> and poorer [[frequency stability]] than linear oscillators.<ref name="Edson" /><ref name="Abidi" />