View source for Pearson–Anson effect

[[File:Neon bulb oscillator circuit.svg|thumb|upright=1.2|Pearson-Anson oscillator circuit]]
The '''Pearson–Anson effect''', discovered in 1922 by [[Stephen Oswald Pearson]]<ref>Stephen Oswald Pearson,''Dictionary of Wireless Technical Terms'' (London: Iliffe & Sons, 1926).</ref> and [[Horatio Saint George Anson]],<ref name="Pearson1">{{cite journal
|last=Pearson
|first=S. O.
|author2=H. St. G. Anson
|title=Demonstration of Some Electrical Properties of Neon-filled Lamps
|journal=Proceedings of the Physical Society of London
|volume=34
|issue=1
|pages=175–176
|date=December 1921
|doi=10.1088/1478-7814/34/1/435
|bibcode=1921PPSL...34..175P
|url=https://zenodo.org/record/1431513
}}</ref><ref name="Pearson2">{{cite journal
|last=Pearson
|first=S. O.
|author2=H. St. G. Anson
|title=The Neon Tube as a Means of Producing Intermittent Currents
|journal=Proceedings of the Physical Society of London
|volume=34
|pages=204–212
|date=August 1922
|issue=1
|doi=10.1088/1478-7814/34/1/341
|bibcode=1921PPSL...34..204P
|url=https://zenodo.org/record/1431511
}}</ref> is the phenomenon of an [[oscillating]] electric voltage produced by a [[neon bulb]] connected across a [[capacitor]], when a direct current is applied through a [[resistor]].<ref name="Kinoshita">{{cite conference
|first=Shuichi
|last=Kinoshita
|title=Introduction to Ionequilibrium Phenomena
|book-title=Pattern Formations and Oscillatory Phenomena
|pages=17
|publisher=Newnes
|year=2013
|url=https://books.google.com/books?id=geQWCKsFhcUC&pg=PA17
|isbn=978-0123972996
|access-date=February 24, 2014}}</ref> This circuit, now called the '''Pearson-Anson oscillator''', '''neon lamp oscillator''',<ref name="Morris">{{cite book
|last=Morris
|first=Christopher G.
|title=Academic Press Dictionary of Science and Technology
|publisher=Gulf Professional Publishing
|year=1992
|pages=1453
|url=https://books.google.com/books?id=nauWlPTBcjIC&q=%22neon+bulb+oscillator&pg=PA1453
|isbn=0122004000}}</ref><ref name="Pollack">{{cite journal
|last=Pollack
|first=Dale
|title=Neon Tube Oscillators, Part 1
|journal=Radio News
|volume=14
|issue=6
|pages=342–343
|date=December 1932
|url=http://www.americanradiohistory.com/Archive-Radio-News/30s/Radio-News-1932-12-R.pdf
|access-date=April 14, 2014}}</ref> or sawtooth oscillator,<ref name="GE">{{cite book
|last=Daugherty
|first=C. L.
|title=G.E. Glow Lamp Manual, 2nd Ed
|publisher=General Electric
|year=1965
|location=Cleveland, Ohio
|pages=14–19
|url=https://books.google.com/books?id=JhgoAQAAMAAJ&q=GE+%22glow+lamp+manual%22
|display-authors=etal}}</ref> is one of the simplest types of [[relaxation oscillator]].<ref name="Bauman">{{cite book
|last=Bauman
|first=Edward
|title=Applications of Neon Lamps and Discharge Tubes
|publisher=Carleton Press
|year=1966
|location=USA
|pages=18
|url=https://www.scribd.com/doc/7086241/Applications-of-Neon-Lamps-and-Discharge-Tubes-Incomplete
|url-status=dead
|archive-url=https://web.archive.org/web/20140416182155/http://www.scribd.com/doc/7086241/Applications-of-Neon-Lamps-and-Discharge-Tubes-Incomplete
|archive-date=2014-04-16
}}</ref> It generates a [[sawtooth wave|sawtooth]] output waveform.<ref name="GE"/> It has been used in low frequency applications such as blinking warning lights,<ref name="Burton">{{cite journal
|last=Burton
|first=Walter E.
|title=Magic with neon glow lamps
|journal=Popular Science
|volume=152
|issue=2
|pages=194–196
|date=February 1948
|url=https://books.google.com/books?id=RigDAAAAMBAJ&q=neon+blinker+stroboscope&pg=PA194
|issn=0161-7370
|access-date=April 14, 2014}}</ref> stroboscopes,<ref name="Burton"/> tone generators in electronic organs<ref name="Bauman"/><ref name="Dance">{{cite book
|last=Dance
|first=J. B.
|title=Cold Cathode Tubes
|publisher=Iliffe Books
|year=1967
|location=London
|pages=25–27
|url=http://elinux.org/images/4/4c/Dance-ColdCathodeTubes.pdf
}}</ref> and other electronic music circuits,<ref name="Holmes">{{cite book
|last=Holmes
|first=Thomas B.
|title=Electronic and Experimental Music: Pioneers in Technology and Composition
|publisher=Psychology Press
|year=2002
|pages=66
|url=https://books.google.com/books?id=ILkquoGXEq0C&q=sawtooth+oscillator+neon&pg=PA66
|isbn=0415936446}}</ref> and in [[time base generator]]s and deflection circuits of early [[cathode-ray tube]] [[oscilloscope]]s.<ref name="Bauman"/><ref name="Wahl">{{cite web
|last=Wahl
|first=Horst D.
|title=Tutorial Oscilloscope
|work=Phys4822L Advanced Lab-Experiment 11: Studies of electrons with a CRT
|publisher=Prof. Horst D. Wahl, Physics Dept., Florida State Univ.
|year=2005
|url=http://www.hep.fsu.edu/~wahl/phy4822/expinfo/crt/neva_crt.pdf
|access-date=April 14, 2014}}</ref> Since the development of microelectronics, these simple negative resistance oscillators have been superseded in many applications by more flexible semiconductor relaxation oscillators such as the [[555 timer IC]].

==Neon bulb as a switching device==
[[File:Neon lamp on DC.JPG|thumb|upright=0.4|NE-2 neon lamp]]

A [[neon bulb]], often used as an [[Nixie tube|indicator lamp]] in appliances, consists of a glass bulb containing two electrodes, separated by an inert gas such as [[neon]] at low pressure. Its [[linear circuit|nonlinear]] current-voltage characteristics ''(diagram below)'' allow it to function as a switching device.<ref name="Gottlieb">{{cite book
|last=Gottlieb
|first=Irving M.
|title=Understanding oscillators
|publisher=H. W. Sams
|year=1971
|pages=69
|url=https://books.google.com/books?id=CqtZAAAAYAAJ&pg=PA69
|isbn=0672208377}}</ref>

When a [[voltage]] is applied across the electrodes, the gas conducts almost no [[electric current]] until a threshold voltage is reached ''(point b)'', called the ''firing'' or ''[[breakdown voltage]]'', ''V''<sub>b</sub>.<ref name="GE"/><ref name="Dance2">[http://elinux.org/images/4/4c/Dance-ColdCathodeTubes.pdf Dance, 1967], p.6-7</ref> At this voltage electrons in the gas are accelerated to a high enough speed to knock other electrons off gas atoms, which go on to knock off more electrons in a chain reaction. The gas in the bulb [[ionization|ionizes]], starting a [[glow discharge]], and its resistance drops to a low value. In its conducting state the current through the bulb is limited only by the external circuit. The voltage across the bulb drops to a lower voltage called the ''maintaining voltage'' ''V''<sub>m</sub>. The bulb will continue to conduct current until the applied voltage drops below the ''extinction voltage'' ''V''<sub>e</sub> ''(point d)'', which is usually close to the maintaining voltage. Below this voltage, the current provides insufficient energy to keep the gas ionized, so the bulb switches back to its high resistance, nonconductive state ''(point a)''.

The bulb's "turn on" voltage ''V''<sub>b</sub> is higher than its "turn off" voltage ''V''<sub>e</sub>. This property, called [[hysteresis]], allows the bulb to function as an oscillator. Hysteresis is due to the bulb's [[negative resistance]], the fall in voltage with increasing current after breakdown,<ref name="GE"/><ref name="Dance2"/> which is a property of all [[gas-discharge lamp]]s.

Up until the 1960s sawtooth oscillators were also built with [[thyratron]]s.<ref name="Lytel">{{cite journal
|last1=Lytel
|first1=Allan
|title=Gas Tube Oscillators
|journal=Radio-Electronics
|volume=20
|issue=3
|pages=33–34
|date=December 1948
|url=http://www.americanradiohistory.com/Archive-Radio-Electronics/40s/Radio-Electronics-1948-12.pdf
|access-date=March 27, 2015}}</ref><ref name="Puckle">{{cite book
|last1=Puckle
|first1=O. S.
|title=Time Bases (Scanning Generators), 2nd Ed.
|publisher=Chapman and Hall
|date=1951
|location=London
|pages=[https://archive.org/details/TimeBasesTheirDesignDevelopment/page/n96 15]–27
|url=https://archive.org/details/TimeBasesTheirDesignDevelopment
}}</ref> These were gas-filled [[triode]] electron tubes. These worked somewhat similarly to neon bulbs, the tube would not conduct until the cathode to anode voltage reached a breakdown voltage. The advantage of the thyratron was that the breakdown voltage could be controlled by the voltage on the grid.<ref name="Puckle"/> This allowed the frequency of the oscillation to be changed electronically. Thyratron oscillators were used as [[time base generator]]s in oscilloscopes.<ref name="Puckle"/>

==Operation==
[[File:Neon bulb relaxation oscillator hysteresis curve.svg|thumb|upright=1.6|''IV'' curve of neon bulb ''(right)''<ref name="GE"/> showing the oscillator hysteresis loop ''(abcd)'', the load line ''<span style="color:blue;">(blue)</span>'', and output waveforms ''(left)''. The load line must lie within the shaded region for the circuit to oscillate. ''v'' is the voltage across the neon bulb, and ''i'' is the current through it.]]

In the Pearson-Anson oscillator circuit ''(top)'' a [[capacitor]] ''C'' is connected across the neon bulb ''N''<ref name="GE"/> The capacitor is continuously charged by current through the resistor ''R'' until the bulb conducts, discharging it again, after which it charges up again.<ref name="Miller">{{cite book
|last=Miller
|first=Walter G.
|title=Using and Understanding Miniature Neon Lamps
|publisher=Howard W. Sams
|year=1969
|location=New York
|pages=37–39
|url=http://electro-music.com/forum/phpbb-files/neonbook_169.pdf
}}</ref> The detailed cycle is illustrated by the [[hysteresis loop]] ''abcd'' on the current-voltage diagram at right:<ref name="Kinoshita"/><ref name="GE"/><ref name="Dance"/>
*When the supply voltage is turned on, the neon bulb is in its high resistance condition and acts like an open circuit. The current through the resistor begins to charge the capacitor and its voltage begins to rise toward the supply voltage.
*When the voltage across the capacitor reaches ''b'', the breakdown voltage of the bulb ''V''<sub>b</sub>, the bulb turns on and its resistance drops to a low value. The charge on the capacitor discharges rapidly through the bulb in a momentary pulse of current ''(c)''. When the voltage drops to the extinction voltage ''V''<sub>e</sub> of the bulb ''(d)'', the bulb turns off and the current through it drops to a low level ''(a)''. The current through the resistor begins charging the capacitor up again, and the cycle repeats.
The circuit thus functions as a low-frequency [[relaxation oscillator]], the capacitor voltage oscillating between the breakdown and extinction voltages of the bulb in a [[sawtooth wave]]. The period is proportional to the time constant ''RC''.

The [[neon lamp]] produces a brief flash of light each time it conducts, so the circuit can also be used as a "flasher" circuit. The dual function of the lamp as both light source and switching device gives the circuit a lower parts count and cost than many alternative flasher circuits.

==Conditions for oscillation==
The supply voltage ''V''<sub>S</sub> must be greater than the bulb breakdown voltage ''V''<sub>b</sub> or the bulb can never conduct.<ref name="GE"/> Most small neon lamps have breakdown voltages between 80 and 150 volts, so they can operate on 120&nbsp;Vrms mains voltage, which has a peak voltage of about 170&nbsp;V. If the supply voltage is close to the breakdown voltage, the capacitor voltage will be in the "tail" of its exponential curve by the time it reaches ''V''<sub>b</sub>, so the frequency will depend sensitively on the breakdown threshold and supply voltage levels, causing variations in frequency.<ref name="Miller"/> Therefore, the supply voltage is usually made significantly higher than the bulb firing voltage.<ref name="GE"/> This also makes the charging more linear, and the sawtooth wave more triangular.<ref name="Miller"/>

The resistor R must also be within a certain range of values for the circuit to oscillate.<ref name="GE"/> This is illustrated by the [[load line (electronics)|load line]] (''<span style="color:blue;">blue</span>'') on the ''IV'' graph. The slope of the load line is equal to R. The possible DC operating points of the circuit are at the intersection of the load line and the neon lamp's ''IV'' curve (''black'') In order for the circuit to be unstable and oscillate, the load line must intersect the ''IV'' curve in its [[negative resistance]] region, between ''b'' and ''d'', where the voltage declines with increasing current.<ref name="GE"/> This is defined by the shaded region on the diagram. If the load line crosses the ''IV'' curve where it has positive resistance, outside the shaded region, this represents a stable operating point, so the circuit will not oscillate:
*If R is too large, of the same order as the "off" leakage resistance of the bulb, the load line will cross the ''IV'' curve between the origin and ''b''. In this region, the current through R from the supply is so low that the leakage current through the bulb bleeds it off, so the capacitor voltage never reaches ''V''<sub>b</sub> and the bulb never fires.<ref name="GE"/> The leakage resistance of most neon bulbs is greater than 100MΩ, so this is not a serious limitation.
*If R is too small, the load line will cross the ''IV'' curve between ''c'' and ''d''. In this region the current through R is too large; once the bulb has turned on, the current through R will be large enough to keep it conducting without current from the capacitor, and the voltage across the bulb will never fall to ''V''<sub>e</sub> so the bulb will never turn off.<ref name="GE"/>

Small neon bulbs will typically oscillate with values of ''R'' between 500kΩ and 20MΩ.<ref name="GE"/>
If ''C'' is not small, it may be necessary to add a resistor in series with the neon bulb, to limit current through it to prevent damage when the capacitor discharges.<ref name="Dance"/> This will increase the discharge time and decrease the frequency slightly, but its effect will be negligible at low frequencies.

==Frequency==
The period of oscillation can be calculated from the breakdown and extinction voltage thresholds of the lamp used.<ref name="Pollack"/><ref name="GE"/><ref name="Dance"/><ref name="Hill">{{cite web
|last=Hill
|first=Eric
|author-link=eric_hill@redlands.edu
|title=Lecture 7a – Waveform Generators & Timers
|work=Course Notes Physics 310: Electronics Applications
|publisher=Prof. Eric Hill website, Physics Dept., Univ. of Midlands
|year=2014
|url=http://bulldog2.redlands.edu/facultyfolder/eric_hill/Phys310/Lectures/P310%20-%20lecture%207a.pdf
|access-date=April 14, 2014}}</ref> During the charging period, the bulb has high resistance and can be considered an open circuit, so the rest of the oscillator constitutes an [[RC circuit]] with the capacitor voltage approaching ''V''<sub>S</sub> [[exponential function|exponentially]], with [[time constant]] ''RC''. If ''v''(''t'') is the output voltage across the capacitor
{| class="wikitable" width=100%;
|-
|
{{show
|Derivation of ''v''(''t'')
|
and ''i''(''t'') is the current through the resistor
:<math>V_S = v + Ri\,</math>&nbsp;&nbsp;&nbsp;&nbsp;and&nbsp;&nbsp;&nbsp;&nbsp;<math>i = C{dv \over dt}\,</math>
so the differential equation of the circuit is
:<math>RC{dv \over dt} + v = V_S \,</math>
The general solution is
:<math>v(t) = A_1e^{-t/RC} + A_2 \,</math>
Applying boundary conditions <math>v(\infty) = A_2 = V_S \,</math>&nbsp;&nbsp;&nbsp;&nbsp;and&nbsp;&nbsp;&nbsp;&nbsp;<math>v(0) = A_1 + V_S = 0 \,</math>
gives the constants ''A''<sub>1</sub> and ''A''<sub>2</sub>, so the solution is
}}
|}
:<math>v(t) = V_S(1 - e^{-t/RC}) \,</math>
Solving for the time
:<math>t = RC\ln\Bigl[{V_S \over {V_S - v}}\Bigr] \,</math>
Although the first period is longer than the others because the voltage starts from zero, the voltage waveforms of subsequent periods are identical to the first between ''V''<sub>e</sub> and ''V''<sub>b</sub>. So the period ''T'' is the interval between the time when the voltage reaches ''V''<sub>e</sub>, and the time when the voltage reaches ''V''<sub>b</sub>
:<math>T = t(V_b) - t(V_e) \,</math>

:<math>T = RC\ln\Bigl[{V_S \over {V_S - V_b}}\Bigr] - RC\ln\Bigl[{V_S \over {V_S - V_e}}\Bigr]\, </math>

:<math>T = RC\ln\Bigl[{{V_S - V_e} \over {V_S - V_b}}\Bigr]\, </math>

This formula is only valid for oscillation frequencies up to about 200&nbsp;Hz;<ref name="GE"/> above this various time delays cause the actual frequency to be lower than this.<ref name="Bauman"/> Due to the time required to ionize and deionize the gas, neon lamps are slow switching devices, and the neon lamp oscillator is limited to a top frequency of about 20&nbsp;kHz.<ref name="GE"/><ref name="Bauman"/><ref name="Dance"/>
The breakdown and extinction voltages of neon lamps may vary between similar parts;<ref name="Miller"/> manufacturers usually specify only wide ranges for these parameters. So if a precise frequency is desired the circuit must be adjusted by trial and error.<ref name="Miller"/> The thresholds also change with temperature, so the frequency of neon lamp oscillators is not particularly stable.<ref name="Dance"/>

==Forced oscillations and chaotic behavior==
Like other relaxation oscillators, the neon bulb oscillator has poor [[frequency stability]], but it can be synchronized ([[entrainment (physics)|entrained]]) to an external periodic voltage applied in series with the neon bulb. Even if the external frequency is different from the natural frequency of the oscillator, the peaks of the applied signal can exceed the breakdown threshold of the bulb, discharging the capacitor prematurely, so that the period of the oscillator becomes locked to the applied signal.<ref name="Jenkins">{{Cite journal |last1=Jenkins |first1=Alejandro |author-link1=Alejandro Jenkins |title=Self-oscillation |doi=10.1016/j.physrep.2012.10.007 |journal=Physics Reports |volume=525 |issue=2 |pages=167–222 |year=2013 |arxiv=1109.6640 |bibcode=2013PhR...525..167J |s2cid=227438422}}</ref>

Interesting behavior can result from varying the amplitude and frequency of the external voltage. For instance, the oscillator may produce an oscillating voltage whose frequency is a submultiple of the external frequency. This phenomenon is known as "submultiplication" or "demultiplication", and was first observed in 1927 by [[Balthasar van der Pol]] and his collaborator Jan van der Mark.<ref name="van der Pol">{{cite journal
|last=van der Pol
|first=Balthasar
|author2=Jan van der Mark
|title=Frequency Demultiplication
|journal=Nature
|volume=120
|issue=3019
|pages=363–364
|date=September 10, 1927
|doi=10.1038/120363a0
|bibcode=1927Natur.120..363V |s2cid=4142485
}}</ref><ref name="Sprott">{{cite book
|last=Sprott
|first=Julien C.
|title=Elegant Chaos: Algebraically Simple Chaotic Flows
|publisher=World Scientific
|date=2010
|pages=234–235
|url=https://books.google.com/books?id=buILBDre9S4C&q=neon+oscillator&pg=PA235
|isbn=978-9812838827}}</ref> In some cases the ratio of the external frequency to the frequency of the oscillation observed in the circuit may be a [[rational number]], or even an [[irrational number|irrational]] one (the latter case is known as the "[[quasiperiodic motion|quasiperiodic]]" regime).<ref name="Jenkins"/> When the periodic and quasiperiodic regimes overlap, the behavior of the circuit may become aperiodic, meaning that the pattern of the oscillations never repeats. This aperiodicity correspond to the behavior of the circuit becoming ''chaotic'' (see [[chaos theory]]).<ref name="Jenkins"/><ref name="Sprott"/>

The forced neon bulb oscillator was the first system in which chaotic behavior was observed.<ref name="Eisencraft">{{cite book
|last=Eisencraft
|first=Marcio, Romis Attux, Ricardo Suyama
|author2=Romis Attux |author3=Ricardo Suyama
|title=Chaotic Signals in Digital Communications
|publisher=CRC Press
|date=2013
|pages=87
|url=https://books.google.com/books?id=aYIAAQAAQBAJ&q=chaos+%22balthasar+van+der+pol&pg=PA87
|isbn=978-1466557222}}</ref> Van der Pol and van der Mark wrote, concerning their experiments with demultiplication, that
{{blockquote|Often an irregular noise is heard in the telephone receivers before the frequency jumps to the next lower value. However this is a subsidiary phenomenon, the main effect being the regular frequency demultiplication.<ref name="van der Pol"/>}}

Any periodic oscillation would have produced a musical tone; only aperiodic, chaotic oscillations would produce an "irregular noise". This is thought to have been the first observation of chaos, although van der Pol and van der Mark didn't realize its significance at the time.<ref name="Jenkins"/><ref name="Sprott"/><ref name="Eisencraft"/>

==See also==
* [[Relaxation oscillator]]
* [[Schmitt trigger]]
* [[555 timer]]
* [[Negative resistance]]

==Notes==
{{Reflist}}

==References==
* S. O. Pearson and H. St. G. Anson, ''[http://www.iop.org/EJ/abstract/-search=11154593.1/1478-7814/34/1/435 Demonstration of Some Electrical Properties of Neon-filled Lamps]'', ''Proceedings of the Physical Society of London'', vol.34, no. 1 (December 1921), pp.&nbsp;175–176 {{doi|10.1088/1478-7814/34/1/435}}
* S. O. Pearson and H. St. G. Anson, ''[http://www.iop.org/EJ/abstract/1478-7814/34/1/341 The Neon Tube as a Means of Producing Intermittent Currents]'', ''Proceedings of the Physical Society of London'', vol. 34, no. 1 (December 1921), pp.&nbsp;204–212 {{doi|10.1088/1478-7814/34/1/341}}
*{{cite book
|last=Daugherty
|first=C. L.
|title=G.E. Glow Lamp Manual, 2nd Ed.
|publisher=General Electric
|year=1965
|location=Cleveland, Ohio
|pages=14–19
|url=https://books.google.com/books?id=JhgoAQAAMAAJ&q=GE+%22glow+lamp+manual
|display-authors=etal}}

{{DEFAULTSORT:Pearson-Anson effect}}
[[Category:Analog circuits]]
[[Category:Electronic oscillators]]