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{{For|the noise in the output of a ferromagnet upon a change in the magnetizing force|Barkhausen effect}}
[[File:Oscillator diagram1.svg|thumb|250px|Block diagram of a feedback oscillator circuit to which the Barkhausen criterion applies. It consists of an amplifying element ''A'' whose output ''v<sub>o</sub>'' is fed back into its input ''v<sub>f</sub>'' through a feedback network ''β(jω)''.]]
[[File:Oscillator diagram2.svg|thumb|250px|To find the [[loop gain]], the feedback loop is considered broken at some point and the output ''v<sub>o</sub>'' for a given input ''v<sub>i</sub>'' is calculated:<br>
:<math>G = \frac {v_o}{v_i} = \frac{v_f}{v_i}\frac {v_o}{v_f} = \beta A(j \omega)\,</math>]]
 
In [[electronics]], the '''Barkhausen stability criterion''' is a mathematical condition to determine when a [[linear circuit|linear electronic circuit]] will [[oscillate]].<ref name="Basu">{{cite book 
  | last = Basu
  | first = Dipak
  | title = Dictionary of Pure and Applied Physics
  | publisher = CRC Press
  | date = 2000
  | location =
  | pages = 34-35
  | url = http://books.google.com/books?id=-QhAkBSk7IUC&pg=PA35
  | doi =
  | id =
  | isbn = 1420050222}}</ref><ref name="Rhea">{{cite book 
  | last = Rhea
  | first = Randall W.
  | title = Discrete Oscillator Design: Linear, Nonlinear, Transient, and Noise Domains
  | publisher = Artech House
  | date = 2010
  | location =  
  | pages = 3
  | url = http://books.google.com/books?id=4Op56QdHFPUC&pg=PA3
  | doi =  
  | id =  
  | isbn = 1608070484}}</ref><ref name="Carter">{{cite book 
  | last = Carter
  | first = Bruce
  | coauthors = Ron Mancini
  | title = Op Amps for Everyone, 3rd Ed.
  | publisher = Newnes
  | date = 2009
  | location =
  | pages = 342-343
  | url = http://books.google.com/books?id=nnCNsjpicJIC&pg=PA342
  | doi =
  | id =
  | isbn = 0080949487}}</ref>  It was put forth in 1921 by [[Germany|German]] physicist [[Heinrich Georg Barkhausen]] (1881–1956).<ref name="Barkhausen">{{cite book 
  | last = Barkhausen
  | first = H.
  | title = Lehrbuch der Elektronen-Röhren und ihrer technischen Anwendungen |volume=3 |trans_title=Textbook of Electron Tubes and their Technical Applications |language=German
  | publisher = S. Hirzel
  | date = 1935
  | location = Leipzig
  | pages =
  | url =
  |asin=B0019TQ4AQ
  |oclc=682467377 <!-- for 1945 5th edition -->
  | isbn = }}</ref> It is widely used in the design of [[electronic oscillator]]s, and also in the design of general [[negative feedback]] circuits such as [[op amp]]s, to prevent them from oscillating.
 
==Limitations==
Barkhausen's criterion applies to linear circuits with a [[feedback loop]].  Therefore it cannot be applied to one port [[negative resistance]] active elements like [[tunnel diode]] oscillators.
 
==Criterion==
It states that if ''A'' is the [[gain]] of the amplifying element in the circuit and β(''j''ω) is the [[transfer function]] of the feedback path, so β''A'' is the [[loop gain]] around the [[feedback loop]] of the circuit, the circuit will sustain steady-state oscillations only at frequencies for which:
#The loop gain is equal to unity in absolute magnitude, that is, <math>|\beta A| = 1\,</math> and
#The [[phase shift]] around the loop is zero or an integer multiple of 2π: <math>\angle \beta A = 2 \pi n, n \in 0, 1, 2,\dots\,.</math>
 
Barkhausen's criterion is a ''necessary'' condition for oscillation but not a ''sufficient'' condition: some circuits satisfy the criterion but do not oscillate.<ref name="Lindberg">{{cite conference
  | first = Erik
  | last = Lindberg
  | title = The Barkhausen Criterion (Observation ?)
  | booktitle = Proceedings of 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems (NDES2010), Dresden, Germany
  | pages = 15-18
  | publisher = Inst. of Electrical and Electronic Engineers
  | date = 26-28 May 2010
  | location =
  | url = http://www.qucosa.de/fileadmin/data/qucosa/documents/3913/ProceedingsNDES2010.pdf
  | doi =
  | id =  
  | accessdate = 2 February 2013}} discusses reasons for this. (Warning: large 56MB download)</ref>   Similarly, the [[Nyquist stability criterion]] also indicates instability but is silent about oscillation. Apparently there is not a compact formulation of an oscillation criterion that is both necessary and sufficient.<ref>{{Citation |last= von Wangenheim |first= Lutz
|title=On the Barkhausen and Nyquist stability criteria
|journal=Analog Integrated Circuits and Signal Processing
|volume=66 |issue=1
|pages=139&ndash;141
|date=
|publisher= Springer Science+Business Media, LLC
|year= 2010
|issn= 1573-1979
|doi= 10.1007/s10470-010-9506-4 }}. Received: 17 June 2010 / Revised: 2 July 2010 / Accepted: 5 July 2010.</ref>
 
==Erroneous version==
Barkhausen's original "formula for self-excitation", intended for determining the oscillation frequencies of the feedback loop, involved an equality sign: |β''A''| = 1. At the time conditionally-stable nonlinear systems were poorly understood; it was widely believed that this gave the boundary between stability (|β''A''| < 1) and instability (|β''A''| ≥ 1), and this erroneous version found its way into the literature.<ref>{{cite web
  | last = Lundberg
  | first = Kent
  | authorlink =
  | coauthors =
  | title = Barkhausen Stability Criterion
  | work = [http://web.mit.edu/klund/www/ Kent Lundberg faculty website]
  | publisher = MIT
  | date = 2002-11-14
  | url = http://web.mit.edu/klund/www/weblatex/node4.html
  | doi =
  | accessdate = 2008-11-16| archiveurl= http://web.archive.org/web/20081007072144/http://web.mit.edu/klund/www/weblatex/node4.html| archivedate= 7 October 2008 <!--DASHBot-->| deadurl= no}}</ref> However, ''stable'' oscillations only occur at frequencies for which equality holds.
 
== See also ==
*[[Nyquist stability criterion]]
 
== References ==
{{reflist|30em}}
 
{{Use dmy dates|date=August 2011}}
 
[[Category:Oscillation]]
[[Category:Electronic circuits]]

Latest revision as of 05:29, 19 March 2013

28 year-old Painting Investments Worker Truman from Regina, usually spends time with pastimes for instance interior design, property developers in new launch ec Singapore and writing. Last month just traveled to City of the Renaissance.

Block diagram of a feedback oscillator circuit to which the Barkhausen criterion applies. It consists of an amplifying element A whose output vo is fed back into its input vf through a feedback network β(jω).
To find the loop gain, the feedback loop is considered broken at some point and the output vo for a given input vi is calculated:
 :

In electronics, the Barkhausen stability criterion is a mathematical condition to determine when a linear electronic circuit will oscillate.[1][2][3] It was put forth in 1921 by German physicist Heinrich Georg Barkhausen (1881–1956).[4] It is widely used in the design of electronic oscillators, and also in the design of general negative feedback circuits such as op amps, to prevent them from oscillating.

Limitations

Barkhausen's criterion applies to linear circuits with a feedback loop. Therefore it cannot be applied to one port negative resistance active elements like tunnel diode oscillators.

Criterion

It states that if A is the gain of the amplifying element in the circuit and β(jω) is the transfer function of the feedback path, so βA is the loop gain around the feedback loop of the circuit, the circuit will sustain steady-state oscillations only at frequencies for which:

  1. The loop gain is equal to unity in absolute magnitude, that is, and
  2. The phase shift around the loop is zero or an integer multiple of 2π:

Barkhausen's criterion is a necessary condition for oscillation but not a sufficient condition: some circuits satisfy the criterion but do not oscillate.[5] Similarly, the Nyquist stability criterion also indicates instability but is silent about oscillation. Apparently there is not a compact formulation of an oscillation criterion that is both necessary and sufficient.[6]

Erroneous version

Barkhausen's original "formula for self-excitation", intended for determining the oscillation frequencies of the feedback loop, involved an equality sign: |βA| = 1. At the time conditionally-stable nonlinear systems were poorly understood; it was widely believed that this gave the boundary between stability (|βA| < 1) and instability (|βA| ≥ 1), and this erroneous version found its way into the literature.[7] However, stable oscillations only occur at frequencies for which equality holds.

See also

References

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