查看“︁巴克豪森稳定性准则”︁的源代码

[[File:Oscillator diagram1.svg|thumb|250px|回授振盪器的方塊圖，可以用巴克豪森稳定性准则來分析。其中包括放大元件''A''，其輸出''v<sub>o</sub>''經過回授線路''β(jω)''後，變成放大元件的輸入''v<sub>f</sub>'']]
[[File:Oscillator diagram2.svg|thumb|250px|為了要找[[迴路增益]]，先將回授環切斷，計算特定輸入''v<sub>i</sub>''下的輸出''v<sub>o</sub>''：<br>
<math>G = \frac {v_o}{v_i} = \frac{v_f}{v_i}\frac {v_o}{v_f} = \beta A(j \omega)\,</math>]]
'''巴克豪森稳定性准则'''（Barkhausen stability criterion）是[[電子學]]裡判斷{{le|線性電路|linear circuit}}是否會[[振盪]]的準則<ref name="Basu">{{cite book   
  | last = Basu
  | first = Dipak 
  | title = Dictionary of Pure and Applied Physics
  | publisher = CRC Press
  | year = 2000
  | pages = 34–35
  | url = https://books.google.com/books?id=-QhAkBSk7IUC&pg=PA35
  | 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
  | year = 2010
  | pages = 3
  | url = https://books.google.com/books?id=4Op56QdHFPUC&pg=PA3
  | isbn = 978-1608070480}}</ref><ref name="Carter">{{cite book   
  | last = Carter
  | first = Bruce 
  |author2=Ron Mancini
  | title = Op Amps for Everyone, 3rd Ed.
  | publisher = Newnes
  | year = 2009
  | pages = 342–343
  | url = https://books.google.com/books?id=nnCNsjpicJIC&pg=PA342
  | isbn = 978-0080949482}}</ref>。此準則是[[德國]]物理學家[[海因里希·巴克豪森]]在1921年所發現<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=de
  | publisher = S. Hirzel
  | year = 1935
  | location = Leipzig
  |asin=B0019TQ4AQ 
  |oclc=682467377 <!-- for 1945 5th edition -->
  }}</ref>。在[[電子振盪器]]的設計上常會用到此準則，在[[負回授]]電路（像是使用[[運算放大器]]）中也會利用此一準則，避免電路振盪。

==準則==
若''A''是放大元件的[[增益]]，而β(''j''ω)是回授電路的[[传递函数]]，則β''A''是回授電路的[[环路增益]]，巴克豪森稳定性准则指出，只有在以下的頻率下，電路才會有穩態的振盪：
#迴路增益的絕對值等於1，<math>|\beta A| = 1\,</math>
#迴路產生的相位移為0或是2π的整數倍，<math>\angle \beta A = 2 \pi n, n \in \{0, 1, 2,\dots\}\,.</math>

巴克豪森稳定性准则是振盪的必要條件，不是充份條件，有些電路滿足巴克豪森稳定性准则，但不是振盪<ref name="Lindberg">{{cite conference
  | first = Erik
  | last = Lindberg
  | title = The Barkhausen Criterion (Observation ?)
  | book-title = 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
| url = http://www.qucosa.de/fileadmin/data/qucosa/documents/3913/ProceedingsNDES2010.pdf
  | access-date = 2 February 2013
  | archive-url = https://web.archive.org/web/20160304040330/http://www.qucosa.de/fileadmin/data/qucosa/documents/3913/ProceedingsNDES2010.pdf
  | url-status = dead
  | archive-date = 4 March 2016}} discusses reasons for this. (Warning: large 56MB download)</ref>。[[奈奎斯特穩定判據]]和系統是否穩定有關。但也沒有提及系統是否會挀盪。目前還沒有一個既是充份條件也是必要條件，簡單的振盪準則<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
 |publisher= Springer Science+Business Media, LLC
 |year= 2010
 |issn= 1573-1979
 |doi= 10.1007/s10470-010-9506-4 |s2cid= 111132040
 }}. Received: 17 June 2010 / Revised: 2 July 2010 / Accepted: 5 July 2010.</ref>。

==限制==
巴克豪森稳定性准则只適用於有[[回授]]的線性電路中。巴克豪森稳定性准则無法用在有[[負阻特性]]的主動元件上（例如[[隧道二極體]]振盪器）。

此準則的核心是為了讓系統有[[穩態_(系統)|穩態]]的振盪，需要將[[極點 (複分析)|複數極點對]]放在[[复平面]]的虛軸上。

==錯誤版本==
巴克豪森原始的「自激振盪公式」（目的是要確定回授路徑上的振盪頻率），其中包括一個等式：|β''A''| = 1。在科學家對條件穩定非線性系統還不瞭解時，普遍認為這是穩定（|β''A''| < 1）和不穩定（|β''A''| ≥ 1）的分界，這個錯誤版本也出現在一些文獻中<ref>{{cite web
  | last = Lundberg
  | first = Kent
  | title = Barkhausen Stability Criterion
  | work = Kent Lundberg
  | publisher = MIT
  | date = 14 November 2002
  | url = http://web.mit.edu/klund/www/weblatex/node4.html
  | access-date = 16 November 2008| archive-url= https://web.archive.org/web/20081007072144/http://web.mit.edu/klund/www/weblatex/node4.html| archive-date= 7 October 2008 | url-status= live}}</ref>。不過只有在等式成立時，才會有自激振盪。

==相關條目==
*[[奈奎斯特穩定判據]]
==參考資料==
{{reflist}}
[[分類:振盪]]
[[分類:電路]]