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| [[Image:Mostek Wiena.svg| right| thumb| Wien bridge schematic]]
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| The '''Wien bridge''' is a type of [[bridge circuit]] that was developed by [[Max Wien]] in 1891.<ref>{{Harvnb|Wien|1891}}</ref> The bridge comprises four [[resistor]]s and two [[capacitor]]s.
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| Bridge circuits were a common way of measuring component values by comparing them to known values. Often an unknown component would be put in one arm of a bridge, and then the bridge would be nulled by adjusting the other arms or changing the frequency of the voltage source. See, for example, the [[Wheatstone bridge]].
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| The Wien bridge is one of many common bridges.<ref>{{Harvnb|Terman|1943|p=904}}</ref> Wien's bridge is used for precison measurement of capacitance in terms of resistance and frequency.<ref>{{Harvnb|Terman|1943|p=904}} citing {{Harvnb|Ferguson|Bartlett|1928}}</ref> It was also used to measure audio frequencies.
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| The Wien bridge does not require equal values of ''R'' or ''C''. At some frequency, the reactance of the series ''R<sub>2</sub>–C<sub>2</sub>'' arm will be an exact multiple of the shunt ''R<sub>x</sub>–C<sub>x</sub>'' arm. If the two ''R<sub>3</sub>'' and ''R<sub>4</sub>'' arms are adjusted to the same ratio, then the bridge is balanced.
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| The bridge is balanced when:<ref>{{Harvnb|Terman|1943|p=905}}</ref>
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| :<math>\omega^2 = {1 \over R_x R_2 C_x C_2}</math> and <math> {C_x \over C_2} = {R_4 \over R_3} - {R_2 \over R_x} \, .</math>
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| The equations simplify if one chooses ''R<sub>2</sub>'' = ''R<sub>x</sub>'' and ''C<sub>2</sub>'' = ''C<sub>x</sub>''; the result is ''R<sub>4</sub>'' = 2 ''R<sub>3</sub>''.
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| In practice, the values of ''R'' and ''C'' will never be exactly equal, but the equations above show that for fixed values in the ''2'' and ''x'' arms, the bridge will balance at some ''ω'' and some ratio of ''R<sub>4</sub>''/''R<sub>3</sub>''.
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| == See also ==
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| * [[THD analyzer]]
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| * [[Wien bridge oscillator]]
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| == References ==
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| {{Reflist}}
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| *{{Citation
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| |last = Ferguson |first= J. G. |author-link=
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| |last2= Bartlett |first2= B. W. |author-link2=
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| |title= The Measurement of Capacitance in Terms of Resistance and Frequency
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| |url= http://www.alcatel-lucent.com/bstj/vol07-1928/articles/bstj7-3-420.pdf
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| |journal= Bell System Technical Journal
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| |volume = 7
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| |issue = 3
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| |date= July 1928
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| |page= 420–437
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| |doi= }}
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| *{{Citation
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| |last = Terman
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| |first = Frederick
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| |author-link = Frederick Terman
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| |title = Radio Engineers' Handbook
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| |year = 1943
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| |publisher = McGraw-Hill
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| |doi=}}
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| *{{Citation
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| |last=Wien |first=M. |author-link = Max Wien
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| |title= Messung der Inductionsconstanten mit dem "optischen Telephon" (Measurement of Inductive Constants with the "Optical Telephone")
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| |language=German
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| |journal= [[Annalen der Physik|Annalen der Physik und Chemie]]
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| |year= 1891
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| |volume= 280
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| |issue= 12
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| |page= 689–712
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| |doi= 10.1002/andp.18912801208 |bibcode = 1891AnP...280..689W }}
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| ==External links==
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| * http://www.ecelab.com/wien-bridge.htm{{dead link|date=August 2013}} {{wayback|http://www.ecelab.com/wien-bridge.htm}}
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| [[Category:Electrical circuits]]
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