# Wien Bridge

The Vienna bridge is a type of bridge circuit that was developed by Max Wien in 1891  The bridge consists of four resistors and two capacitors . At the time of the Wien bridge’s invention, bridge circuits were a common method of measuring component values ​​by comparing known values. Often an unknown component will be put into one arm of a bridge, and then the bridge will be reduced to zero by adjusting the other arms or by changing the frequency of the voltage source. For example, see Wheatstone Bridge .

The Wien bridge is one of several common bridges.  Wien’s bridge is used for precise measurement of capacitance in terms of resistance and frequency.  It was also used to measure audio frequencies.

The Wien bridge does not need to be the same value as R or C. At some frequency, the reactance of the series 2 – 2 arm will be an exact multiple of the shunt x – x arm. If the two arms R3 and R4 are adjusted to the same ratio, then the bridge is balanced.

When the bridge is balanced:

\omega ^{2}={1 \over R_{x}R_{2}C_{x}C_{2}}And{C_{x} \over C_{2}}={R_{4} \over R_{3}}-{R_{2} \over R_{x}}\,।


If one chooses 2 = x and 2 = x then the equations become simpler; The result is r4 = r3 .

In practice, the values ​​of R and C will never be exactly equal, but for the values ​​fixed in the above equations that the 2 and X arms , the bridge will equilibrate on some and some ratio of R4 / R3 .

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