Wien bridge

The Wien bridge is a type of bridge circuit that was developed by Max Wien in 1891.^[1] The bridge consists of four resistors and two capacitors.

At the time of the Wien bridge's invention, 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.

The Wien bridge is one of many common bridges.^[2] Wien's bridge is used for precision measurement of capacitance in terms of resistance and frequency.^[3] It was also used to measure audio frequencies.

The Wien bridge does not require equal values of R or C. At some frequency, the reactance of the series R₂–C₂ arm will be an exact multiple of the shunt R_x–C_x arm. If the two R₃ and R₄ arms are adjusted to the same ratio, then the bridge is balanced.

The bridge is balanced when:^[4]

${\displaystyle \omega ^{2}={1 \over R_{x}R_{2}C_{x}C_{2}}}$ and ${\displaystyle {C_{x} \over C_{2}}={R_{4} \over R_{3}}-{R_{2} \over R_{x}}\,.}$

The equations simplify if one chooses R₂ = R_x and C₂ = C_x; the result is R₄ = 2R₃.

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 R₄/R₃.