Wien bridge

Wien bridge schematic, U_wy- sinusoidal power supply voltage, U_we- measured voltage

The Wien bridge is a type of bridge circuit that was developed by Max Wien in 1891. The bridge comprises four resistors and two capacitors.

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. Wien's bridge is used for precison measurement of capacitance in terms of resistance and frequency. 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:

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

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

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.

Use in an Oscillator

See also: Wien bridge oscillator

If the bridge is constructed such that R_x = R₂, C_x = C₂ and R₄ = 2R₃, the AC signal U_wy is exactly one sixth of the applied signal U_we. If an amplifying circuit is connected such that U_wy is connected to its input and U_we is connected to its output and provided the amplifying circuit has a gain of six giving a loop gain of unity, then a steady oscillation will be maintained at a frequency of (ω/2π) Hertz (The ω comes from the balance equation above). In a practical arangement, some means has to be provided of stabilising the output and making the loop gain greater than unity for startup. This circuit has the advantage, that because of the low gain required by the amplifing circuit, it has a very low distortion of the generated sine wave.

See also

• THD analyzer

References

• Ferguson, J. G.; Bartlett, B. W. (July 1928), "The Measurement of Capacitance in Terms of Resistance and Frequency" (PDF), Bell System Technical Journal, 7 (3): 420–437, doi:10.1002/j.1538-7305.1928.tb01234.x
• Terman, Frederick (1943), Radio Engineers' Handbook, McGraw-Hill
• Wien, M. (1891), "Messung der Inductionsconstanten mit dem "optischen Telephon" (Measurement of Inductive Constants with the "Optical Telephone")", Annalen der Physik und Chemie (in German), 280 (12): 689–712, Bibcode:1891AnP...280..689W, doi:10.1002/andp.18912801208

External links

• http://www.ecelab.com/wien-bridge.htm Template:Wayback