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.[25] Wien's bridge is used for precision measurement of capacitance in terms of resistance and frequency.[26] It was also used to measure audio frequencies.
The Wien bridge does not require equal values of R or C. The phase of the signal at Vp relative to the signal at Vout varies from almost 90° leading at low frequency to almost 90° lagging at high frequency. At some intermediate frequency, the phase shift will be zero. At that frequency the ratio of Z1 to Z2 will be purely real (zero imaginary part). If the ratio of Rb to Rf is adjusted to the same ratio, then the bridge is balanced and the circuit can sustain oscillation. The circuit will oscillate even if Rb / Rf has a small phase shift and even if the inverting and non-inverting inputs of the amplifier have different phase shifts. There will always be a frequency at which the total phase shift of each branch of the bridge will be equal. If Rb / Rf has no phase shift and the phase shifts of the amplifiers inputs are zero then the bridge is balanced when:[27]