## Wien Parallel Bridge | frequency measurement

Wien parallel bridge is also a ratio bridge used mainly as the feedback network in the wide-range audio-frequency R-C oscillators. This bridge may be used for measuring audio-frequencies although it is not as accurate as the modern digital frequency meters.

The bridge circuit of wien parallel bridge is shown in figure 1. In the simple theory of this bridge, capacitors C_{1} and C_{2} are assumed to be loss-free and resistance R_{1} and R_{2} are separate resistors.

The usual relationship for balance gives

Separating the real and imaginary terms, we have

And,

Or,

Note. Equation (ii) may be used to find angular frequency ω of the source if other terms are known. For such purpose, it is convenient to make C_{1} = 2C_{2}, R_{3} = R_{4 }and R_{2} = 2R_{1}. In that case, the bridge has equal ratio arms so that equation (i) will always satisfied. The bridge is balanced simultaneously by adjusting R_{2} and R_{1} (through maintaining R_{2} = 2R_{1}). Then, as sheen from equation (ii) above

**ω ^{2} = 1/(R_{1}.2R_{1}.2C_{2}.C_{2}) or ω = 1/(2R_{1}C_{2})**