Wien’s Bridge Circuit and the expression for the unknown element at balance.

• Wien’s Bridge :

Circuit and derives the expression for the unknown element at balance,

Wien Bridge  has a series RC combination in one and a parallelcombination in the adjoining arm. Wien's bridge shown in fig 2.1.

its basic form is designed to measure f r e qu ency. It can also be used for the instrument of an unknown capacitor with great accuracy, The impedance of one arm is

The admittance of the parallelarm is

Using the bridge balance equation,we have

We have

Therefore

Equating the real and imaginary terms we have as,

Therefore,

                                                

                                                                                       .................. (1.1)

       

And,

The two conditions for bridge balance, (1.1) and (1.3), result in an expression determining the required

resistance ratio R2/R4 and another express determining the frequency of the applied voltage. If we satisfy

Eq. (1.1) an also excite the bridge with the frequency of Eq. (1.3), the bridge will be balanced.

In most Wien bridge circuits, the components are chosen such that R 1 = R3 = R and C1 = C3 = C.

Equation (1.1) therefore reduces to R2IR4 =2 at Eq. (1.3) to f= 1/2ПRC, which is the general equation

for the frequency of fl bridge circuit.

The bridge is used for measuring frequency in the audio range. Resistances R1 and R3 can be ganged together to have identical values. Capacitors C1 and C3 are normally of fixed values

The audio range is normally divided into 20 - 200 - 2 k - 20 kHz range In this case, the resistances can be used for range changing and capacitors, and C3 for fine frequency control within the range. 

The bridge can also be use for measuring capacitance. In that case, the frequency of operation must be known.

The bridge is also used in a harmonic distortion analyzer, as a Notch filter, an in audio frequency and radio frequency oscillators as a frequency determine element.

An accuracy of 0.5% - 1% can be readily obtained using this bridge. Because it is frequency sensitive, it is difficult to balance unless the waveform of the applied voltage is purely sinusoidal.