The Wien Bridge

• As shown in Figure, one arm of a Wien bridge consists of a capacitor in series with a resistor (C1 and R3) and another arm consists of a capacitor in parallel to a resistor (C2 and R4).
• The other two arms simply contain a resistor each (R1 and R2).
• The values of R1and R2 are known, and R4 and C2 are both adjustable.
• The unknown values are those of C1 and R3.

 

• Like other bridge circuits, the measuring ability of a Wien Bridge depends on 'balancing' the circuit.
• Balancing the circuit in Figure means adjusting R4 and C2 until the current through the ammeter between points A and B becomes zero.
• This happens when the voltages at points A and B are equal.
• When the Wien Bridge is balanced, it follows that R2/R1 = Z1/Z2 where Z1 is the impedance of the arm containing C1 and Z2 is the impedance of the arm containing C2.

 

• Mathematically, when the bridge is balanced,  

R2/R1 = (1/ωC1 + R3) / (R4/[ωC2(R4 + 1/ωC2)]) wherein ω = 2πf; or 
R2/R1 = (1/ωC1 + R3) / (R4/[ωC2R4 + 1]); or 
R2/R1 = (1/ωC1 + R3) (ωC2 + 1/R4); or 
R2/R1 = C2/C1 + ωC2R3 + 1/(ωC1R4) + R3/R4.

• When the bridge is balanced, the capacitive reactances cancel each other out, so   

R2/R1 = C2/C1 + R3/R4. Thus, C2/C1 = R2/R1 - R3/R4.

 

• Note that the balancing of a Wien Bridge is frequency-dependent. 
• The frequency f at which the Wien Bridge in Figure becomes balanced is the frequency at which ωC2R3 = 1/(ωC1R4), or 2πfC2R3 = 1/(2πfC1R4). 
• Thus, the frequency f is given by the following equation:  f = (1 / 2π) x (sqrt(1/[R3R4C1C2])).