What is Owen’s Bridge? Theory, Diagram, Derivation & Advantages

Owen’s Bridge bridge is used for measurement of inductance in terms of a standard capacitance. The Fig. 1 shows the circuit diagram. The bridge has the following components.

Fig. 1: Owen’s Bridge

L₁ = Unknown inductance

R₁ = Resistance contained in L₁

R₂ = Variable non-inductive resistance

R₃ = Fixed non-inductive resistance

C₂ = Variable capacitor

C₄ = Standard capacitor

At balance condition,

\[{{\text{Z}}_{\text{1}}}{{\text{Z}}_{\text{4}}}\text{ = }{{\text{Z}}_{\text{2}}}{{\text{Z}}_{\text{3}}}\]

\[\left( {{\text{R}}_{\text{1}}}\text{+ j}\omega {{\text{L}}_{\text{1}}} \right)\frac{1}{\text{j}\omega {{\text{C}}_{\text{4}}}}\text{ =  }\left[ {{\text{R}}_{\text{2}}}\text{+ }\frac{1}{\text{j}\omega {{\text{C}}_{\text{2}}}} \right]{{\text{R}}_{\text{3}}}\]

or

\[\frac{{{\text{R}}_{1}}}{\text{j}\omega {{\text{C}}_{\text{4}}}}\text{+}\frac{{{\text{L}}_{1}}}{{{\text{C}}_{\text{4}}}}\text{ }=~\text{ }{{\text{R}}_{\text{2}}}{{\text{R}}_{\text{3}}}\text{+ }\frac{{{\text{R}}_{\text{3}}}}{\text{j}\omega {{\text{C}}_{\text{2}}}}\]

Now equating real terms

\[\frac{{{\text{L}}_{\text{1}}}}{{{\text{C}}_{\text{4}}}}\text{ =  }{{\text{R}}_{\text{2}}}{{\text{R}}_{\text{3}}}\]

or

\[{{\text{L}}_{\text{1}}}\text{ =  }{{\text{R}}_{\text{2}}}{{\text{R}}_{\text{3}}}{{\text{C}}_{\text{4}}}          ….(i)\]

Equating imaginary terms

\[\frac{{{\text{R}}_{\text{1}}}}{\text{j}\omega {{\text{C}}_{\text{4}}}}\text{ = }\frac{{{\text{R}}_{\text{3}}}}{\text{j}\omega {{\text{C}}_{\text{2}}}}\]

or

\[{{\text{R}}_{\text{1}}}\text{ = }\frac{{{\text{R}}_{\text{3}}}{{\text{C}}_{\text{4}}}}{{{\text{C}}_{\text{2}}}}    ….(ii)\]

The value of unknown inductance L₁ can be obtained in terms of standard capacitor C₄ by eq. (i)

The value of resistance R₁ contained in the inductance L₁ can also be found out by eq. (ii) in terms of known quantities R₃, R₄ and C₂.

Advantages of Owen’s Bridge

1. The balance equations are very simple and are independent of frequency.
2. A wide range of inductance can be measured by this bridge.
3. The two adjustable elements R₂ and C₂ are in the same arm. This makes reactive adjustment independent of resistive adjustment and avoids interlocking effect of sliding balance which sometimes causes difficulty when the two adjustments are in the different arms.

Disadvantages of Owen’s Bridge

1. The bridge requires a variable capacitor, which is a very expensive component moreover, its accuracy is very less (about 1% only).
2. For measuring inductance of coils having high Q factor, the value of C₂ required will be very large. It requires a decade capacitor (decade mean 10) which is difficult to obtain