We generally use an Owen bridge to measure inductance in a wide range. Here we can measure the value of inductance in terms of capacitance and resistance only. Before going to actual theory of Owen bridge let us first draw its basic circuit diagram.
Owen Bridge Circuit
Here in the figure, we connect one capacitor of known capacitance C1 across the arm AB of the bridge. Then we connect a coil of inductance L3 and resistance R3 across the arm CD. Now we connect another capacitor of capacitance C4 with a resistance R4 in series with it across the arm DA. But we keep the remaining arm BC fully resistive with a pure resistance R2. Lastly, we connect the detector between node B and D and the alternating supply between node A and C as shown in the circuit diagram.
We can see from the circuit diagram that which is an AC Bridge. Hence, we have to treat this Owen bridge as an AC Bridge. Here the capacitance C4 and resistance R4 are adjustable. We achieve the balanced condition of the bridge by adjusting the capacitance and the resistance. The balanced condition of the bridge means the potential of node B and node D will be the same in respect of its magnitude and phase angle.
Theory of Owen Bridge
If we compare with the general AC Bridge we can easily come to the equations for the balanced condition of the Owen Bridge. Before going to the actual theory of Owen Bridge, let us draw a generalized circuit of an AC Bridge.
At balanced condition,
Now we will compare the impedance of each arm of the above shown Owen Bridge with that generalized AC Bridge circuit. And by doing this we get,
Now by applying balanced conditions of the AC Bridge to the Owen Bridge, we get
Now equating the real and imaginary parts to zero of the above equation we get,
Here, we see that in the expression of unknown inductance, there is no term related to the frequency of the supply source. So, we can conclude that the supply frequency cannot affect the measurement of the inductance. This is the main advantage of this type of bridge circuit.
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