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Anderson’s Bridge Circuit and Theory of Anderson Bridge

For very accurate measurement of inductance, we have to modify the Maxwell Wien Bridge.  And then, we call this modified form as Anderson’s bridge. Here actually, we compare the unknown inductance with a standard fixed capacitance. Although instead of connecting the capacitor in the side arm we connect it in between two arms of the bridge.

Circuit of Anderson Bridge

Anderson Bridge
Anderson Bridge

Like other AC Bridges, an Anderson bridge has also four side arms. The arm AB consists of a resistance R1 and the arm BC consists of a resistance R2. Also, the arm DA consists of a resistance R4. A coil of unknown inductance L3 forms the arm CD, as shown. We have also shown in the figure, the inherent resistance (R3) of the coil in series with the inductance.  There are one standard capacitor and a variable resistor in series between node A and B. Now we shall apply the star delta transformation technique to the star circuit formed by resistance R1, R4, and R5 in respect of node A. For better understanding the star delta conversion in the above Anderson Bridge, let us look into the figure given below.

Star Delta Transform in Anderson Bridge
Star Delta Transform in Anderson Bridge

After applying formulas for expression of delta branch resistances in terms of existing star branch resistances, we get

Theory of Anderson’s Bridge

With these delta branch resistances, if we redraw the same Anderson bridge, we will have the circuit shown below.

modified anderson bridge
Modified Anderson Bridge

Now, we will recall the condition of balanced Maxwell Wien Bridge. This is because the AC bridge circuit just above is similar to the circuit of Maxwell Wien Bridge. Hence, we can write

After, putting the expression of RBO and ROD in the above equations, we get


As we told at the beginning of this article, an Anderson Bridge Bridge is capable of measuring inductance in a very precise manner. It can measure a very wide range of inductance. This is the most common AC Bridge circuit which we use for measuring inductance.

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