Anderson Bridge

Theory

The Anderson's bridge gives the accurate measurement of self-inductance of the circuit. The bridge is the advanced form of Maxwell's inductance capacitance bridge. In Anderson bridge, the unknown inductance is compared with the standard fixed capacitance which is connected between the two arms of the bridge.

Construction of Anderson's Bridge

The bridge has fours arms ab, bc, cd and ad. The arm ab consists unknown inductance along with the resistance. And the other three arms consist the purely resistive arms connected in series with the circuit.

circuit
Fig. 1 Anderson's Bridge

The static capacitor and the variable resistor are connected in series and placed in parallel with the cd arm. The voltage source is applied to the terminal a and c.

Let, \( L_1 \) – unknown inductance having a resistance \( R_1 \).
\( R_2 \), \( R_3 \), \( R_4 \) – known non-inductive resistance
\( C \) – standard capacitor

At balance Condition,

\( I_1 = I_3 \)
\( I_2 = I_C + I_4 \)

Now,

\( I_1 R_3 = I_C \times \frac{1}{j\omega C} \)
\( I_C = I_1 j\omega CR_3 \)

Phasor Diagram of Anderson’s Bridge

The phasor diagram of the Anderson bridge is shown in the figure below. The current \( I_1 \) and the \( E_3 \) are in phase and represented on the horizontal axis. When the bridge is in balance condition the voltage across the arm bc and ec are equal.

circuit2
Fig. 2 Phasor Diagram of Anderson's Bridge

The current enters into the bridge is divided into the two parts \( I_1 \) and \( I_2 \). The \( I_1 \) is entered into the arm ab and causes the voltage drop \( I_1(R_1+R) \) which is in phase with the \( I_1 \). As the bridge is in the balanced condition, the same current is passed through the arms bc and ec.

Advantages of Anderson's Bridge:

  1. The balance point is easily obtained on the Anderson bridge as compared to Maxwell’s inductance capacitance bridge.
  2. The bridge uses fixed capacitor because of which accurate reading is obtained.
  3. The bridge measures the accurate capacitances in terms of inductances.

Disadvantages of Anderson's Bridge:

  1. The circuit has more arms which make it more complex as compared to Maxwell’s bridge.
  2. The equation of the bridge is also more complex.
  3. The bridge has an additional junction which arises the difficulty in shielding the bridge.