Anderson′s Bridge | Advantages Disadvantages of Anderson′s Bridge

Anderson’s Bridge

Let us understand why there is a need for Anderson’s bridge though we have Maxwell bridge and Hay’s bridge to measure the quality factor of the circuit. The main disadvantage of using Hay’s bridge and Maxwell bridge is that they are unsuitable for measuring the low-quality factor.

Hay’s and Maxwell bridges are good for measuring high and medium quality factors accurately. However, we need a bridge for low-quality factors. Anderson’s Bridge, a modified Maxwell’s bridge, fulfills this need.

Anderson’s Bridge is a modified Maxwell inductor capacitance bridge. It achieves double balance by fixing the capacitance value and only changing the electrical resistance.

Anderson’s Bridge is known for accurately measuring inductors ranging from micro Henry to several Henry. It measures the unknown inductor value by comparing known resistance and capacitance values. Let’s look at the actual circuit diagram of Anderson’s Bridge.

In this circuit, the unknown inductor is connected between the point a and b with electrical resistance r₁ (which is pure resistive).

The arms bc, cd and da consist of resistances r₃, r₄ and r₂ respectively which are purely resistive. A standard capacitor is connected in series with variable electrical resistance r and this combination is connected in parallel with cd.

A supply is connected between b and e.
Now let us derive the expression for l₁ and r₁:

At the balance point, we have the following relations that hold good and they are:

Now equating voltages drops we get,

Putting the value of i_c in the above equations, we get


The above equation (7) obtained is more complex than we have obtained in the Maxwell bridge. On observing the above equations we can easily say that to obtain convergence of balance more easily, one should make alternate adjustments of r₁ and r in Anderson’s bridge.

Now let us look at how we can obtain the value of unknown inductors experimentally. At first set the signal generator frequency at audible range. Now adjust r₁ and r such that the phones give a minimum sound.

Measure the values of r₁ and r (obtained after these adjustments) with the help of a multimeter. Use the formula that we have derived above in order to find out the value of unknown inductance. The experiment can be repeated with the different values of the standard capacitor.

Phasor Diagram of Anderson’s Bridge

Let us mark the voltage drops across ab, bc, cd, and ad as e₁, e₂, e₃ and e₄ as shown in the figure above.

Here in the phasor diagram of Anderson’s bridge, we have taken i₁ as the reference axis. Now i_c is perpendicular to i₁ as the capacitive load is connected at ec, i₄ and i₂ are lead by some angle as shown in the figure.

Now the sum of all the resultant voltage drops i.e. e₁, e₂, e_3, and e₄ is equal to e, which is shown in phasor diagram. As shown in the phasor diagram of Anderson’s bridge the resultant of voltages drop i₁ (R₁ + r₁) and i₁.ω.l₁ (which is shown perpendicular to i₁) is e₁. e₂ is given by i₂.r₂ which makes angle ‘A’ with the reference axis.

Similarly, e₄ can be obtained by voltage drop i₄.r₄ which is making angle ‘B’ with the reference axis.

Advantages of Anderson’s Bridge

1. It is very easy to obtain the balance point in Anderson’s bridge as compared to Maxwell bridge in the case of low-quality factor coils.
2. There is no need for a variable standard capacitor is required instead of thin a fixed value capacitor is used.
3. This bridge also gives accurate results for the determination of capacitance in terms of inductance.

Disadvantages of Anderson’s Bridge

1. The equations obtained for the inductor in this bridge are more complex as compared to Maxwell’s bridge.
2. The addition of capacitor junction increases complexity as well as the difficulty of shielding the bridge.

Considering above all the advantages and disadvantages, the Maxwell bridge is preferred over Anderson’s bridge whenever the use of a variable capacitor is permissible.