Maxwell Bridge, Advantages and Disadvantages

The Maxwell Bridge is shown in the figure below. It measures an unknown inductance in terms of a known capacitance. The unknown inductance with its resistance is represented as L_X and R_X respectively. The parallel combination of the variable resistance R₁ and the capacitor C₁ forms a ratio arm. A variable resistance R₃ and resistance R₂ take the positions of the two other arms of the bridges.

Maxwell Bridge Circuit Diagram

The balance condition is obtained as shown below:

Taking  Z_x = Z₂Z₃Y₁

Z₂ = R₂

Z₃ = R₃

Y₁ = 1/R₁ + jωC₁

Therefore Z_x = R_x + jωL_x = R₂R₃ (Y₁)

= R_x + jωL_x = R₂R₃ (1/R₁ – jωC₁)

= R_x + jωL_x = ((R₂R₃)/R₁) + R₂R₃ jωC₁

Equating real terms:

R_x = R₂R₃/R₁

Equating imaginary terms:

L_x = R₂R₃C₁

Hence we have two variables R₁ and C₁ that appear in one of the two balance equations and hence the two equations are independent. The expression for Q factor:

Q = ωL_x/R₁ = ωC₁R₁

The Maxwell Bridge Advantages and Disadvantages are as follows.

(a) Advantages of Maxwell Bridge:

1. The two balance equations are independent if we chose R₁ and C₁ as variable elements.

2. The frequency does not appear in any of the two equations.

3. This bridge gives simple expression for unknown values of L_x and R_x in terms of known bridge elements. Physically R₂ and R₃ can be each say 10, 100, 1000 or 10,000 Ω. and their value is selected to give suitable value of product R₂ R₃ that appears in both the balance equations. C₁ can be a decade capacitor and R₁ can be a decade resistor. If the product R₂ R₃ = 10⁶, then the inductance is given by

L_x = C₁ x 10⁶.

Therefore when the balance is achieved the value of C₁ directly in micro-farads gives the value of inductance in henry.

4. This bridge is useful for measurement of wide range of inductance at power and audio frequencies.

(b) Disadvantages of Maxwell Bridge :

1. The bridge requires a variable standard capacitor which can be very costly if the degree of accuracy is high. In some cases fixed value of capacitance are used. The balance adjustment may be done by either varying R₂ or R₁. As R₂ appears in both the balance equations, the balance adjustment will be difficult. Other method is to place extra resistance in series with the inductance under measurement and then varying the resistance R₁.

2. This bridge can measure values of inductance of medium Q coils. The reason is that the phase angles of arms 2 and 3 put together must be equal to the phase angles of arms 1 and 4 added up and that must be equal to 0°.

To accommodate the measurement of high Q coil the phase angle of the capacitive arm must be nearly 90° (negative), as the phase angle of a high Q coil will be nearly 90°. This needs a very large value of resistance R₁ which is practically not possible.

Low Q coils also cannot be measured with this bridge due to the interaction of R₁ and R₃. When R₃ is adjusted for inductive balance, the resistive balance is upset. This is termed sliding balance. That is when once balanced with R₁ and then with R₃ if we try to balance again with R₁ we get new balance point. The balance appears to be moving or sliding towards the final point after several adjustments. Therefore this bridge is to be balanced first with R₃ for inductance balance and then with R₁ for resistive balance. The process is to be repeated to get the final balance.

Hence we note that this Maxwell bridge is suitable for measuring medium Q coils alone.