MAXWELL BRIDGE CIRCUIT

Maxwell’s bridge measures an unknown inductances in terms of a known capacitor.

The Maxwell bridge circuit diagram is as shown in figure. Maxwell bridge are of the ratio arms has a resistance and a capacitance in parallel.

The Maxwell bridge circuit is as shown in figure below. 

The unknown inductance is connected in the fourth arm of the bridge.

The four bridge arms Z₁, Z₂, Z₃ and Z₄ are impedances and the detector is represented by headphones.

When the bridge is balanced, the detector response is zero or indicates a null. Balance adjustment to obtain a null response is made by varying one or more of the bridge arms.

The conditions for bridge balance requires that the potential difference from point A to C be zero. This will be the case when the voltage drop from B to A equals the voltage drop from B to C, in both magnitude and phase.

I₁Z₁ = I₂Z₂                         .......................            (1)

For zero detector current (the balance condition), the currents are

I₁ = E / Z₁ + Z₃ and I₂ = E / Z₂ + Z_X

Substitution of above equation in equation (1), gives

 E / Z₁ + Z₃ * Z₁ = E / Z₂ + Z_X * Z₂

Z₁ / Z₁Z₃ + Z₂ / Z₂+Z_X

        (or)

Z₁Z_X = Z₂Z₃

Z_X = Z₂Z₃ / Z₁ = Z₂Z₃Y          ....................       (2)

Here Y₁ = 1/Z₁ = 1/R₁ + JωC,

Z₂ = R₂, Z₃ = R₃ and Z_X = R_X + JωL_X

Substitution of these values in equation (2) gives

 R_X + JωL_X = R₂ R₃ (1/R₁ + JωC)

R_X + JωL_X = R₁R₃ / R₁ + JωC, R₂R₃

Separation of the real and imaginary terms, we get

R_X = R₂R₃/ R₁                     ..........................       (3)

And L_X = R₂ R₃ C₁             ............................      (4)

The equation (4) is used to calculate the unknown inductance in terms of a known capacitance.

The Maxwell bridge is limited to the measurement of medium. Q coils

(1<Q<10). The usual procedure for balancing the Maxwell bridge is by first adjusting R₃, for inductive balance and then adjusting R₁ for resistive balance.

Also Q = WL_X / R_X = WC₁R₂R₃ / R₂R₃ * R₁ = WC₁R₁.

APPLICATIONS:

It is used for inductances measurements.

The bridge can be made to read directly in Q.

LIMITATIONS:

Using a fixed capacitor has the disadvantage that there is an interaction between the resistance and reactance balances.

Only low Q values can be measures.

It is independent of the excitation frequency.