# Maxwell bridge

A Maxwell bridge

A Maxwell bridge (in long form, a Maxwell–Wien bridge) is a modification to a Wheatstone bridge used to measure an unknown inductance (usually of low Q value) in terms of calibrated resistance and capacitance. It is a real product bridge.

It uses the principle that the positive phase angle of an inductive impedance can be compensated by the negative phase angle of a capacitive impedance when put in the opposite arm and the circuit is at resonance; i.e., no potential difference across the detector and hence no current flowing through it. The unknown inductance then becomes known in terms of this capacitance.

With reference to the picture, in a typical application ${\displaystyle R_{1}}$ and ${\displaystyle R_{4}}$ are known fixed entities, and ${\displaystyle R_{2}}$ and ${\displaystyle C_{2}}$ are known variable entities. ${\displaystyle R_{2}}$ and ${\displaystyle C_{2}}$ are adjusted until the bridge is balanced.

${\displaystyle R_{3}}$ and ${\displaystyle L_{3}}$ can then be calculated based on the values of the other components:

{\displaystyle {\begin{aligned}R_{3}&={\frac {R_{1}\cdot R_{4}}{R_{2}}}\\L_{3}&=R_{1}\cdot R_{4}\cdot C_{2}\end{aligned}}}

To avoid the difficulties associated with determining the precise value of a variable capacitance, sometimes a fixed-value capacitor will be installed and more than one resistor will be made variable. It cannot be used for the measurement of high Q values. It is also unsuited for the coils with low Q values, less than one, because of balance convergence problem. Its use is limited to the measurement of low Q values from 1 to 10.

The additional complexity of using a Maxwell bridge over simpler bridge types is warranted in circumstances where either the mutual inductance between the load and the known bridge entities, or stray electromagnetic interference, distorts the measurement results. The capacitive reactance in the bridge will exactly oppose the inductive reactance of the load when the bridge is balanced, allowing the load's resistance and reactance to be reliably determined.