Maxwell Bridge

The Maxwell bridge is used to measure lossy inductances , it was named after the physicist James Clerk Maxwell .

theory

Schematic sketch of the Maxwell Bridge

The measuring bridge is similar in structure to the Wheatstone measuring bridge , but it contains complex resistances and must therefore be operated with sinusoidal alternating voltage like all alternating voltage bridges.

The bridge is leveled when

${\displaystyle {\frac {\bar {Z_{1}}}{\bar {Z_{2}}}}={\frac {\bar {Z_{3}}}{\bar {Z_{4}}}}}$

applies. The real part and the imaginary part are to be considered. If the real and imaginary parts are in the same relationship to each other in both bridge branches, the bridge is balanced in phase and amplitude (U becomes zero).

If one of the branches of the bridge does not contain any imaginary components, the voltage at the node (connection point of the voltmeter U) of this branch has no phase shift in relation to the alternating voltage. For zero adjustment, the ratio of the real and imaginary components of the elements Z in the other bridge branch must match - only then does the node of this bridge also have a phase shift of 0 °.

In principle, can with such a bridge circuit capacitors and the equivalent series resistance ( equivalent series resistance , ESR ) and dissipation factors are measured.

execution

Maxwell bridge: Lx is the lossy inductance to be determined, R ₂ represents its equivalent series resistance. The bridge is adjusted to U = 0 with R ₁ and R ₃ .

L ₁ , R ₁ are in a branch with the inductance L _x to be measured , consisting of the inductance value L ₂ and the equivalent series resistance (loss resistance) R ₂

R ₁ and R ₃ are adjustable. L ₁ is a reference inductance.

R ₁ and R ₃ are adjusted so that U = 0. This is achieved by bringing the phase position of the node of the left bridge arm to 0 ° with respect to the feeding AC voltage with R ₁ and by aligning the amplitudes of the nodes of both bridge arms with R ₃ . Only if these two conditions are met does U = 0.

In practice, for this purpose, R ₁ and R ₃ usually have to be repeatedly adjusted to a minimum alternately.

The following then applies:

${\displaystyle (R_{2}+j\omega L_{2})\cdot R_{3}=(R_{1}+j\omega L_{1})\cdot R_{4}}$.

Real part (loss resistance or equivalent series resistance) of the inductance L _x :

${\displaystyle R_{2}={\frac {R_{4}}{R_{3}}}R_{1}}$

Imaginary part (inductance value) of the inductance L _x :

${\displaystyle L_{2}={\frac {L_{1}}{R_{3}}}R_{4}}$