A Maxwell bridge is a modification to a Wheatstone bridge in the case of calibrated induction used to measure an unknown (usually of low Q value) resistance and inductance or resistance and capacitance . When the calibrated components are parallel resistors and capacitors, the bridge is known as a Maxwell Wien bridge. It is named after James C. Maxwell , who first described it in 1873.
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 placed in the opposite arm and the circuit is at resonance; That is, there is no potential difference across the detector (an AC voltmeter or ammeter ) and hence no current flows through it. The unknown inductance is then known in terms of this capacitance.
In terms of diagrams, and in a typical application are known fixed entities, and and are known variable entities. and is adjusted until the bridge is balanced.
R_{1}R_{4}R_{2}C_{2}R_{2}C_{2}R3and can then be calculated based on the values of the other components: L3
{\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 exact 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 measurement of high Q values . Because of the equilibrium convergence problem, it is also unsuitable for coils with low Q values, less than one. Its use is limited to the measurement of low Q values from 1 to 10.
Q={\frac {\omega L}{R}}The frequency of the AC current used to measure the unknown inductor must match the frequency of the circuit in which the inductor will be used – the impedance and therefore the component’s fixed inductance varies with frequency. For ideal inductors, this relationship is linear, so that the inductance value at an arbitrary frequency can be calculated from the inductance value measured at a reference frequency. Unfortunately, for real components, this relationship is not linear, and using a derived or calculated value in place of a measured value can lead to serious inaccuracies.
A practical issue in bridge construction is mutual inductance: the two inductors will have mutual inductance : when the magnetic field of one intersects the coil of the other, it will strengthen the magnetic field in that other coil, and vice versa, in both coils. distorting the installation. To minimize mutual inductance, orient the inductors along their axes perpendicular to each other, and separate them as far as practicable. Likewise, the close presence of electric motors, chokes, and transformers (such as in power supplies for bridges!) can induce mutual inductance in circuit components, so locate the circuit from a distance from any of these.
The frequency dependence of the inductance values gives rise to other constraints on this type of bridge: the calibration frequency must be less than the self-resonance frequency of the inductor and the self-resonance frequency of the capacitor, Fr.(l)> srf , c srf )/10. Before approaching those limits, the capacitor’s ESR will have a significant effect, and must be explicitly modelled.
For ferromagnetic core inductors, there are additional constraints. There is a minimum magnetization current required to magnetize the core of an inductor, so the current in the inductor branches of the circuit must be greater than the minimum, but not so large as to saturate the core of any inductor.
The additional complexity of using a Maxwell Wien bridge over simple bridge types is warranted in situations 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, so that the resistance and reactance of the load can be determined reliably.
