Inductive & Variable-Reluctance Sensors

Inductive sensors are a family, not one transfer law. A moving ferromagnetic part may change reluctance and coil inductance; a conductive target may add eddy-current loss; a toothed wheel passing a biased pole may induce an AC voltage; an LVDT changes transformer coupling and produces a signed differential output.

Variable reluctance #

With coil turns $N$ and magnetic reluctance $\mathcal R$, the unsaturated approximation is

$$L\approx\frac{N^2}{\mathcal R}.$$

Because an air gap often dominates $\mathcal R$, small gap change creates measurable inductance change. The same inverse-gap sensitivity also makes mounting tolerance, runout, and vibration important.

For a passive variable-reluctance speed pickup, Faraday's law gives $e=-N\,d\Phi/dt$. Output therefore falls toward zero at low speed even when the tooth is correctly positioned. A fixed voltage threshold creates speed-dependent timing and may fail completely near standstill.

LVDT reasoning #

An AC-excited primary couples to two opposed secondaries. At electrical null their amplitudes cancel; displacement changes the differential amplitude, while carrier phase identifies direction after synchronous demodulation. Lead phase, excitation stability, magnetic asymmetry, and demodulator reference error shift null and gain.

Eddy-current/inductance conversion #

A conductive target changes both effective inductance and resonator loss. Target conductivity, permeability, thickness, diameter, distance, coil geometry, and excitation frequency matter. Calibration with one metal cannot be transferred blindly to another.

Diagnostic separation #

Verify raw carrier/amplitude, demodulated value, gap, target material, temperature, and speed independently. A final digital position alone cannot reveal which physical quantity the channel actually sensed.