Hall-Effect & Magnetic-Field Sensors

The Hall effect produces a transverse electric field when charge carriers move through a conductor or semiconductor in a perpendicular magnetic field. An integrated sensor supplies bias, amplification, offset cancellation, temperature compensation, and either analogue conversion or a thresholded digital output.

Three output contracts #

• A linear sensor reports one or more components of flux density.
• A switch changes state beyond an operate threshold and returns below a release threshold.
• A latch changes state with one magnetic polarity and resets with the opposite polarity.

Hysteresis between operate and release prevents noise chatter. It also means a switch's state is not a single-valued function of instantaneous field inside the hysteresis band.

Position is inferred through a magnetic model #

The sensor measures $B_x$, $B_y$, or $B_z$, not position directly. Magnet material, dimensions, orientation, air gap, ferromagnetic neighbors, assembly tolerance, temperature, and external current fields define $B(x)$. Calibration is valid only for that magnetic circuit.

For a two-axis rotating magnet, angle can be estimated as

$$\hat\theta=\mathop{\mathrm{atan2}}(B_y-B_{y0},\ B_x-B_{x0}).$$

Offset shifts the circle; gain mismatch makes it an ellipse; axis nonorthogonality distorts phase. A multi-point calibration can correct these errors, but not magnetic saturation or an air gap outside the calibrated geometry.

Failure reasoning #

Test magnet-present and magnet-missing states, both travel directions, full temperature and supply range, worst air gap, nearby steel, and maximum load current. Redundant sensors placed together are not independent if the same displaced magnet or stray field drives both.