AMR angle sensors are two dimensional in design but the complete magnetic field vector is 3D. The field vector parallels the face of the magnet when a magnet is centered on the axis of rotation along the pole boundary.

As a result, when the magnet rotates, the field vector is constrained in two dimensions and this produces the correct input for the sensor (Figure 3-1). The magnetic field vector varies in all three axes if the sensor is moved away from the axis of rotation.

The magnetic sensor is exposed to all three field components, with a circular profile presumption, but a significant portion of the input field in the z-direction is left undetected by the sensor. As a result, some input non-linearity is introduced. Consider the Lissajous plot in Figure 3-3 that uses the full vector and projection onto the XY plane when the Z component is ignored in Figure 3-4.

The resulting input magnetic field angle changes at a different rate than the mechanical rotation measured because the resulting projection is elliptical instead of circular (the extremes for the X direction are ±45 mT while the Y direction is closer to 50 mT). The outputs generated by the device can take an unexpected form due to this non-linear change in angle. Careful examination of Figure 3-5 reveals that the output waveforms are slightly distorted and not demonstrating correct sine and cosine behavior.

The sensor outputs a non-linear angle calculation since the input to the sensor changes with a non-linear angle. This angle change is cyclical, so calibrating the sensor using techniques like multipoint linearization, a Look-up table, or harmonic approximation is available if necessary. These techniques are further described in Achieving Highest System Angle Sensing Accuracy.