From our findings based on sensor placement we can deduce a method to minimize the error that results from mismatch in each field component. Consider Figure 4-1 which shows a side view of the 20-pole ring magnet we have been analyzing.

We have already closely examined positions I and II. In position I (out-of-plane), the z-component is the strongest field component, and in position II (in-plane) the z-component is zero. It is reasonable to expect that as there is a position III at some angle of rotation outward where the z-component will equalize with one of the other two field components. Likewise, the radial component has the largest magnitude in position II, where is it the smallest component in position I.

A simulation sweep to find a possible position III resulted with an angle of 38.9°. Matching between B_r and B_θ was achieved at this angle when using a fixed range of 3.25 mm to the center of the face of the magnet. Magnetic field components can be seen in Figure 4-2.

The resulting B_r and B_θ fields have a peak amplitude of 12.4 mT, and the resulting worst case angular error of 0.85° will be entirely due to sensitivity mismatch.

While position I and II are common and easily implemented, position III can be difficult to achieve in practice. It does, however, provide optimal input matching for the best overall performance.

As an alternative to finding the ideal placement of the sensor, it will also be beneficial to consider how to modify the magnet to improve performance as well.