After removing signal chain errors from the calculation, there are still several possible mechanical sources that may impact the quality of the input magnetic field used to calculate angle:

• Motor Shaft tilt – results in an orthogonality error between TIDA-060040 and the rotating magnet. This produces a fixed shift to the expected field alignment.
• Motor Shaft offset – results with the sensor in a different location and orientation than targeted. Depending on the offset direction this can influence either peak input amplitude to or phase alignment of the inputs.
• Magnet tilt – results when the magnet is not installed orthogonally to the shaft rotation axis. The magnet appears to wobble during rotation and produces a changing field orientation.
• Magnet and Shaft Eccentricity – results from either the axis of rotation not aligning to the center of the shaft or the magnet not having its center aligned to the axis of rotation. This produces a lateral change of position during rotation which impacts the B-field magnitude.
• Soldering and assembly alignment errors – Errors resulting from package alignment during solder-reflow to tolerances when mounting the TIDA-060040 PCB may result in various orientation and position errors that may similarly impact the phase and magnitude of the inputs
• Near field behavior – At close proximity to many magnet types, the magnetic field may produce a non-ideal input for the sensor. The target input field is a purely sinusoidal waveform. The observed field when a sensor is placed very close to a magnet will typically take on some degree of distortion which is dependent on the magnet geometry.

All of the preceding errors combine to create non-linearity in the angle measurement. While these factors are not predictable, they may combine to create a substantial error which, if unaccounted for, results with poor system control. Given these factors it is necessary to implement a final calibration to resolve the resulting error for the highest precision control.

Multi-point linearization is one useful approach and may be used to quickly adapt to system-to-system variations. Consider the hypothetical error in Cyclical Angle Error.

In this example, a multi-point linearization captures the absolute error at any number of discrete points. The controller then assumes a linear estimation of error between those points. As the number of points increases, the accuracy of the estimation approaches the real error. When an approximation of the error for any given angle is determined, it may then be directly subtracted from the measured angle.

As the number of samples increases, the resulting peak error is continually reduced. Depending on the required system accuracy, 8 points to 64 points can often provide adequate accuracy. In a more advanced approach, it is possible to match the error profile to a set of equations which are a combination of harmonics of the rotation frequency. By performing complex analysis, it is possible to generate a series of coefficients, α_i and β_i, that may be used as shown in Equation 10:

Here, the total error is a combination of the scalar factors for each harmonic of the measured angle. Using this approach can produce superior results to the multi-point linearization method and does not require storing as much data in memory.

For all of the test results, the data was captured at 0.25° intervals and analyzed for harmonic reduction.

To achieve consistent results in a real manufacturing environment, some degree of calibration for each system is likely necessary as each unit would exhibit slight variations in the various mechanical tolerances.