In rotary encoding systems that require both speed and direction, the sensors should be placed ideally 90° out of phase from each other. Using a 2D sensor enables the user to achieve this 90° offset more simply because the sensors are naturally orthogonal to each other, meaning there is a natural 90° phase difference from each sensor. This means that, when picking a 2D sensor, it is necessary to pick the two directions that have the closest phase angle difference of 90° from each other. To calculate this, we can use the following formula:

Where X₂- X₁ is the difference between the leading and lagging sinusoidal waveforms. This difference is converted to a fraction by dividing it by the entire period of the signals.

The fraction multiplied by 360° will provide the phase difference between the two sinusoidal waveforms. On the encoder board that was created, due to the rotation of the sensor (board image in Figure 9-2), a 65.45° offset was estimated from the simulation. The phase angle calculation is below.

With ideal Hall sensor placement, meaning a 90° angle is achieved, the signal should yield a 50% duty cycle on the output. When the offset is greater or lesser than 90°, it may lead to uneven periods in the duty cycle, as seen for this system in Figure 8-6.