Selecting magnet to be used along with hall effect sensors.

[voskos]

Hi,
I am trying to create a hall effect based position sensor to be attached onto a DC motor to generate feedback for position control. I am thinking of the following arrangement:

4 hall sensors are placed 90 degrees apart around the magnetic element. Each sensor surface is directed at the axis, so if the magnetic field vector is perpendicular to the surface, the measured voltage is at maximum (or minimum depending on the polarity).

By computing the mangitude (and polarity) along the two axes by measuring the induced hall effect voltage onto the 2 pairs of sensors, I should be able to determine the angle of the axis pretty accurately.

I am trying to determine what type of magnet should I be using. Unfortunately, I skiped class and I have no idea on how to calculate the best possible shape. What I need is the perperdicular component of the magnetic field vector on each of the four sensors to be propoprtional to B * sin(theta) where theta is angle (of orientation on a x-y plane) of the magnet, and therefore the axis.

From what I can gather, I need the direction of the magnetic field line to be proportional to the angle from the axis of the magnet, and the magnitude to be constant at fixed distance. The intent here is to generate a Voltage output that is as much as possible proportional to sin(θ) and cos(θ) on the two axes.

I can only find N50 disc magnets that can fit to the available space.

Is there a closed form solution for the disc shaped magnet`s magnetic field, which I could use to estimate the sensor outputs, say in MATLAB?

I apologize in advance if this has been answered before. I did search, but I was unable to find something

 

[mfb]

In general, all those magnetic fields are not proportional to anything, and you need something more complicated to calculate the position. Can you measure the field, and make a map of its strength along the axis the Hall sensors will measure?
Small magnets will give an easier, but weaker field.