Off-axis magnetic angular sensor using a magnetic sensing probe and multi-pole magnet array

A method for measuring a position of a movable device versus a fixed device, the method comprising:

• disposing at least one magnetic field sensor proximate to a two-dimensional (2D) surface magnet array, wherein the 2D surface magnet array and the at least one magnetic field sensor are in a specific relative orientation such that a relative trajectory of the at least one magnetic field sensor is configured to be at a tilted, acute angle θ with respect to a length direction of a plurality adjacent magnetized tracks of the 2D surface magnet array,
• wherein the at least one magnetic field sensor is configured to output at least one periodic sine signal and at least one periodic cosine signal in response to relative movement along the relative trajectory, such that the at least one magnetic field sensor allows for an absolute position measurement of the 2D surface magnet array relative to the at least one magnetic field sensor within a period of the at least one periodic sine signal and the at least one periodic cosine signal,
• wherein the 2D surface magnet array comprises an axial cylindrical helical multipole magnet array having an outer radius R,
• wherein, in response to relative movement along the relative trajectory, the at least one magnetic field sensor is configured to generate a periodic position signal having a period Pθ that depends, at least in part, upon a width w and the tilted, acute angle θ according to an equation:
• P
• θ
• =
• a
• ⁢
• w
• cos
• ⁢
• θ
• ,
• with α=1 or α=2,
• wherein the tilted, acute angle θ is set so that the at least one magnetic field sensor is configured to generate N periods of the periodic position signal per 360° revolution of the axial cylindrical helical multipole magnet array based on a formula:
• tan
• (
• θ
• N
• )
• =
• Nw
• 2
• ⁢
• π
• ⁢
• R
• .
• wherein θN is an angle that generates N cycles.