An apparatus for detecting a rotation angle, comprising: an annular stator around an axis of revolution Z, comprising: at least a first pole, a second pole, and a third pole arranged at constant azimuthal intervals around the axis of revolution of the annular stator, each of the poles comprising one or more electrical windings, and each of the poles comprising a flange that is a portion of a first surface of revolution around the annular stator's axis of revolution, the flange having an area distribution substantially that, within a coordinate system, of a sin(α) function from a low α bound of about 0 radians to a high α bound of about π radians. The apparatus may comprise a rotor that comprises sectors having the azimuthal extent of one flange and having different magnetic permeabilities. Methods for forming the apparatus and for obtaining measurements are also presented.