An integrated motor-position sensor, comprising: a motor comprising: a rotor assembly comprising an axially polarized rotor magnet between an upper rotor pole cap and a lower rotor pole cap with both having a plurality of peripherally-spaced radially-projecting rotor teeth (12, 13), the rotor teeth of the upper rotor pole cap aligned with gaps between the rotor teeth of the lower rotor pole cap, the magnetically soft upper rotor pole cap and the magnetically soft lower rotor pole cap having rotor teeth (12, 13), and the rotor teeth of the lower rotor pole cap having a magnetic field corresponding to the polarity of the lower side of the rotor magnet; a stator assembly coaxial with the rotor assembly and having a plurality of radially-projecting stator poles, the stator poles each having a plurality of stator pole teeth projecting radially to a circle coaxial with the rotor assembly, and coils for electrically energizing the stator poles; and a plurality of position sensing elements (4, 5) energized by the axially polarized rotor magnet of the rotor assembly and a relative motion of the rotor assembly with respect to the stator assembly, wherein each of the position sensing elements (4, 5) includes: a large Barkhausen jump sensor with a sense coil for producing pulses responsive to a change in a magnetic field across the large Barkhausen jump sensor, and a flux collector for directing magnetic flux having an alternating magnetic polarity from one or more of the rotor teeth (12, 13) to the large Barkhausen jump sensor, wherein a relative position of the rotor assembly with respect to the stator assembly is determinable within a fraction of an electrical cycle of the motor. a motor comprising: a rotor assembly comprising an axially polarized rotor magnet between an upper rotor pole cap and a lower rotor pole cap with both having a plurality of peripherally-spaced radially-projecting rotor teeth (12, 13), the rotor teeth of the upper rotor pole cap aligned with gaps between the rotor teeth of the lower rotor pole cap, the magnetically soft upper rotor pole cap and the magnetically soft lower rotor pole cap having rotor teeth (12, 13), and the rotor teeth of the lower rotor pole cap having a magnetic field corresponding to the polarity of the lower side of the rotor magnet; a stator assembly coaxial with the rotor assembly and having a plurality of radially-projecting stator poles, the stator poles each having a plurality of stator pole teeth projecting radially to a circle coaxial with the rotor assembly, and coils for electrically energizing the stator poles; and a plurality of position sensing elements (4, 5) energized by the axially polarized rotor magnet of the rotor assembly and a relative motion of the rotor assembly with respect to the stator assembly, wherein each of the position sensing elements (4, 5) includes: a large Barkhausen jump sensor with a sense coil for producing pulses responsive to a change in a magnetic field across the large Barkhausen jump sensor, and a flux collector for directing magnetic flux having an alternating magnetic polarity from one or more of the rotor teeth (12, 13) to the large Barkhausen jump sensor, a rotor assembly comprising an axially polarized rotor magnet between an upper rotor pole cap and a lower rotor pole cap with both having a plurality of peripherally-spaced radially-projecting rotor teeth (12, 13), the rotor teeth of the upper rotor pole cap aligned with gaps between the rotor teeth of the lower rotor pole cap, the magnetically soft upper rotor pole cap and the magnetically soft lower rotor pole cap having rotor teeth (12, 13), and the rotor teeth of the lower rotor pole cap having a magnetic field corresponding to the polarity of the lower side of the rotor magnet; a stator assembly coaxial with the rotor assembly and having a plurality of radially-projecting stator poles, the stator poles each having a plurality of stator pole teeth projecting radially to a circle coaxial with the rotor assembly, and coils for electrically energizing the stator poles; and a plurality of position sensing elements (4, 5) energized by the axially polarized rotor magnet of the rotor assembly and a relative motion of the rotor assembly with respect to the stator assembly, wherein each of the position sensing elements (4, 5) includes: a large Barkhausen jump sensor with a sense coil for producing pulses responsive to a change in a magnetic field across the large Barkhausen jump sensor, and a flux collector for directing magnetic flux having an alternating magnetic polarity from one or more of the rotor teeth (12, 13) to the large Barkhausen jump sensor, a large Barkhausen jump sensor with a sense coil for producing pulses responsive to a change in a magnetic field across the large Barkhausen jump sensor, and a flux collector for directing magnetic flux having an alternating magnetic polarity from one or more of the rotor teeth (12, 13) to the large Barkhausen jump sensor, wherein a relative position of the rotor assembly with respect to the stator assembly is determinable within a fraction of an electrical cycle of the motor.