Single (1x) speed variable reluctance resolver

An N-phase variable reluctance (VR) resolver apparatus, N being an integer greater than or equal to three, the N-phase VR resolver apparatus comprising:

• a stator comprising:
• 2N number of coil-poles that are positioned at equal intervals around inside of the stator;
• and
• a primary coil and secondary coils that are wound at each of the 2N coil-poles,
• wherein the secondary coils include a sine signal sensing coil and a cosine signal sensing coil, and all primary coils are wound with the same number of coil turns, with the winding direction alternating between clock-wise (CW) and counter clock-wise (CCW) across the 2N coil-poles, wherein the number of coil turns and winding polarities for the secondary coils are determined by synthesis coefficients of a 2N-phase cosine-zero-force (ZF) transform,
• wherein coil turns ratios of the sine signal sensing and cosine signal sensing coils relative to the primary coil at coil-pole position n (1≤n≤2N) are determined by the absolute values of the corresponding sine synthesis and cosine synthesis coefficients at position n (1≤n≤2N) of the 2N-phase cosine-ZF transform, respectively,
• wherein coil-winding polarities of the sine signal sensing and cosine signal sensing coils at coil-pole position n (1≤n≤2N) are determined by signs of the corresponding sine synthesis and cosine synthesis coefficients at position n (1≤n≤2N) of the 2N-phase cosine-ZF transform, respectively,
• wherein coil-winding polarities of secondary coils at a coil-pole position where the primary coil is wound in the CCW direction are reversed relative to the signs of the corresponding synthesis coefficients;
• and
• a rotor comprising:
• a lobe defining one electrical period on the stator over one mechanical turn of the rotor.