The stator-PM variable reluctance (VR) resolver has been proposed as a new position sensor for a wide speed range. The high-frequency (HF) signal injection is only required to measure the rotor position at low-speeds. Alternatively, at higher speeds, without requiring the HF excitation, the position measurement can be achieved by the back-EMF generated by the stator-PM. This novel resolver has a simple rotor structure and the analog signals can be efficiently decoded at high-speeds. In the first proposed stator-PM VR resolver, the prototype must have even number of rotor salient poles. However, the resolvers with odd number of rotor poles are also useful in many scenarios. To complete the design scheme of this resolver category, this article practices a solution on the basis of the theory of field modulation. The design issue and solution are illustrated and addressed in this paper. The winding function approach is applied to analyze the signals. With the low-cost materials, the proposed resolver measurement system is prototyped.