A precise converter for resolvers and sinusoidal encoders based on a novel ratiometric technique

Resolvers and other sinusoidal encoders provide electrical signals related to the sine and cosine of the unknown angular position of their rotor shafts. Conventional tangent/cotangent converter used with these transducers for determining the angular position is based on the computation of the ratio between the smallest and largest absolute values of the sine and cosine signals. This produces highly non-linear segments of tangent and cotangent requiring large-size look-up tables for the determination of the unknown angle. In this work, a novel method is presented for implementing this technique without the need for the determination of the absolute values of the sensor signals and of the cotangent. Additionally the precision of the proposed technique is guaranteed even by using a small size look-up table or a simple linear computation. The method is based on computing the ratio of sine and cosine segments of a number of phase-shifted sine and cosine signals such that non-linearity of the resulting tangent is greatly reduced due to the limitation of the angle interval in which it needs to be computed. The paper describes full details of the proposed method and provides a comparison with previously-reported techniques through extensive computer simulation.