A Sinusoidal Encoder-to-Digital Converter Based on an Improved Tangent Method

Sinusoidal encoders are used for the measurement of angular position and linear displacement. These provide electrical signals dependent on the sine and cosine of the position θ of their moving part relative to the stationary one. Conventional tangent/cotangent converters for determining θ from the encoder signals produce alternating highly non-linear segments of tangent and cotangent. Lookup tables are used for determining θ. This paper presents a novel converter for estimating θ without the lookup table. The method is based on dividing the circle angular interval into N sections. A crude or coarse measure θ
_C
of the unknown angle θ is first determined by identifying the section in which θ is located. This is followed by the determination of a fine measure θ
_F
. These measures are combined to yield a precise measure of θ; the maximum error of the method depends on N. The converter has been implemented on a dSPACE set and has been successfully tested both with a sensor emulator and a real Hall-Effect sinusoidal encoder. This paper describes full details of the theory, simulation, and experimental results. The experimental results demonstrate excellent agreement with theory and simulation.