A Direct Phase Resolver With Zero Transient Against Phase Jump and Variable Frequency Conditions

The switch from Cartesian to polar coordinates is mathematically represented by the arctangent function, however, the time-consuming computation and numerical precision for the arctangent function are still an issue in real-time applications. This article presents a simple algebraic method to resolve the phase angle for a vector expressed in the Cartesian coordinate. The proposed phase resolver (PR) is based on the one-norm conversion for normalizing the vectors with distinct lengths into a shrunken space. The magnitude-constrained vector not only benefits the digit efficiency but also has a strong linear dependence on phase angle. To meet various precision needs, the bases of error registered in the PR can be extracted for phase error compensation. Four different precision levels of the PR are presented and the optimal coefficients of the error bases are derived. Both simulation and experimental results are agreed with each other and show the proposed PR is with better computing efficiency as compared with conventional approaches.