A Novel Direct Geometric Algorithm for Worst-Case Error Analysis of Six-Port Reflectometer and Its Guiding Significance in Application

In this article, a novel direct geometric algorithm for worst-case error analysis of six-port reflectometer is proposed. Due to the inevitable power measurement uncertainty, six-port reflectometer shows an inherent deviation that can be represented as an irregular area based on the classical geometrical theory. The previous worst-case error analysis geometric algorithm approximates the boundary of the irregular area with straight lines and utilizes several special points in comparison. Without approximation, points on the boundary of the irregular error distribution area can be directly obtained in the proposed algorithm. After traversing all points, the maximum errors of the reflection coefficient in magnitude and phase around the entire Smith Chart can be determined accurately. This algorithm is first verified by comparing state-of-the-art approximating algorithm in simulation. After plotting the error distributions of five classical six-port models, a novel common conclusion is obtained that the area that shows the minimum error in the entire Smith Chart can be found in geometry for an arbitrary six-port reflectometer. A practical six-port reflectometer system is set up, calibrated, and utilized for the algorithm verification. The consistent results show the availability and the fundamental guiding significance on specific six-port reflectometer applications design of the proposed algorithm.