Fully Analytical Approach to Calibration of Six-Port Reflectometers Using Matched Load and Unknown Loads for One-Port Measurements

Abstract

In this article, the first fully analytical procedure for calibration of six-port reflectometers with a match load and unknown calibration loads, allowing for relative measurements of complex reflection coefficient, is proposed. The used loads may vary in both magnitudes and phases, with no particular requirement on their values; however, for a good performance, they should be reasonably spread over the complex plane. The proposed closed-form solution for six-port reflectometers' calibration does not require any sophisticated numerical algorithm or convergence analysis. Hence, it is significantly simpler to implement even in systems with reduced computational resources. The comparison against the previously reported numerical solution shows that the execution time is reduced by a factor of 800. The calibration is validated with the use of two six-port reflectometers with integrated power detectors over a bandwidth of 2.5-3.5 GHz. The results confirm high robustness to imperfect power measurement and very good agreement with values measured using a commercial vector network analyzer (VNA) for a large range of both magnitude and phase of the measured reflection coefficients.