Although based on the use of simple amplitude detectors, it is possible to obtain complex values of reflection coefficient, via the six-port technique, from the intersection of three circles in the complex plane. In a typical case, the circle centers are determined primarily by the six-port design and are nominally constant, while the radii are proportional to the square root of the ratio of the output of three of the detectors to a fourth one. As a practical matter, however, these circles will not intersect in a point because of noise or other errors in the detectors.
This paper develops a procedure for choosing Gamma in this context. Moreover, the question of what may be inferred about the system performance from the extent of this intersection failure is briefly considered.
Glenn F. Engen, "A least squares solution for use in the six-port measurement technique," IEEE Transactions on Microwave Theory and Techniques, vol. 28, no. 12, pp. 1473-1477, December 1980.
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