Analysisof Six-Portmeasurement Resolution by Conformal Mapping

Microwave measurement systems based on the six-port principle fully reconstruct complex wave-vector ratios from sets of redundant magnitude-only readings. This leads to determining the representative points in the complex plane of the vector-ratios as intersections of three or more circles. A simple conformal mapping may be used to visualize the resolution of this method and its sensitivity to errors in the magnitude readings. This mapping transforms families of constant-magnitude-ratio circles in straight parallel lines. The coordinates in the transformed plane are the measured magnitude ratio in dB and the angle between the tangents to the intersecting circles at the intersection points. An example of computer-generated mapping representing a typical location of the q-points is presented and discussed.