A comparative worst-case error analysis of some proposed six-port designs

A detailed analysis of the accuracy in complex-reflection coefficient measurement by the six-port technique is discussed. The expression of the relative error in amplitude measurement of the complex reflection due to power-reading errors are derived in worst-case situation using both the basic six-port and sensitivity analysis theories. The precision of measurement of any point in the Smith chart is obtained by reference to lines of constant errors (amplitude and phase) drawn on the Smith chart for various proposed six-port correlators (junctions). A comparison of three proposed six-port designs shows that the Engens six-port design presents the best performance for a given power measurement accuracy. A maximum dynamic range of 60 dB seems to be a limit for six-port reflectometers using a good-quality power detector (α=0.1%)