General line-line method for propagation constant measurement of non-reciprocal networks

A general "line-line "(LL) method is proposed for propagation constant determination (y+ and y-) of nonrecip-rocal networks using multiple reference networks. The new formalism provides flexibility in implementation of LL methods so that not only more accurate y+ (and y-) could be retrieved but also the effect of inaccurate length information of the non-reciprocal network on y(+) (and y(-)) evaluation could be suppressed. For validation of the method, y+ and y- of a microwave phase shifter (a nonreciprocal network) are determined using uncalibrated scattering parameter measurements at X-band (8.2-12.4 GHz). Two different statistical analyses based on normalized root-mean-square-error and goodness of fit and based on coefficient of variation and confidence interval are individually performed to evaluate the performance and accuracy of our method.