Determination of propagation constant and impedance of non-reciprocal networks/lines using a generalized line-line method

A novel “line-line” (LL) method is generalized to determine forward and backward propagation constants (γ+ and γ−) and wave impedances (Z+ and Z−) of non-reciprocal networks/lines. It considers a reference network/line with any propagation constant, impedance, and length for this goal. A theoretical analysis is carried out to examine under which circumstance wave impedance together with propagation constant can be determined by the new general LL method. Measurements of γ+, γ−, Z+, and Z− of a microwave phase shifter (a nonreciprocal network) are conducted to validate our proposed method and examine its accuracy, through normalized root-mean-square and goodness of fit values, using uncalibrated scattering parameter measurements.