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A new formalism using line-line measurements is proposed to improve the accuracy of propagation constant measurement of reflection-asymmetric networks using non-calibrated scattering (S-) parameters. For this measurement, the method uses a reference network with arbitrary forward and backward impedance, propagation constant, and length, thus giving flexibility in the application of line-line methods. S-parameter measurements were carried out for propagation constant extraction of a reflection-asymmetric waveguide loaded with a bianisotropic metamaterial slab made by C-shaped split-ring-resonators using two different kinds of reference networks (two empty waveguide sections as the first kind and the same sections loaded by polyethylene samples as the second kind). It is observed that the standard deviation in the extracted real part of the propagation constant of this network by our method could be reduced by using the first kind of reference network, indicating that the accuracy of our method could be improved using a suitable reference network.

A general “line-line” (LL) method is proposed for propagation constant determination (γ+ and γ−) of nonreciprocal networks using multiple reference networks. The new formalism provides flexibility in implementation of LL methods so that not only more accurate γ+ (and γ−) could be retrieved but also the effect of inaccurate length information of the non-reciprocal network on γ+ (and γ−) evaluation could be suppressed. For validation of the method, γ+ and γ− 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. © 2022