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In this work, a comparison between three broadband methods used to estimate the propagation constant of planar transmission lines is presented. The goal of this comparison is to study how possible random measurement errors can affect the use of the aforementioned methods commonly used, since in ideal conditions the same solution is obtained from all of them. For this purpose, a sensitivity analysis is carried out in order to study the similarities and differences and how errors in measured S-parameters and in line lengths affect the attenuation and the phase constant obtained from each method. Subsequently, a minimization approach that consists of a least-square estimation using a criteria to choose the optimal line lengths is proposed to minimize measurement errors. Finally, an experiment has been designed, manufactured using microstrip transmission lines, and measured to validate the developed theory. Results corroborate the proposed theory and show an excellent agreement with electromagnetic simulations in the 0.1- to 50-GHz frequency band, therefore assessing the suitability of the proposed error analysis.

Random Errors in Broadband Characterization of the Propagation Constant of Transmission Lines Using Multiple Two-Port Measurements