Broadband Continuous Extraction of Complex Propagation Constants in Methods Using Two-Line Measurements

This letter proposes a new set of formulas that readily remove the sign-assignment problem of square roots frequently occurring in complex propagation constant extractions and error-box calibrations by using two-line test vehicles or standards. Instead of direct complex-number calculations, real transcendental functions of attenuation and phase factors are calculated first. They are then combined, with a proper sign assignment, to recover eigenvalues that contain information on the propagation constant γ. The forward and backward γ's are continuously extracted by taking the logarithms of the calculated eigenvalues.