Improved Propagation Constant Determination Using Two-Line Measurements

Accurate determination of the propagation constant ($\gamma$) in uniform microwave lines is critical but challenging due to the requirement for complex calibration and susceptibility to measurement noise. In order to overcome these limitations, a new objective function has been derived for improved propagation constant $\gamma$ measurement of uniform lines with symmetric reflections through calibration-free line–line measurements. Well-known methods in the literature on the determination of propagation constants with reflection asymmetry and non-reciprocal behavior structures are investigated and compared. To this end, mathematical derivations related to theory of microwave networks are validated by measurements in microwave frequency range X-band (8.2–12.4 GHz). Its advantage relies on the fact that it uses a term which is in the product form of determinants of two characteristic terms, whose value is close to unity both in theory and experiments. Eigenfactor (complex exponential) and $\gamma$ measurements of an X-band uniform (empty) waveguide section with symmetric reflections were carried out to validate our proposed formalism.