Measurement of Propagation Characteristics of Nonreciprocal Networks/Lines Using a Line–Line Method

Abstract

In this article have proposed a new calibration-free line–line method for propagation constant ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> ) determination of homogeneous nonreciprocal networks or lines with symmetric reflection property. To achieve our goal, wave-cascading matrices for impedance, amplitude, and phase changes for a line step from a homogeneous reciprocal network or line to a homogeneous nonreciprocal network or line (and vice versa). Two different approaches based on the proposed line–line method are proposed for unique extraction of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> in forward and backward directions. Measurements of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> for two reciprocal lines (waveguide straights at X-band and Ku-band with different lengths) and a nonreciprocal line (microwave phase shifter) were first carried out and then compared with measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> of these lines by different methods to validate our method and monitor its accuracy.