Propagation constant measurements of reflection-asymmetric and nonreciprocal microwave networks from S-parameters without using a reflective standard

We propose a simple method for determination of forward and backward propagation constants of nonreciprocal uniform networks or lines with asymmetric reflections. The wave cascading matrix presentation is used to diagonalize and decompose the line in terms of impedance and amplitude/phase transitions. The proposed method uses scattering parameters of the line/network connection and the thru connection, thus eliminating errors arising from fabrication tolerance and thickness of the second line. Besides, compared with conventional methods which necessitate calibration techniques such as the thru-reflect-line, our method has the advantage that it determines propagation constants without resorting the measurement of any reciprocal reflective standard. Propagation constant measurements of a reciprocal network (different-length X-band waveguide straights) and a nonreciprocal network (microwave phase shifter) were first carried out and then compared with those measured by different methods to validate and monitor the accuracy of our method.