Design of Optimal Length for Waveguide Offset Shorts in D-band based on Uncertainty Analysis

Recently we established a D-band waveguide impedance standard. However, since it is very inefficient to use a primary standard for routine calibration service, here we design another offset shorts calibration kit. The optimal length of the offset shorts was set so that the uncertainty with respect to 1-port calibrations was the smallest when calibrating the DUT using the designed offset short. To meet this goal, we developed a novel design process to propagate the uncertainty of our primary standard to the uncertainty of the designed offset shorts, and then re-propagate to the uncertainty of the DUT to be calibrated. Then, to find the optimal length, the uncertainty of the DUT was made as small as possible by using a global optimization algorithm. We designed three offsets; in this case, the uncertainty was about 2 dB when the DUT had a reflection coefficient of -20 dB, and had an uncertainty of about 0.35 dB for the reflection coefficient of 0 dB. The proposed method can easily design a calibration kit composed of an arbitrary number of offset shorts and a calibration kit using reference standards with arbitrary reflection coefficients, such as load or mismatch.