Accuracy and Bandwidth Optimization of the Over-Determined Offset-Short Reflectometer Calibration

We present a new method for calculating line lengths of offset-short standards so as to provide a broadband and accurate one-port vector-network-analyzer (VNA) calibration. Our method is based on an approximate uncertainty analysis of corrected VNA measurements. We estimate the maximum value of the total variance (i.e., the trace of the covariance matrix) of errors in those measurements at a single frequency, and then quantify the quality of the offset-short calibration in a given frequency range with two metrics: the upper bound for the total variance and the lower calibration frequency. We then apply a global bi-objective optimization to these metrics in order to determine the optimal lengths. In order to verify our approach we first validate assumptions made in the approximate uncertainty analysis through a Monte Carlo simulation. We further perform an experiment in which we compare measurements of verification devices after calibrating the VNA with different offset-short sets designed with our method and with a set of reference airlines. Finally, we perform an uncertainty analysis for these measurements, which demonstrates the tradeoff between the offset-short calibration bandwidth and accuracy, and shows that our approach for selecting the offset-short line lengths provides the broadest bandwidth for a given calibration accuracy.