Line-length optimization of offset-short standards for broadband VNA calibration

The paper introduces a novel method for selecting optimal line lengths of multiple offset-short standards that are applied to broadband calibration of vector network analyzers (VNAs). The method is based on the design of experiments (DOE) approach and analysis of the determinant of the Fisher information matrix. To interpret results of the analysis, new terms, adopted from the filter theory, are suggested. The analysis reveals a tradeoff between solutions that provide low uncertainty and broad bandwidth of the VNA calibration. Both aspects are vital at millimeter wavelengths, when using calibration standards based on 1.85 or 1 mm coaxial lines. The length optimization, using the DOE criterion of D-optimality, enables expanding the calibration frequency range much over that provided by the offset shorts currently available in commercial calibration kits.