Uncertainty Analysis of Scattering Parameters Calibrated by an Electronic Calibration Unit Based on a Residual Model

We propose a new residual model to analyze the uncertainty of scattering parameters (S-parameters) calibrated by an electronic calibration unit (ECU). Residual errors are usually estimated from the observed ripple after connecting a load or a short at the end of an airline. Therefore, this ripple method can only be used in a frequency range where the airline loss was not large. We, however, obtained the residual error from the uncertainty of the calibration kit using a simple numerical approach. As a result, we can determine the correlations between real/imaginary and magnitude/phase uncertainties. The proposed residual model showed the same results as a VNA error model. We also added a new error term to account for the effect of temperature-dependent drift of the ECU. In addition, we analytically derived the sensitivity coefficients for a 2-port DUT based on the proposed residual model. The proposed residual model will be helpful for the uncertainty analysis of S-parameters calibrated using the ECU.