Residual error models for the SOLT and SOLR VNA calibration algorithms

Uncertainty calculation of vector network analyzers (VNAs) using the SOLT or SOLR calibration algorithms is often performed using residual directivity, match and tracking. In the literature the uncertainty equations are often stated without a derivation from a proper model equation. In this paper we derive the model equations for both the SOLT and SOLR calibration, the two cases do not result in the same model equation. The results are also compared to the commonly used expressions for uncertainty in the EA guidelines for VNA evaluation. For one-port measurements our results confirm the expressions in the EA guide but for two-ports there are significant differences. The symbolically derived model equations are verified using numerical simulations.