General method of seven-term statistical calibration with partially defined standards

Calibration is essential for accurate high-frequency measurements with Vectorial Network Analyzer. Even though many methods have been already presented, they either base on some additional assumptions or allow to use limited type of standards. In this paper we describe a general seven-term calibration method, which accepts any combination of fully-known and partially defined calibration standards. The method combines symbolic formulation of the problem with its numerical solution. The calibration procedure has been evaluated in a broad frequency range of [0.5, 110] GHz using standards made of a PDMA container filled with different liquids. Air and water-based standards were considered as fully-known, since their parameters were obtained in simulation. However, for the ethanol-water mixture only parametrized model was provided. Calibration method was proven accurate, as the residual errors did not exceed 1.3e-3. It also allowed to determine the unknown parameters of the partially-defined standard. Method was also found very efficient, as its evaluation time was 0.62 s for a single frequency.