Investigation of the polynomial models in the definition of short and open calibration standards

Measurement errors in network analysis can be separated into two categories: random and systematic errors. Both random and systematic errors are vector quantities. Random errors are non-repeatable measurement variations and are usually unpredictable. Systematic errors are repeatable measurement variations in the test setup. A measurement calibration is a process which mathematically derives the systematic error model for the VNA. Short and open standards are widely used in the calibration of network analyzers. And the definition precision of short and open standards has great influence on the measurement results of the VNA. Two types of calibration standard definitions-the calibration coefficient model and the data-based model are supported. In this paper, we focus on investigation of the coefficient models in the definition of short and open calibration standards. Based on coefficient model, they are usually simulated by a third order polynomial mode, which would introduce large fitting errors. By lots of definition experiments with different types of calibration kits, we do have found that the third order polynomial model yields less accuracy for the definition of short standards though it works well for the definition of open standards. Detailed research demonstrates that better fitting accuracy can be achieved by using higher order polynomial models. And also based on the analysis of the condition number with these models, proper polynomial model is recommended for the definition of short standards. Verification experiments have been conducted to assess the validity of the recommended polynomial model.