A Reformulation and Sensitivity Analysis of TRL

This article reformulates the thru-reflect-line (TRL) calibration algorithm based on the T-matrix representation and further investigates the influence of non-ideal TRL standards on S-parameter measurements. To reformulate the TRL calibration algorithm, the T-matrices of error boxes are constructed by the thru measurement, and only three wave ratios need to be solved with low calculation complexity. Furthermore, expressions representing the S-parameter deviations with respect to the non-ideal TRL standards are deduced in a simple and novel way. From the experiment, a good agreement between the reformulated and classical TRL calibration algorithms can be observed. In addition, the sensitivity coefficients of S-parameters are calculated and compared with the results obtained by the classical work, which proves the validity of the proposed.