A Reformulation and Sensitivity Analysis of TRL

This article reformulates the thru-reflect-line (TRL) calibration algorithm based on the <inline-formula> <tex-math notation="LaTeX">{T} </tex-math></inline-formula>-matrix representation and further investigates the influence of non-ideal TRL standards on S-paramet...

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Bibliographic Details
Published inIEEE transactions on instrumentation and measurement Vol. 69; no. 7; pp. 5107 - 5115
Main Authors Zhao, Wei, Wang, Yibang
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Calibration
Mathematical analysis
Mathematical model
Matrix representation
Measurement uncertainty
microwave measurement
Parameter sensitivity
Scattering parameters
Sensitivity analysis
Uncertainty
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Summary:This article reformulates the thru-reflect-line (TRL) calibration algorithm based on the <inline-formula> <tex-math notation="LaTeX">{T} </tex-math></inline-formula>-matrix representation and further investigates the influence of non-ideal TRL standards on S-parameter measurements. To reformulate the TRL calibration algorithm, the <inline-formula> <tex-math notation="LaTeX">{T} </tex-math></inline-formula>-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 method.
ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2019.2950825