Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration

Ziad Hatab; Michael Ernst Gadringer; Wolfgang Bösch

doi:10.1109/tim.2023.3296123

Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration

Ziad Hatab^*, Michael Ernst Gadringer, Wolfgang Bösch

^*Corresponding author for this work

Institute of Microwave and Photonic Engineering (4510)

Research output: Contribution to journal › Article › peer-review

Abstract

This study proposes a linear approach for propagating uncertainties in the multiline thru-reflect-line (TRL) calibration method for vector network analyzers (VNAs). The multiline TRL formulation we are proposing applies the law of uncertainty propagation as outlined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) to both measurement and model uncertainties. In addition, we conducted a Monte Carlo (MC) analysis using a combination of measured and synthetic data to model various uncertainties, such as measurement noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the MC analysis and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.

Original language	English
Article number	1007409
Number of pages	9
Journal	IEEE Transactions on Instrumentation and Measurement
Volume	72
Early online date	17 Jul 2023
DOIs	https://doi.org/10.1109/tim.2023.3296123
Publication status	Published - 2023

Keywords

Uncertainty
Calibration
Standards
Mathematical models
Matrix decomposition
Measurement uncertainty
metrology
traceability
uncertainty propagation
microwave measurement
vector network analyzer
Eigenvalues and eigenfunctions
calibration
vector network analyzer (VNA)

ASJC Scopus subject areas

Instrumentation
Electrical and Electronic Engineering

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10.1109/tim.2023.3296123Licence: CC BY 4.0

Propagation_of_Linear_Uncertainties_Through_Multiline_Thru-Reflect-Line_CalibrationFinal published version, 3.87 MBLicence: CC BY 4.0

Cite this

@article{62b48e0f6e114249bd8a339665b1f284,

title = "Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration",

abstract = "This study proposes a linear approach for propagating uncertainties in the multiline thru-reflect-line (TRL) calibration method for vector network analyzers (VNAs). The multiline TRL formulation we are proposing applies the law of uncertainty propagation as outlined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) to both measurement and model uncertainties. In addition, we conducted a Monte Carlo (MC) analysis using a combination of measured and synthetic data to model various uncertainties, such as measurement noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the MC analysis and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.",

keywords = "Uncertainty, Calibration, Standards, Mathematical models, Matrix decomposition, Measurement uncertainty, metrology, traceability, uncertainty propagation, microwave measurement, vector network analyzer, Eigenvalues and eigenfunctions, calibration, vector network analyzer (VNA)",

author = "Ziad Hatab and Gadringer, {Michael Ernst} and Wolfgang B{\"o}sch",

year = "2023",

doi = "10.1109/tim.2023.3296123",

language = "English",

volume = "72",

journal = "IEEE Transactions on Instrumentation and Measurement",

issn = "1557-9662",

publisher = "IEEE",

}

TY - JOUR

T1 - Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration

AU - Hatab, Ziad

AU - Gadringer, Michael Ernst

AU - Bösch, Wolfgang

PY - 2023

Y1 - 2023

N2 - This study proposes a linear approach for propagating uncertainties in the multiline thru-reflect-line (TRL) calibration method for vector network analyzers (VNAs). The multiline TRL formulation we are proposing applies the law of uncertainty propagation as outlined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) to both measurement and model uncertainties. In addition, we conducted a Monte Carlo (MC) analysis using a combination of measured and synthetic data to model various uncertainties, such as measurement noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the MC analysis and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.

AB - This study proposes a linear approach for propagating uncertainties in the multiline thru-reflect-line (TRL) calibration method for vector network analyzers (VNAs). The multiline TRL formulation we are proposing applies the law of uncertainty propagation as outlined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) to both measurement and model uncertainties. In addition, we conducted a Monte Carlo (MC) analysis using a combination of measured and synthetic data to model various uncertainties, such as measurement noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the MC analysis and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.

KW - Uncertainty

KW - Calibration

KW - Standards

KW - Mathematical models

KW - Matrix decomposition

KW - Measurement uncertainty

KW - metrology

KW - traceability

KW - uncertainty propagation

KW - microwave measurement

KW - vector network analyzer

KW - Eigenvalues and eigenfunctions

KW - calibration

KW - vector network analyzer (VNA)

UR - http://www.scopus.com/inward/record.url?scp=85165306115&partnerID=8YFLogxK

U2 - 10.1109/tim.2023.3296123

DO - 10.1109/tim.2023.3296123

M3 - Article

SN - 1557-9662

VL - 72

JO - IEEE Transactions on Instrumentation and Measurement

JF - IEEE Transactions on Instrumentation and Measurement

M1 - 1007409

ER -

Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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