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

Ziad Hatab; Michael Ernst Gadringer; Wolfgang Bösch

doi:10.48550/arXiv.2301.09126

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

Ziad Hatab, Michael Ernst Gadringer, Wolfgang Bösch

Institute of Microwave and Photonic Engineering (4510)

Research output: Working paper › Preprint

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
Publisher	arXiv
Number of pages	9
Volume	72
DOIs	https://doi.org/10.48550/arXiv.2301.09126
Publication status	Published - 22 Jan 2023

Keywords

eess.SP
physics.app-ph
Uncertainty
metrology
Calibration
Matrix decomposition
traceability
Standards
uncertainty propagation
microwave measurement
Measurement uncertainty
vector network analyzer
Eigenvalues and eigenfunctions
Mathematical models
calibration
vector network analyzer (VNA)

ASJC Scopus subject areas

Instrumentation
Electrical and Electronic Engineering

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Experimental

Access to Document

10.48550/arXiv.2301.09126Licence: CC BY-SA 4.0

2301.09126v1Accepted author manuscript, 6.67 MBLicence: CC BY-SA 4.0

1 Active

CD-Laboratory for Technology guided electronic component design and characterization
Bösch, W. (Co-Investigator (CoI)), Hatab, Z. (Co-Investigator (CoI)), Gadringer, M. E. (Co-Investigator (CoI)), Takahashi, H. (Co-Investigator (CoI)), Maier, C. (Co-Investigator (CoI)), Sarbandi Farahani, H. (Co-Investigator (CoI)), Pauser-Greistorfer, C. (Co-Investigator (CoI)), Paulitsch, H. (Co-Investigator (CoI)), Rezaee, B. (Co-Investigator (CoI)) & Fuchs, M. (Co-Investigator (CoI))
1/11/20 → 31/10/27
Project: Research project

1 Talk at conference or symposium

Advanced PCB Measurement Techniques for Millimeter-wave Frequencies and Beyond
Gadringer, M. E. (Speaker) & Hatab, Z. (Speaker)
23 Sept 2024
Activity: Talk or presentation › Talk at conference or symposium › Science to science

2 Article
1 Conference paper

Modified Semi-Additive Manufacturing of PCBs for Enabling Accurate Device Measurements at Millimeter-Wave and Sub-Terahertz Frequencies
Arsanjani, A., Hatab, Z., Alterkawi, A. B. A., Gadringer, M. E. & Bösch, W., 21 Jun 2024, 103rd ARFTG Microwave Measurement Conference: Advanced Measurement Techniques for Next-G Communication Systems, ARFTG 2024. IEEE CSP, 4 p. 10660794
Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review
Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration
Hatab, Z., Gadringer, M. E. & Bösch, W., 2023, In: IEEE Transactions on Instrumentation and Measurement. 72, 9 p., 1007409.
Research output: Contribution to journal › Article › peer-review

Open Access
File
Validation of the Reference Impedance in Multiline Calibration with Stepped Impedance Standards
Hatab, Z., Gadringer, M. E., Alterkawi, A. B. A. & Bösch, W., 14 Sept 2023, In: IEEE Open Journal of Instrumentation and Measurement. 2, 12 p., 10251578.
Research output: Contribution to journal › Article › peer-review

Open Access
File

Cite this

@techreport{d42917bfdf324c04ab7024279f39c0d1,

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 = "eess.SP, physics.app-ph, Uncertainty, metrology, Calibration, Matrix decomposition, traceability, Standards, uncertainty propagation, microwave measurement, Measurement uncertainty, vector network analyzer, Eigenvalues and eigenfunctions, Mathematical models, calibration, vector network analyzer (VNA)",

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

note = "GitHub: https://github.com/ZiadHatab/uncertainty-multiline-trl-calibration",

year = "2023",

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doi = "10.48550/arXiv.2301.09126",

language = "English",

volume = "72",

publisher = "arXiv",

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TY - UNPB

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

AU - Hatab, Ziad

AU - Gadringer, Michael Ernst

AU - Bösch, Wolfgang

N1 - GitHub: https://github.com/ZiadHatab/uncertainty-multiline-trl-calibration

PY - 2023/1/22

Y1 - 2023/1/22

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 - eess.SP

KW - physics.app-ph

KW - Uncertainty

KW - metrology

KW - Calibration

KW - Matrix decomposition

KW - traceability

KW - Standards

KW - uncertainty propagation

KW - microwave measurement

KW - Measurement uncertainty

KW - vector network analyzer

KW - Eigenvalues and eigenfunctions

KW - Mathematical models

KW - calibration

KW - vector network analyzer (VNA)

U2 - 10.48550/arXiv.2301.09126

DO - 10.48550/arXiv.2301.09126

M3 - Preprint

VL - 72

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

PB - arXiv

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Treatment code (Nähere Zuordnung)

Access to Document

Fingerprint

Projects

CD-Laboratory for Technology guided electronic component design and characterization

Activities

Advanced PCB Measurement Techniques for Millimeter-wave Frequencies and Beyond

Research output

Modified Semi-Additive Manufacturing of PCBs for Enabling Accurate Device Measurements at Millimeter-Wave and Sub-Terahertz Frequencies

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

Validation of the Reference Impedance in Multiline Calibration with Stepped Impedance Standards

Cite this