Evaluating the measurement uncertainty of complex quantities: a selective review

Hall, B. D.

doi:10.1088/0026-1394/53/1/s25

Cited by 11 publications

(3 citation statements)

References 23 publications

(35 reference statements)

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“…Ultimately, some concepts from the International Vocabulary of Metrology (VIM) [33] and in the Guide to the Expression of Uncertainty in Measurement (GUM) [34] (see also [35,36]) should be introduced in phase noise measurements. Going through the VIM, the following definitions are relevant to our experiments: Type A and Type B evaluation of uncertainty (2.28 and 2.29), the influence quantities (2.52), the definitional uncertainty (2.27), and the null measurement uncertainty (4.29).…”

Section: Discussionmentioning

confidence: 99%

Artifacts and errors in cross-spectrum phase noise measurements

Gruson

Rus²,

Rohde

et al. 2020

Metrologia

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This article is intended to give a warning about: (i) the internal processing inside the phase-noise analyzers, (ii) the oscillators whose white phase noise floor seems too low, chiefly the 100-MHz OCXOs, and (iii) the need to introduce in the domain of phase-noise measurements the basic concepts of uncertainty found in the International Vocabulary of Metrology (VIM).The measurement of low-noise quartz oscillators, or of other lownoise oscillators exhibiting a noise floor of the order of −180 dBc/Hz or less, relies on the cross-spectrum method. The measurement may take long time, from hours to 1-2 days, for the number of averaged cross spectra to be sufficient to reject the background of the noise analyzer. That said, something anomalous is often seen in a region approximately one decade wide, located where higher-slope noise joins the white floor or the 1/f noise. The plot may be quite thick and irregular, and a dip may appear, where the phase noise looks lower than the white noise floor. Such anomalies reveal something worse. The white region of the PM noise spectrum may be affected by gross errors and, in the not-so-rare worst case, is a total nonsense. We address the problem trough a simple experiment, where we insert a dissipative attenuator between the oscillator and the PN analyzer. Surprisingly, in some cases the attenuation results in a lower noise floor. Such erratic behavior is reproducible, having been observed separately in three labs with instruments from the two major brands. We provide the experimental evidence, the full theory, and suggestions to mitigate the problem.

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Section: Discussionmentioning

confidence: 99%

Artifacts and errors in cross-spectrum phase noise measurements

Gruson

Rus²,

Rohde

et al. 2020

Metrologia

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“…The uncertainty propagation of the presented models can be accomplished following the guidelines in [31] and [32].…”

Section: Mapping Functionsmentioning

confidence: 99%

mm-Wave Complex Permittivity Extraction of LTCC Substrate Under the Influence of Surface Roughness

Hatab

Gadringer

Habib

et al. 2022

IEEE Trans. Instrum. Meas.

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As many emerging technologies require the use of high-speed signals, the understanding of dielectric properties of materials used in manufacturing printed circuit boards (PCBs) is an essential aspect for accurate high-speed circuit designs, especially at millimeter-wave (mm-wave) frequencies. This work demonstrates a methodology for extracting complex relative permittivity of dielectric substrates covering mm-wave frequencies. For this purpose, low-temperature cofired ceramic (LTCC) substrate was measured up to 85 GHz and its complex relative permittivity was extracted. The approach used in this work is based on multiline thru-reflect-line (TRL) calibration for measuring the propagation constant and electromagnetic (EM) simulations to estimate the losses contributed by the conductor while accounting for surface roughness. An estimate of complex relative effective permittivity is obtained, from which the actual relative dielectric constant and the loss tangent of LTCC substrate are extracted. The estimated values for the relative dielectric constant and the loss tangent show an excellent agreement compared with the results obtained via split cavity resonator measurements.

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“…However, for assessing the complex uncertainty of S-parameters involving multiple frequency points and variables, the covariance matrix method is preferred. The covariance matrix is considered an extension of linear propagation, which can effectively address the uncertainty evaluation and propagation of such complex objects [ 3 , 4 , 5 , 6 ].…”

Section: Introductionmentioning

confidence: 99%

Assessment of Measurement Uncertainty for S-Parameter Measurement Based on Covariance Matrix

Zhu,

Wang,

Zhao

et al. 2024

Sensors

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S-parameters are widely used to detail the scattering parameters of radio frequency (RF) components and microwave circuit modules. The vector network analyzer (VNA) is the most commonly used device for measuring S-parameters. Given the multiple frequency points, complex values, and intricate uncertainty propagation involved, accurately assessing the uncertainty of S-parameter measurements is difficult. In this study, we proposed a new method for assessing S-parameter uncertainty based on the covariance matrices, tracing back to the nominal uncertainty of calibration standards. First, we analyzed the relevant theory of uncertainty assessment using covariance matrices and subsequently deduced the mechanism of Type B uncertainty propagating from calibration standards to error model coefficients and S-parameter measurements to evaluate Type B measurement uncertainty. In this study, a novel measurement system was constructed for measuring grounded coplanar waveguides by using a VNA and calibration standards with 8- and 12-error models. Initially, the model assessed the Type B uncertainty of measuring four S-parameters of a grounded coplanar waveguide. Next, the VNA calibrated with the 12-error model was used to conduct multiple repeated measurements to assess the Type A uncertainty of the grounded coplanar waveguide. Finally, the composite uncertainty was constructed, which demonstrated that the proposed method can be used for assessing the uncertainty of S-parameters.

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Evaluating the measurement uncertainty of complex quantities: a selective review

Cited by 11 publications

References 23 publications

Artifacts and errors in cross-spectrum phase noise measurements

Artifacts and errors in cross-spectrum phase noise measurements

mm-Wave Complex Permittivity Extraction of LTCC Substrate Under the Influence of Surface Roughness

Assessment of Measurement Uncertainty for S-Parameter Measurement Based on Covariance Matrix

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