Evaluating and expressing uncertainty in complex S-parameter measurements

Ridler, N M; Salter, M J

doi:10.1109/arftg.2000.327429

Cited by 33 publications

(15 citation statements)

References 3 publications

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“…This computation is applied separately to both the real and imaginary components of the complex-valued linear reflection coefficient. We avoid performing the analysis using the magnitude and phase components of the reflection coefficient due to problems with such calculations that have been described in [4].…”

Section: Discussionmentioning

confidence: 99%

“…Zero correlation will leave the axes of the ellipse aligned with the real and imaginary axes of the complex reflection coefficient plane. The use of ellipses to depict the uncertainty in complex-valued quantities has been discussed in [4] and their use has been demonstrated experimentally (for measurements of complex S-parameters) in [6,7]. Finally, it should be noted that calculated values of correlation coefficients, based on relatively small sample sizes, are not very reliable [8].…”

Section: Further Observationsmentioning

confidence: 98%

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Investigating connection repeatability of waveguide devices at frequencies from 750 GHz to 1.1 THz

Ridler

Clarke

2013

82nd ARFTG Microwave Measurement Conference

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This paper describes some investigations into the repeatability of connection of some waveguide devices in the WM-250 (WR-01) waveguide size over the recommended operational bandwidth 750 GHz to 1100 GHz. Three devices are investigated -a flush short-circuit, an offset short-circuit, and a near-matched load. These devices can be used as calibration standards for network analyzers, and so can be found in network analyzer calibration kits. The repeatability of the measured reflection coefficient is assessed using statistical techniques. The repeatability is expressed in terms of the experimental standard deviation in both the real and imaginary components of the complex-valued linear reflection coefficient. Finally, recommendations are given on propagating uncertainty when these devices are considered as calibration standards during a network analyzer calibration and measurement process.

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Section: Discussionmentioning

confidence: 99%

Section: Further Observationsmentioning

confidence: 98%

Investigating connection repeatability of waveguide devices at frequencies from 750 GHz to 1.1 THz

Ridler

Clarke

2013

82nd ARFTG Microwave Measurement Conference

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show abstract

“…Experimental design/analysis errors, for example:  Uncertainty not considered as a function of frequency  Uncertainty not considered as a function of device under test (DUT) response  Statistics calculated directly from log/angle quantities [6]  Statistics calculated on truncated distributions [6]  Ignoring that data consists of vector quantities  Incorrectly assuming independence in quantities [6] Metrology issues, grouped as:  Instrument noise  Errors in the calibration standards model  Connector repeatability While only the second group would commonly be attributed to measurement uncertainty, both groups needed to be addressed in order to accurately estimate uncertainties.…”

Section: Introductionmentioning

confidence: 99%

“…In essence it appeared that while National Metrology Institutes (NMI"s) and the International Standards Organization (ISO) had provided substantial guidance on quantifying the uncertainty in VNA measurements (e.g. [1]- [6]), this guidance may not be applied consistently.…”

Section: Introductionmentioning

confidence: 99%

Multiport VNA measurement uncertainty - Signal integrity applications

Grossman

Peterson

Torres

2011

2011 IEEE International Symposium on Electromagnetic Compatibility

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Vector network analyzer (VNA) measurements are often stated without an indication of the estimated uncertainty. Understanding the uncertainty can lead to understanding the sources of uncertainty and targeting improvements in the metrology to address the largest sources.Connector repeatability in manually probed measurements can be a primary source of uncertainty with this metrology. A measurement capability assessment provides the method for evaluating the total uncertainty. Evaluation of the probe launch and cable movement provided substantial opportunities to improve the capability. Implementing improvements identified through the measurement capability assessment (MCA) process has resulted in a doubling of the highest frequency where the metrology is deemed capable.

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“…So, the evaluation of uncertainty in an estimate of S dif is not trivial. Techniques for propagating uncertainty are usually described in terms of a single measurement function [1], [2]. So, if these are to be applied here, one function for the difference is required, like…”

Section: Introductionmentioning

confidence: 99%

Using uncertain complex numbers with VNA measurements

Hall

2008

2008 71st ARFTG Microwave Measurement Conference

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The uncertain complex number is a simple construct that can be used to achieve full uncertainty propagation in multi-step processing of measurement data. The entity encapsulates information about a measured complex quantity and propagates it through equations by using a few simple algorithms. Software can easily automate the operations involved. The paper shows how uncertain complex numbers can be used to implement calibration and dataprocessing routines for VNA measurements. An example is presented in which the uncertainties associated with a pair of reflection measurements are evaluated, as well as the uncertainties associated with the ratio and difference of these measurements. It is shown that, by using uncertain complex numbers, the variances associated with the ratio and difference results can be reduced by an order of magnitude, by correctly accounting for correlated errors associated with the VNA calibration.

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Evaluating and expressing uncertainty in complex S-parameter measurements

Cited by 33 publications

References 3 publications

Investigating connection repeatability of waveguide devices at frequencies from 750 GHz to 1.1 THz

Investigating connection repeatability of waveguide devices at frequencies from 750 GHz to 1.1 THz

Multiport VNA measurement uncertainty - Signal integrity applications

Using uncertain complex numbers with VNA measurements

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