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Research & Development

Development of standards and related research

National standards for some RF and microwave quantities are being developed at MSL. The three quantities considered to be of most importance are:


Power is the quantity usually measured when characterising signals at radio frequencies and above, rather than voltage, or current, which are more commonly used at low frequencies. It is important to maintain a national standard for power, so that the accuracy of power measuring instruments can be traced back to fundamental physical quantities.

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At low frequencies, electrical networks are represented by lumped parameters, like inductance, resistance, etc. However, as frequency increases the more common representation used is based on the scattering of waves. The so-called S-parameters commonly describe networks at  radio frequencies and above.

The instrument of choice for measuring S-parameters is a vector network analyzer (VNA), which operates by generating a wave of known amplitude and phase and recording the amplitude and phase of scattered waves (transmitted and reflected) from a device under test.

It is important to maintain national standards of impedance so that the accuracy of impedance measuring instruments can be traced back to fundamental physical quantities.

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Detection of weak signals is involved in many domains of RF and microwave technology. For this reason, the instrumentation used to develop and test such technology must operate over a very wide range of signal strength. One of the fundamental performance requirements for such instruments is linearity: the ability to respond in the same way to a change in signal strength whatever the signal level.

Attenuation standards can be used to characterise instrument linearity, so it is important to maintain national attenuation standards and allow the accuracy of wide dynamic range measuring instruments can be traced back to fundamental physical quantities.

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Recent research:

Since 1993, most metrologists have followed guidelines for evaluating and reporting uncertainty provided in an internationally-recognised document, the Guide to the Expression of Uncertainty in Measurement.

However, complex quantities are not fully covered in the Guide.

Accompanying the development of new standards, research into better methods of dealing with the measurement uncertainty of complex-valued quantities has been undertaken in recent years. This work has led to a number of developments in this area recently.

Simplifying uncertainty calculations

According to the Guide, a proper uncertainty analysis will require all the partial derivatives of an equation that describes the measurement. However, the equations that describe microwave networks can become very complicated. In RF and microwave problems, the large number of terms involved usually discourages this type of analysis. However, we have developed ways to take advantage of complex-number calculus, and the chain rule, and make these calculations more tractible.

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Evaluating the effective degrees-of-freedom

In conventional statistics, the degrees-of-freedom is related to the size of the sample used to estimate a quantity of interest. For example, if the mean and standard error of the mean are estimated from a sample of 10 measurements, 9 degrees-of-freedom are usually associated with the standard error estimate (called the standard uncertainty in metrology). In measurement problems, we loosely associate a number of effective degrees-of-freedom with the uncertainty of a result.

The Guide provides a method for calculating an effective number of degrees-of-freedom, called the Welch-Satterthwaite formula. However, Welch-Satterthwaite cannot be applied to problems involving complex quantities. We have developed an extension method for complex and multivariate problems.

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Evaluating uncertainty when phase is unknown

The phase characteristics of RF and microwave components are not always known. It is common, for example, to specify a VSWR or a return-loss, but these parameters give no information about the phase of the underlying complex reflection coefficient. This phase will nevertheless influence a measurement result, so it is necessary to account for the phase uncertainty when estimating the complex reflection coefficient. We have developed some simple ways of doing this.

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The validity of uncertainty calculations

Current internationally-recognised methods of evaluating measurement uncertainty are not exact in many cases of practical interest. Real measurements are often complicated from a mathematical perspective, so robust general-purpose methods of data-processing are recommended in documents like the Guide. While they are very good, these methods are approximate and, in certain circumstances, questions can arise about their validity.

Recent work at MSL has developed a general method for checking the validity of uncertainty calculations. This approach can be used to evaluate the performance of uncertainty calculations objectively and to compare different candidate methods with each other.

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Some recent conference presentations:

Recent research reports:

  • VNA error models: Comments on EURAMET/cg-12/v.01 (IRL Report 2444, June 2010)

    This report looks at expressions for the uncertainty of vector network analyser (VNA) measurements given in the EURAMET Calibration Guide cg-12/v.01. The work provides a more rigorous derivation of the uncertainty expressions and corrects some errors. It is a useful companion document to the EURAMET Guide, which is a valuable reference about technical methods of assessing residual errors in a calibrated VNA.