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
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.
Impedance
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 socalled Sparameters commonly describe networks at radio frequencies and above.
The instrument of choice for measuring Sparameters 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.
Attenuation
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.
Recent research:
Since 1993, most metrologists have followed guidelines for evaluating and reporting uncertainty provided in an internationallyrecognised 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 complexvalued quantities has been undertaken in recent years. This work has led to a number of developments in this area recently.
 Simplifying uncertainty calculations
 Effective degreesoffreedom
 The uncertainty of unknown phase
 Checking the validity of uncertainty calculations
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 complexnumber calculus, and the chain rule, and make these calculations more tractible.
Evaluating the effective degreesoffreedom
In conventional statistics, the degreesoffreedom 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 degreesoffreedom are usually associated with the standard error estimate (called the standard uncertainty in metrology). In measurement problems, we loosely associate a number of effective degreesoffreedom with the uncertainty of a result.
The Guide provides a method for calculating an effective number of degreesoffreedom, called the WelchSatterthwaite formula. However, WelchSatterthwaite cannot be applied to problems involving complex quantities. We have developed an extension method for complex and multivariate problems.
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 returnloss, 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.
The validity of uncertainty calculations
Current internationallyrecognised 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 generalpurpose methods of dataprocessing 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.
Some recent conference presentations:
 The uncertainty of a complex quantity with unknown phase (ANAMET 33, May 2010)

Assessing the performance of uncertainty calculations by simulation (ARFTG 74, December 2009)
Recent research reports:
 VNA error models: Comments on EURAMET/cg12/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 cg12/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.