General Information on Statistical Treatment Columns
Specification Style
In combining sources of uncertainty, international standards
usually call for using the method of the GUM (Guide to the expression of
uncertainty in measurement).
The GUM calls for computing the “standard uncertainty”
(standard deviation) of each contributor, then combining these using a
root-sum-square computation to compute the “combined standard uncertainty, then
multiplying by 2 (the coverage factor, k) to give the “expanded uncertainty.”
The expanded uncertainty is also known as the 95th percentile measurement
uncertainty.
The documentation of each contributor may be given in
different forms, such as median, mean, or 95th percentile, as shown in the
drop-down list for those parameters where the user of the calculator might need
to vary the style of the specification.
Distribution
The statistical distribution of
contributors to the uncertainty depend on the contributor and our
knowledge of that parameter. In many cases, the value is known, thus a “Fixed”
distribution is appropriate. With Keysight PXA, MXA and EXA analyzers,
the distribution is known to be a Rayleigh probability density function (pdf) with a different value in each band. The Keysight CXA
does not have a Rayleigh distribution. Further information on the distribution
of mismatch uncertainties is available in “Revisiting Mismatch Uncertainty with
the Rayleigh Distribution,” available in the Keysight website.
Field-by-field instructions
DUT Type
Choose 'Amplifier' if the DUT (device under test) has
the same input and output frequencies, such as would be the case with
amplifiers, attenuators and filters. Choose 'Freq Converter' for
frequency-converting devices such as mixers.
Ext Preamp
Choose “In use” if an external preamplifier is used in
the measurement system.
NS (Noise Source) Model
Choosing one of the listed noise sources from the drop-down
menu conveniently sets default values providing typical parameters for standard
Keysight Technologies noise sources. For unlisted noise sources, or especially
for the most accurate estimation of uncertainty, choose the “User Defined”
option. This option can be selected whenever the actual value of the noise
source calibration data is available. The values are available at each
frequency on the Calibration Data Report, also known as the Calibration
Certificate. This allows the entry of the actual uncertainty of the Excess
Noise Ratio (ENR) and the 50Ω match (in dB, VSWR or reflection
coefficient).
Instr Model
Choosing one of the listed instruments from the
drop-down menu conveniently sets default values providing typical parameters
for Keysight Technologies analyzers. For the most
accurate estimation of uncertainty, choose the “User Defined” option from the
pull-down menu and enter actual parameters to the extent known. For example,
the NF of the instrument at the exact operating frequency can be found by
actual measurement or by reading graphs from the analyzer
data sheet or Specifications Guide. The analyzer
match may be measured with a network analyzer, or
with X-Series analyzers it can be estimated from
graphs provided in the Specifications Guide, or for convenience in the PXA analyzer, the 95th percentile of the Rayleigh distribution
of reflection coefficient can be taken from the Specifications Guide in the
Preamplifier chapter. Instrument Uncertainty for NF and Instrument Uncertainty
for Gain are both listed in the data sheets and Specifications Guides of
Keysight analyzers. “NFE Improvement” is listed in the
Specifications Guide for X-Series analyzers that have
NFE available and thus are capable of Internal Cal.
For most critical applications, the uncertainty is
dominated by the ENR uncertainty of the noise source and only weakly dependent
of instrument performance. Therefore, the convenience of using the drop-down
menu is sufficient for most needs.
Instr Calibration
Some X-Series analyzers can
make excellent measurements without the usual calibration (“Cal”) step using a
process called Internal Calibration. Internal Cal uses a model of the noise
level of the analyzer built-in to the analyzer to compensate for the noise floor of the analyzer and minimize its effect on the apparent noise at
the DUT input. Internal Cal is not available on other analyzers.
DUT NF
Enter the noise figure of the DUT. It is best to set
this to the best estimate of the NF, such as from the measurement itself. But
changes in DUT NF only weakly effect the uncertainty.
DUT Gain
Enter the gain of the DUT. It is best to set this to
the best estimate of the gain, such as from the measurement itself. But changes
in DUT gain only weakly effect the uncertainty.
DUT Input Match and Output Match
Enter the match parameters of the DUT. The input match
especially can have a significant, though rarely dominant, effect of the
uncertainty of the measurement. Therefore, a measured value of the match gives
the best estimate of the uncertainty by the calculator.
As noted in the on-calculator footnote, the match can
be entered as a return loss (any number that is negative is treated as return
loss in decibels), as a reflection coefficient (any number between 0 and 1 is
treated as the magnitude of the reflection coefficient) or as a voltage
standing-wave ratio, VSWR (any number larger than 1 is treated as a VSWR).
The values used for the DUT match, whether read from a
DUT data sheet or measured, is usually best treated as a value that is not
statistically varying. So the “Specification Style” and “Distribution” columns
are best set to Fixed.
NS ENR Uncert and Match
Reiterating the information from the NS Model text
above: For the most accurate estimation of uncertainty, choose the “User
Defined” option for NS Model instead of a particular noise source model. This option can be selected whenever the actual value of the noise
source calibration data is available. The values are available at each
frequency on the Calibration Data Report, also known as the Calibration
Certificate. This allows the entry of the actual uncertainty of the Excess
Noise Ratio (ENR) and the 50Ω match (in dB, VSWR or reflection
coefficient).
The calibration data report gives the 95th percentile (two sigma) uncertainty of the ENR, which has a Gaussian
probability density function.
The match can come from the calibration report, too,
in which case the specification style and distribution are both “fixed.” If the
match comes from the data sheet of the noise source, statistical study of the
data has shown that for some models and frequency ranges, using “maximum” for
the specifications style and “Rayleigh” for the distribution gives a very
accurate estimation of the uncertainty. For all other models and bands, the use
of maximum and Rayleigh gives a modestly conservative estimate of uncertainty.
(The statistical study showed that the distribution is not very well modelled
as Rayleigh in these cases, but also that the specified value is highly
conservative. So treatment as maximum/Rayleigh is not too surprisingly an
excellent way to get either a very good or conservative estimate of
uncertainty.)
Inst, NF, etc.
Reiterating the information from the Instr Model text
above: For the most accurate estimation of uncertainty, choose the “User Defined”
option from the pull-down menu and enter the actual parameters to the extent
known. For example, the NF of the instrument at the exact
operating frequency can be found by actual measurement or by reading graphs
from the analyzer data sheet or Specifications Guide.
The analyzer match may be measured with a network analyzer, or with X-Series analyzers
it can be estimated from graphs provided in the Specifications Guide, or for
convenience in the PXA analyzer, the 95th percentile
of the Rayleigh distribution of reflection coefficient can be taken from the
Specifications Guide in the Preamplifier chapter. Instrument Uncertainty for NF
and Instrument Uncertainty for Gain are both listed in the data sheets and
Specifications Guides of Keysight analyzers. “NFE
Improvement” is listed in the Specifications Guide for X-Series analyzers that have NFE available and thus are capable of
Internal Cal.
For most critical applications, the uncertainty is
dominated by the ENR uncertainty of the noise source and only weakly dependent
of instrument performance. Therefore, the convenience of using the drop-down
menu is sufficient for most needs. With low gain or lossy
devices, the analyzer parameters can be significant
or dominant contributors to uncertainty.
The specifications style for Instrument Uncertainty
for NF, and Instrument Uncertainty for Gain, for
Keysight Analyzers is always “worst case.” Statistical
study shows that treating these as 3 sigma specifications with Gaussian
distribution is on the conservative side of an accurate estimation of
uncertainty.
The specifications style for NFE improvement is always
95th percentile and the distribution is Gaussian.
When an external preamplifier is used, the match of the analyzer and the NFE
improvement have negligible effect on the uncertainty.
Ext Preamp NF, etc.
Enter the parameters of any external-to-the-analyzer preamplifier used. See the instructions for
similar fields above for details.
Sweep
This function allows an input parameter to be selected
then swept between lower and upper values so that the variation in uncertainty
can be seen on the “Graphical Results” tab. The number of points in the sweep
may be set here.
