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6. CALCULATING MEASUREMENT
UNCERTAINTY
6.1
THEORY
Calculating measurement uncertainty can be a confusing issue. Once the power meter has been set up with its
head, the measurement errors fall into three categories. These categories are Power Dependent Errors,
Frequency Dependent Errors, and finally Power and Frequency Independent Errors.
Power dependent errors consist of zeroing error, noise error and linearity error. Zeroing error refers to the
residual offset due to noise present during an auto zero operation. This becomes more critical at lower power
levels. Another error that becomes a concern at lower power levels is the noise error. This error can be
reduced by the use of extended averaging, however, this will increase measurement time. The final error that
falls under the category of power dependent is linearity. This is caused due to the nonlinear response of diode
and thermocouple heads at high power levels. AR heads reduce this error through the process of linearity
calibration, as discussed earlier, however the "shaping" that is performed is not without error and must be
added into total uncertainty.
Frequency Dependent Errors are made up of calibration factor uncertainty, mismatch uncertainty, and high
frequency linearity error. Calibration factor uncertainty is a function of the accuracy of the equipment used to
determine the calibration factor. Mismatch uncertainty arises because usually neither power head nor source
under test are perfect matches. Mismatch uncertainty can be calculated from the SWR of the head and the
source under test as shown in Figure 6-1.
For most conditions, the calibration factor uncertainty and mismatch uncertainty will be the largest
contributor to total measurement uncertainty. Linearity error was discussed previously as a power dependent
error, however, it also becomes a concern at high frequencies. The combination of both high frequency and
high power can derate the linearity of the "shaping" process applied to certain types of diode heads.
Instrumentation errors and power reference error fall under the category of Power and Frequency Independent
Errors. Circuit limitations and component tolerance within the power meter makes up the instrumentation
errors. Power reference error is associated with the internal power reference against which power meter and
head are routinely calibrated.
Total measurement uncertainty can be expressed as either a worst case uncertainty or RSS uncertainty. The
worst case approach is a conservative method where the extreme condition of each individual uncertainty is
added to one another. Since each of the individual uncertainties is independent of each other, the probability
of all being at the extreme condition is near zero. For this reason, a more realistic method of combining
uncertainties was developed, the RSS method. RSS is an abbreviation for "root-sum-of-the-squares". In this
method each uncertainty is squared, added to one another, and the square root of the summation is calculated.
The formula for RSS is as follows:
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