Boonton Power Sensor - Manual (Page 41)

6-2 Uncertainty Contributions
The total measurement uncertainty is calculated by combining the following terms:
1. Instrument Uncertainty
2. Calibrator Level Uncertainty
3. Calibrator Mismatch Uncertainty
4. Source Mismatch Uncertainty
5. Sensor Shaping Error
6. Sensor Temperature Coefficient
7. Sensor Noise
8. Sensor Zero Drift
9. Sensor Calibration Factor Uncertainty
The formula for worst-case measurement uncertainty is:
U
WorstCase
= U
1
+ U
2
+ U
3
+ U
4
+ ... U
N
where U
1
through U
N
represent each of the worst-case uncertainty terms.
The worst-case approach is a very conservative method where the extreme condition of each
individual uncertainty is added to one another. If the individual uncertainties are independent
of one another, the probability of all being at the extreme condition is small. For this reason,
these uncertainties are usually combined using the RSS method. RSS is an abbreviation for
“root-sum-of-squares”. In this method, each uncertainty is squared, added to one another, and
the square root of the summation is calculated resulting in the Combined Standard Uncertainty.
The formula is:
U
C
= ( U
1
2
+ U
2
2
+ U
3
2
+ U
4
2
+ ... U
N
2
)
0.5
where U
1
through U
N
represent normalized uncertainty based on the uncertainty's probaility
distribution. This calculation yields what is commonly refered to as the combined standard
uncertainty with a level of confidence of approximately 68%.
To gain higher levels of confidence an Expanded Uncertainty is often employed. Using a
coverage factor of 2 ( 2 * U
C
) will provide an Expanded Uncertainty with a confidence level
of approximately 95%.
6-3 Discussion of Uncertainty Terms
Following is a discussion of each term, its definition, and how it is calculated.
Instrument Uncertainty. This term represents the amplification and digitization uncertainty
in the power meter, as well as internal component temperature drift. In most cases, this is very
small, since absolute errors in the circuitry are calibrated out by the AutoCal process. The
instrument uncertainty is 0.20% for the 4530 Series. (Refer to the Instruction Manual of the
instrument in use for instrument uncertainty.)
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