Boonton 4530 Peak Power Meter User Manual - Manual (Page 156)

Chapter 5 Boonton Electronics
Making Measurements 4530 Series RF Power Meter
5-14
It should be noted that measurement uncertainty calculation is a very complex process, and the techniques shown here
are somewhat simplified to allow easier calculation. For a more complete information, the following publications may
be consulted:
1. “ISO Guide to the Expression of Uncertainty in Measurement” (1995)
International Organization for Standardization, Geneva, Switzerland
ISBN 92-67-10188-9
2. “U.S. Guide to the Expression of Uncertainty in Measurement” (1996)
National Conference of Standards Laboratories, Boulder, CO 80301
ANSI/NCSL Z540-2-1996
5.7.1 Uncertainty Contributions. The total measurement uncertainty is calculated by combining the following
terms:
Uncertainty Source Distribution Shape K
1. Instrument Uncertainty Normal 0.500
2. Calibrator Level Uncertainty Rectangular 0.577
3. Calibrator Mismatch Uncertainty U-shaped 0.707
4. Source Mismatch Uncertainty U-shaped 0.707
5. Sensor Shaping Error Rectangular 0.577
6. Sensor Temperature Coefficient Rectangular 0.577
7. Sensor Noise Normal 0.500
8. Sensor Zero Drift Rectangular 0.577
9. Sensor Calibration Factor Uncertainty Normal 0.500
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 in which the extreme conditions of each of the individual
uncertainties are added together. If the individual uncertainties are all independent of one another, the probability
of all being at their worst-case conditions simultaneously is extremely small. For this reason, the uncertainties
are more commonly combined using the RSS method. RSS is an abbreviation for “root-sum-of-squares”, a
technique in which each uncertainty is squared, the squares are summed, and the square root of the summation
is calculated.
Before the RSS calculation can be performed, however, the worst-case uncertainty values must be scaled, or
“normalized” to adjust for differences in each term’s probability distribution or “shape”. The distribution shape
is a statistical description of how the actual error values are likely to vary from the ideal value. Once normalized
in this way, terms with different distribution shapes can be combined freely using the RSS method.
Three main types of distributions are Normal (Gaussian), Rectangular, and U-shaped. The multipliers for each
type of distribution are as follows:
Distribution Multiplier “K”
Normal 0.500
Rectangular sqrt(1/3) = 0.577
U-shaped sqrt(1/2) = 0.707