Boonton 4500B Peak Power Meter - Manual (Page 327)

Boonton 4500B RF Peak Power Analyzer
Application Notes 6-17
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
The formula for calculating RSS measurement uncertainty from worst-case values and scale factors is:
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
U
RSS
= √(U
1
K
1
) 2 + (U
2
K
2
) 2 + (U
3
K
3
) 2 + (U
4
K
4
) 2 + ... (U
N
K
N
) 2
where U
1
through U
N
represent each of the worst-case uncertainty terms, and K
1
through K
N
represent the normalizing
multipliers for each term based on its distribution shape.
This calculation yields what is commonly referred to as the combined standard uncertainty, or U
C
, 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 (U = 2U
C
) will provide an Expanded Uncertainty with a confidence level of
approximately 95%.
6.5.2 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 Model 4500B.
Calibrator Level Uncertainty. This term is the uncertainty in the calibrator‘s output level for a given setting for
calibrators that are maintained in calibrated condition. The figure is a calibrator specification which depends upon
the output level:
1GHz Calibrator Level Uncertainty:
± (0.065 dB (1.51%) at 0 dBm + 0.03 dB (0.69%) per 5 dB from 0 dBm)