Boonton 4240 RF Power Meter - Manual (Page 114)

Boonton 4240 Series RF Power Meter
T
u
al
his 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
B
“n
st
normalized in this
way, term
Three main e of
d
he worst case approach is a very conservative method in which the extreme conditions of each of the individual
ncertainties are added together. If the individual uncertainties are all independent of one another, the probability of
l being at their worst-case conditions simultaneously is extremely small. For t
uncertainty is squared, the squares are summed, and the square root of the summation is calculated.
efore the RSS calculation can be performed, however, the worst-case uncertainty values must be scaled, or
ormalized” to adjust for differences in each term’s probability distribution or “shape”. The distribution shape is a
atistical description of how the actual error values are likely to vary from the ideal value. Once
s with different distribution shapes can be combined freely using the RSS method.
types of distributions are Normal (Gaussian), Rectangular, and U-shaped. The multipliers for each typ
istribution 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
w
m
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.
U
ap
6.2.2
Follow
is very small, since absolute errors in the circuitry
are maintained in calibrated condition. The figure is a calibrator specification which depends upon
+20 to -39 dBm: ±0.075 dB (1.74%)
-40 to -60 dBm: ±0.105 dB (2.45%)
here U
1
through U
N
represent each of the worst-case uncertainty terms, and K
1
through K
N
represent the normalizing
ultipliers for each term based on its distribution shape.
sing a coverage factor of 2 (U = 2U
C
) will provide an Expanded Uncertainty with a confidence level of
proximately 95%.
Discussion of Uncertainty Terms.
ing 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
are calibrated out by the AutoCal process. The instrument uncertainty is 0.23% for the 4240 Series.
Calibrator Level Uncertainty. This term is the uncertainty in the calibrator’s output level for a given setting for
calibrators that
the output level:
50MHz Calibrator Level Uncertainty:
At 0 dBm: ±0.055 dB (1.27%)
Application Notes
6-6