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Determining System Measurement Uncertainties
Measurement Uncertainty Equations
Measurement Uncertainty Equations
Any measurement result is the vector sum of the actual test device response plus all error
terms. The precise effect of each error term depends on its magnitude and phase
relationship to the actual test device response. When the phase of an error response is not
known, phase is assumed to be worst case (–l80° to +180°).
Forward Reflection Uncertainty
Equation 10-1. Forward Reflection Magnitude Uncertainty
∆S
(
=
Systematic
(
)
11 mag
Where:
Systematic
Stability
2
C
2
R
Noise
Equation 10-2. Forward Reflection Phase Uncertainty
1 –
∆S
=
sin
(
)
11 phase
Where:
Systematic
Stability
2
C
=
2
R
=
Noise
10-8
+
Stability
=
E
+
E
DF
RF
2
2
=
C
+
R
2
4
(
)
=
C
1
+
S
+
4C
RM1
11
2
(
(
)
=
R
1
+
S
+
2R
R1
11
2
2
2
(
)
=
N
S
+
N
T
11
F
(
Systematic
+
Stability
-------------------------------------------------------------------------------------------- -
S
=
E
+
E
S
DF
RF
2
2
=
C
+
R
2
4
(
)
C
1
+
S
+
4C
RM1
11
2
(
(
)
R
1
+
S
+
2R
R1
11
T 1
2
2
2
(
)
=
N
S
+
N
T
11
F
2
2
)
+
Noise
2
S
+
E
S
+
E
S
11
SF
11
LF
2
2
2
2
S
+
C
S
S
TM1
11
RM2
21
2
)
(
S
+
R
S
S
T 1
11
R2
21
12
2
2
)
+
Noise
+
11
2
+
E
S
+
E
S
11
SF
11
LF
21
2
2
2
2
2
S
+
C
S
S
TM1
11
RM2
21
12
2
)
(
S
+
R
S
S
11
R2
21
12
S
+
A
S
21
12
M
11
2
12
2
)
2C
TP1
(
)
S
+
sin
A
S
12
P
11
2
)
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