Agilent Technologies 8753ES

10-8
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
Equation 10-2. Forward Reflection Phase Uncertainty
∆S
11 mag()
Systematic Stability+()
2
Noise
2
+=
Where:
Systematic E
DF
E
RF
S
11
E
SF
S
11
2
E
LF
S
21
S
12
A
M
S
11
Stability
+++ +=
C
2
R
2
+
C
2
C
RM1
2
1 S
11
4
+()4C
TM1
2
S
11
2
C
RM2
2
S
21
2
S
12
2
R
2
++
R
R1
1 S
11
2
+()2R
T1
S
11
+()
2
R
R2
S
21
S
12
()
2
Noise
2
+
N
T
S
11
()
2
N
F
2
+
=
=
=
=
∆S
11 phase()
sin
1–
Systematic Stability+()
2
Noise
2
+
S
11
---------------------------------------------------------------------------------------------



2C
TP1
+=
Where:
Systematic E
DF
E
RF
S
11
E
SF
S
11
2
E
LF
S
21
S
12
A
P
()sin S
11
Stability
+++ +=
C
2
R
2
+
C
2
C
RM1
2
1 S
11
4
+()4C
TM1
2
S
11
2
C
RM2
2
S
21
2
S
12
2
R
2
++
R
R1
1 S
11
2
+()2R
T1
S
11
+()
2
R
R2
S
21
S
12
()
2
Noise
2
+
N
T
S
11
()
2
N
F
2
+
=
=
=
=