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Transmission
Uncertainty
Equations
Transmission Magnitude Uncertainty
(Etm)
An analysis of the error model, located at the end of this appendix, yields an equation for
the transmission magnitude uncertainty. The equation contains
all
of the
first
order terms
and some of the significant second order terms. The terms under the radical are random in
character and are combined on an RSS basis. The terms in the systematic error group are
combined on a worst case basis. In all cases, the error terms are treated as linear absolute
magnitudes.
Transmission magnitude uncertainty (forward direction) = Etm =
Ert
= Systematic +
J(Random)2
+ (Drift and
Stability)2
Systematic = Efc +
(Eft
+
EfsSll
+
EflS22
+
EfsEflSBlSl2
+ Ab2)
S21
Random =
&Ct)2
+ (Rt)2 +
(Nt)2
Ct
= S21J(Ctml)2 +
(Ctm2)2
+
(CrmlS11)2
+
(Crm2S22)2
Rt
= S21d(Crt1)2 +
(C~d2)~
+
(CrrlS11)2
+
(Crr2S22)2
Nt =
-\/(EfntS21)2
+
Efnf2
Drift and Stability = Dm2b2
S21
where
Crt2
= Connector repeatability (transmission) port 2
Crr2
= Connector repeatability (reflection) port 2
Efnt = effective noise on trace
Efnf
=
effective noise floor
Crrl = connector repeatability (reflection)
Crtl = connector repeatability (transmission)
Ctml = cable 1 transmission magnitude stability
Ctm2
=
cable 2 reflection magnitude stability
Crm2
= cable 2 reflection magnitude stability
Dmsl
=
drift
magnitudePC
source to port
Efs = effective source match error
Eft = effective transmission tracking error
Efl = effective load match error
Efc = effective crosstalk error
The detailed equation for each of the above terms is derived from the signal flow model,
located at the end of this appendix.
Determining System Measurement
Unseertsinties
B-6