Agilent Technologies HP 8719D Service Manual page 450

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
generally combined in a root-sum-of-the-squares (RSS) manner.
Due to the complexity of the calculations, the performance
verification/specifications software calculates the system measurement
uncertainty. The following equations are representative of the equations the
performance verification/specifications software uses to generate the system
measurement uncertainty plots and tables.
Reflection Uncertainty Equations
An analysis of the error model in Figure A-l yields an equation for the reflection
magnitude uncertainty, The equation contains all of the first order terms and
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 and the
S-parameters are treated as linear absolute magnitudes.
Reflection magnitude uncertainty
Erm = Systematic + d(Random)2 + (Drift and Stability)2
Systematic = Efd + Efr
Cr = J(Crml)2
= d(Crrl + 2CrtlSll + CrrlS112)2 + (Crr2S21S12)2
Rr
Determining System Measurement Uncertainties
Efs
Random = d(Cr)2 + (Rr)2 + (Nr)2
+ (2CtmlS11)2 + (CrmlS11)2 + (Crm2S21S12)2
Nr = d(EfntSll)2
Drift and Stability
direction) =
(forward
+ Efnf2
= Dmlbl Sll
+ Abl Sll