HP 8753E manual Measurement Uncertainty Equations, Sources of Additional Measurement Errors

Sources of Additional Measurement Errors

Two additional categories of measurement errors are connection techniques and contact surfaces.

The connection techniques category includes torque limits, flush setting of sliding load center conductors, and handling procedures for beadless airlines.

The contact surfaces category includes cleaning procedures, scratches, worn plating, and rough seating.

These types of errors are not accounted for in the uncertainty analysis.

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 (-HO0 to + BOO). Random errors such as noise and connector repeatability are generally combined in a root-sum-of-the-squares (RSS) manner.

Reflection Uncertainty Equations

Total Reflection Magnitude Uncertainty (Erm)

An analysis of the error model in Figure El yields an equation for the reflection magnitude uncertainty. The equation contains all of the llrst 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 (forward direction) =

Erm = Systematic + d(Random)2 + (Drift and Stability)2

Systematic = Efd + Efr Sll + Efs S112 + S21 S12 EfZ + Abl Sll

Random = am + (RT-)~ + (NT)~

Cr = J(Crml)2 + (2CtmlS11)2 + (CrmlS11)2 + (Crm2S21S12)2

Rr = d(Crrl + 2CrtlSll + CrrlS112)2 + (Crr2S21S12)2

Nr = d(EfntSll)z + Efnf2

Drift and Stability = Dmlbl Sll

Determining System Measurement Unwrtainties B-3