Hello Reg,
I brought up this question of uncertainty in measurements several posts ago. Although the calculation is not complicated, obtaining the parameters to find the uncertainty boundaries is a task.
The easiest one to address is S11 and there are papers published by NIST and the Automatic Radio Frequency Test Group (IEEE) that have addressed the exact calculations. I'll see what I can find and can post.
I was unclear what the gentleman in this thread were requesting, but I believe it is the same information required to calculate the uncertainty error for any VNA measurement. For S11 this would include the directivity errors, the reflection tracking errors and the source match errors. These are exactly the three of the five elements posted by the NanoVNA after a cal is complete for S11 only. Additional ones come into play for S21 cal. Hence the measurement uncertainty in S11 is a function of these three LINEAR values which we must obtain (somehow) from the NanoVNA architecture; i.e. the bridge and the mixers.
Once these values are in hand, it is possible to find the difference (error) between the measured S11 and the actual.
For S11 we would find that the difference between the measured and the actual S11 or (S11M-S11A) is given by DELTA(S11) as follows:
DELTA(S11)=(S11M-S11A ) ~ D + TR * S11A + MS * S11A^2
D is the directivity errors, TR is the reflection tracking errors, MS is the source match errors.
Hence, devices with small reflection coefficient, the D value is the source of the major error. While the devices with large reflection coefficient, source match is a most significant error.
This is a very terse answer to a subject that is well documented but not easy to answer in a brief email.
Hope this sheds some light.
Alan
