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#104: On the Criterion of Cross-Ratios

@Erik, PD0EK - 2 January 2020 - /g/nanovna-users/message/9074

Dear Erik,

Thank you, very much indeed, for your time spent on these questions.

1
Well, both cross-ratios are suffering errors in either side of their equation, the
one of measurements because of the unavoidably limited precision or accuracy
in their 4 readings, and the other of loads because of the existing uncertainties
in the values of 3 standards. However, since the linear S-parameter equations
do * N O T * formulate errors of either kind
-
* may we have your attention, please, to this most crucial point ? *
-
the same holds for * E V E R Y * other consequence of them, that is for this very
equation too, as well as of the totality of its consequences. Thus, we have to
confront any error problems within this available S-parameter frame. Thus there
is by any chance possible a "substantial "amplification" of uncertainty" due to
"an unfortunate choice of loads" - see, please, "The Fourth Load" trick [0].

2
Anyway, we search the whole thread for "sufficiently independent" and we found
nothing such that was said by us. Instead, we call "substantially independent" our
experimental results we selected to present "On our Comparison of our [NanoVNA]
with our [HP 8505A] Using the Ultimate Criterion of Cross-Ratios" [1], because we
have in hand other results using a loaded 2-port, which are not appropriate at all to
call its experimental results "substantially independent" from them
-
and although we found the required explanation for that fact, we do not publish t
until we complete our experimentation with another 2-port - see, please, our reply
to Gary O'Neil , N3GO [2]. However, we can assure you right now that there is
absolutely nothing to do in such actually existing 2-port cases to eliminate such
a problem.

3
Finally, although we are not sure at all what you mean by characterizing the SOL
loads as "traditional" ones, regarding your -very interesting, indeed- claim for an
"independence criterion", as well as for the related to it of "maximum independence",
"best comparison" facilitation, and "better set of 3 loads", it may be obvious from
all that said above that such a condition can not be set in anything else different
than the single requirement of their distinctness. However, we already look at the
direction imposed in our three articles "On the Results of Measuring Two-Ports
Using Only [NanoVNA] Channel [CH0] or a [LeastVNA]" [3]-[5].

Best regards,

gin&pez@arg

REFERENCES

[0] #103 : The Fourth Load
3 January 2020 - /g/nanovna-users/message/9108

[1] #97 : "On our Comparison of our [NanoVNA] with our [HP 8505A]
Using the Ultimate Criterion of Cross-Ratios"
29 December 2019 - /g/nanovna-users/message/8763

[2] @Gary O'Neil , N3GO
17 December 2019 - /g/nanovna-users/message/8293

[3] #86: On the Results of Measuring Two-Ports Using Only [NanoVNA] Channel [CH0]
16 December 2019 - /g/nanovna-users/message/8275

[4] #86': UPGRADE : On the Results of Measuring Two-Ports Using Only [NanoVNA] Channel
[CH0] or a [LeastVNA] - 16 December 2019 - /g/nanovna-users/message/8278

[5] #86": Two Notes On #86': UPGRADE : On the Results of Measuring Two-Ports Using Only
[NanoVNA] Channel [CH0] or a [LeastVNA]
19 December 2019 - /g/nanovna-users/message/8400

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