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#73': On the sine qua non Core Uncertainty of AnyVNA - incl. NanoVNA - System
(the message #73 is withdrawn mainly because its conclusion is too weak)

erik@... - 5 November 2019 : /g/nanovna-users/message/6495

Dear Erik,

Thank you very much indeed for your interest in our work and also for the chance
you give us to explain it -always facupov, of course- further !

Therefore, regarding your specific question:

"How are you sure the errors to be corrected are larger than the uncertainty in
your measurement. e.g. you are not trying to correct an already (almost) perfect
VNA?"

allow us, please, to definitely clear without any doubt that in our sow [#24], [#34]
we are only * c u r r e n t l y * sure for the following - but we hope to excuse us
because, maybe unfortunately enough, we selected to explain all that using
purposely a greatly emphatical language:

- - - - - - (c) gin&pez@arg (cc-by-4.0) 2019 : start - - - - - -

(0) "A perfect VNA" is an object of the * i m p e r f e c t * world of mathematics

(1) "An already (almost) perfect VNA" may be an object in other subjective worlds
- we don't know, but we are ready to include it in our sow, as soon as we will be
provided by the specific quantitative data of its existence

(2) "The Least VNA" is simply AnyVNA that is used as a Reflectometer or
Impedance Meter in terms of frequency of One-Port devices using the well-known
("standard", 'Standard' or Standard) set of three 3 loads {S, L, O}, all with known
nominal values given respectively, not at all by us but by their manufacturers, as
the so-called "{-1, 0, +1}" or whatever similar

[ but loosely, because this may be result in a * B I G * source of misunderstanding
[ since this "set of values" is in fact the one of the couples of values:
[
[ { ( 1 , -180 ) , (0 , undefined ) , ( 1 , 0 ) }
[
[ in terms of their ( modulus , argument ) ordered
[ -
[ that is in order to avoid to mess up the things, the modulus value has always to
[ appear first, after the opening left parenthesis and before the separating comma,
[ and then the second argument value to appear before the closing right parenthesis
[ -
[ pairs or couples of values

although a last -apt, as usual- comment made by our Fellow in Knowledge Garry
O' Neil, N3GO [1], forced us to already think a possible reconsideration of this
definition in the direction of an even more simplification; always facupov, of course

(3) "The LeastVNA measured Impedance" is * I N * F A C T * an * I N D I R E C T *
"measurement", that is a * C A L C U L A T E D * or * C O M P U T E D * result,
just an * O U T P U T * of the well-defined * M A T H E M A T I C A L * function
expressed by the well-known * F O R M U L A * [#52]:



in terms of the measurements of these * T H R E E * loads, made * D I R E C T L Y *
using that * A N Y * V N A *

(4) Obviously this is an * I N S E P A R A B L Y * A S S O C I A T E D * to * A N Y *
* V N A * mathematical expression, a so-called "(mathematical) model", of this
very instance LeastVNA of that AnyVNA.

(5) We did * N O T * invent this relation [#52]:



We just simplified the given one [#16]:



-
as, perhaps, they did that others before us, although we don't know if something
that was really happened.

This is easily verified by anyone who would like to use simple, high-school algebra
on these expressions, by ignoring their complex "nature" and substituting:

(i) g, G in Hellenic gamma, Gamma

(ii) -1, 0, 1 in A, B, C, and

(iii) s, l, o in a, b, c,

respectively, and proceeding with the resulting eliminations.

That's all.

(6) Now, since the 8 = 3 x 2 + 1 x 2 measurements s, l, o, and g, were indicated by
our VNA to us with a * F I N I T E *, * L I M I T E D * * A C C U R A C Y * of just
* T H R E E * 3 *, or * F O U R * 4 * at most, decimal * D * I * G * I * T * S *, it was
extremely natural in our sow to ask ourselves :

HOW BIG WILL BE THE EFFECT IN THE UNAVOIDABLY * C O M P U T E D *
IMPEDANCE, IF WE WOULD TAKE INTO ACCOUNT THAT *J U S T * O N L Y *
O N E *, THE LAST ONE, DIGIT OF THESE FOUR MEASURED VALUES WAS IN
DOUBT ?

THAT IS AS IT HAPPENS IN ANY OTHER MEASUREMENT, BY ANY OTHER
INSTRUMENT, SO WHY NOT WITH THOSE BY AnyVNA OR OUR VNA ?

That's all..

And, once again, definitely this has nothing to do with the perfectness or imperfectness
of AnyVNA itself. But, this definitely has to do with the unavoidably finite number of
reliable digits used by AnyVNA to indicate its measurements.

And this finite number of reliable digits in these four 4 measurements is only JUST
ONE source of error in the finally COMPUTED indirect "measurement".

(8) We emphasized in the above the COMPUTED character of the indirect
"measurement" because, if this INDIRECT "measurement" was a usual DIRECT
measurement, all the doubt would unavoidably restrict to just a few, perhaps even
only the last one, of its resulted digits - but, unfortunately enough, this is not the
case here.

(9) Also, and in addition to all that, the range of measured values (small, less than one
1 in modulus), as well as the particular form of the unavoidable mathematical
expression (ratio of differences of small, less than one 1, in modulus values) FORCED
us to attempt such a research
-
and it would be the GREATEST of OMISSIONS by us, if we did not act in this way,
as long as we declared ourselves not only as "researchers" but in addition as "scientific"
ones...

(10) After all that said, we think that we are ready to answer your question as follows:

- We are NOT interested to correct our "measurement" -in fact one of our VNA itself

- We are NOT interested if the errors to be corrected -in fact ones of our VNA itself-
are larger than the uncertainty in our "measurement" -in fact in the computed indirect
"measurement" of our VNA itself

- We are only * c u r r e n t l y * s u r e * about our currently in use method of estimation
of the above inaccuracy errors, which * U N A V O I D A B L Y * C O N T R I B U T E *
to the ENTIRE "MEASUREMENT" UNCERTAINTY of our two VNA systems
-
that is either of our VNA or of our * N a n o V N A *, * P L U S * our THREE Standards
in just this, the simplest of all the possible uses of these (also currently "the simplest"
use, after our reservation (2) above, that is after Garry O' Neil's comment

- We are * c u r r e n t l y * s u r e * about our currently in use general method of estimation
of all the errors we are currently in place to recognize as REALLY EXISTING in AnyVNA
measurements, that is (a) the above Inaccuracy Errors, PLUS (b) those, definitely larger
than these, Uncertainty Errors given to our three 3 Standards by their manufacturers
-
all together count to finding 28 (real) numbers at most, by taking into account that all
these are in general (real) intervals with two 2 end-point numbers, a lower and an upper one,
so that 2 x (8 + 3 x 2) = 2 x 14 = 28
-
contribute UNAVOIDABLY to the ENTIRE "MEASUREMENT" UNCERTAINTY at least of our
two VNA systems, if nobody's else.

And this is the reason we call this component of the entire uncertainty:

"The sine qua non Core Uncertainty of AnyVNA - incl. NanoVNA - System"

In conclusion:

We are currently sure for that:

Facupov, * UNCERTAINTY * LOWER * THAN* THIS * CORE * UNCERTAINTY *
* IS * ENTIRELY * IMPOSSIBLE * in AnyVNA - incl. NanoVNA - SYSTEM under
its LeastVNA application, as well as,

We are currently sure for that:

Our current method of estimation of this Core Uncertainty is the only known one
as an objectively existing one, even as an object of just our sow - that is it has
a deterministic character - for more than ten years now.

Others may have their own methods of estimation of other types of uncertainty
components, as objects of their subjective worlds - that is they have a statistical
character.

However, facupov, currently we are definitely not interested either on those
uncertainty components or on their estimating methods - fullstop.

- - - end : (c) gin&pez@arg (cc-by-4.0) 2019 - - - - - - - - - -

* You * Have * Been * Warned *

REFERENCES

[1] Gary O'Neil , N3GO - 4 November 2019 :
/g/nanovna-users/message/6432

[#16] : 27 September 2019 :
/g/nanovna-users/message/3161


[#24] : The Main Frame of a Possible Communication - 1 October 2019:
/g/nanovna-users/message/3649

[#34] : Trying to Limit the Misunderstanding up to its Removal - 5 October 2019:
/g/nanovna-users/message/4108

[#52] : Update : The compact SLO formula for [AnyVNA] - 17 October 2019:
/g/nanovna-users/message/5100


With the Best of our Regards,

73

Nikolitsa, OE3ZGN/SV7DMC and Petros, OE3ZZP/SV7BAX

:73'#