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GIN&PEZ;

I have only advanced in my understanding to the extent that I have been able to confirm that the results of complex load measurements using the G-mini equations map virtually 1:1 to those obtained from and computed by the stand-alone NanoVNA. I have not looked at, nor have I attempted to identify and compare differences between the computational processes used to arrive at their respective results.

To obtain the confirmation, required that I perform a single calibration of my NanoVNA using my imperfect set of calibration standards, immediately followed by a single sweep of my DUT*. This exercise yielded a calibrated NanoVNA measurement of my DUT and the set of the 4 raw data files (S, O, L , and DUT) that the NanoVNA used to compute its results, plus the NanoVNA's internally computed results that resulted from those same raw data measurements. All of the above were exported into a spreadsheet where using the G-mini equations I computed a new set of results which I could then compare with those produced by the NanoVNA.

I have done a limited amount of "what-if" experiments to emulate a crude but viable simulated differential analysis, but only to the extent that I was able to confirm that such testing can be performed in a quantifiable manner.

For example; I made the observation that the load value is a single interpolated data point along a logarithmic line that extends from 0 to infinity, and concluded that the accuracy of all measurements made with respect to this single fixed data point are highly dependent on the accuracy of the data point itself. It also appeared obvious (perhaps only to me) that the severity of the inaccuracy in the placement of this single calibrated data point is most critical, and possibly only critical in the immediate vicinity of the data point itself; observing that the extrapolated influence of the absolute error in the load standard compresses in significance as distance from the center of the chart increases. It seems intuitive that the ability to resolve any load standard error contribution erodes rapidly with distance from Z0, and the contribution of other uncertainties (linearity, noise, resolution in the vicinity of the measurement, etc.) would rapidly dominate elsewhere.

I have however only confirmed that the measurements near the value of the load standard being used (Z0) are highly sensitive to differential values (alternative loads) in close proximity to Z0, and the errors do not appear to propagate sufficiently to degrade the DUT measurement results noticeably. More exhaustive testing is required to perform this test in a satisfactorily convincing manner to yield quantifiable results, but I am severely limited in my ability to do so with the instrumentation I have on hand. My hope is that those with capabilities such as near perfect standards, calibrated reference impedance standards, and/or a very well balanced HW bridge are eavesdropping and gaining in their own understanding of what you are doing; and that they will eventually become motivated to chime in and contribute to this exercise.

Whatever the outcome; my ability to contribute is going to be limited to reproducing results that become useful and meaningful FACUPOV. :-)




* The DUT used in my measurements is a 7 foot length of foam RG8X coaxial cable terminated in a 1/10 Watt 3.3 ohms metal film resistor, and yields an approximately 15:1 VSWR collapsing spiral vs. frequency.



--
73

Gary, N3GO

Forgive me to add something trying to create a simple mental picture of what you are saying.
As the nanoVNA has a almost perfect bridge below 300MHz (apart from a phase shift due to transmission line lengths) the relation between a measured R and the output of the bridge (M) is mathematically M=(R-Z0)/(R+Z0) and graphically (for Z0 is 50) and when only varying the real impedance of R

Am I correct to assume your conclusion can be linked to the shape of this transform?
Around Z0 the dominant factor is the placement of Z0 and the uncertainty in the measurement of M leads to a linear relation to an uncertainty in log(R) but as the first derivative of relation between R and M is at a global maximum the impact of measurement uncertainties of M is at its minimum.
For high and low values of R the opposite is true. Even the smallest uncertainty of M around +1 and -1 leads to a substantial uncertainty in R.
I assume the same is true for the imaginary component where instead of R=50 (real component of Z0) the center of the graph is around iR = i0 (imaginary component of Z0)

This then would explain why during calibration the value of the real resistance of the load and its electrical length or its reactance are important to determine the center of the graph and the uncertainty in the center and the open and short for determining the extremes and the related uncertainties there.
--
NanoVNA Wiki: /g/nanovna-users/wiki/home
NanoVNA Files: /g/nanovna-users/files
Erik, PD0EK

Hello again Erik;

I think you may be confusing the uncertainty in M with the uncertainty in the calibration standard. For example; if the calibration standard is 45 ohms (a substantial 10 percent error), Only the value of Z0 changes in your equation. However; calibration of the VNA with this standard (uncorrected) equates the value of Z0 to 45 ohms, but declares it to be 50 ohms. "IF" there are "NO" other sources of uncertainty in our measurement, this would force a 5 ohms real uncertainty in our measurement results. The mathematical (and graphical) consequence of this (now hidden) error is that it shortens (compresses) the length of the perfectly linear distance to the right from 50 to infinity by 5 units, the entire length which then gets normalized to the length of 1, such that all values remain inside the boundary of the Smith Chart. Conversely; it also lengthens (stretches) the the line representing the perfectly linear distance to the left from 50 to 1/infinity (zero).

Because we have decided that there are no other uncertainties in the measurement, we get a clear picture of the consequence of the 5 ohms of uncertainty as we move away from the center of the chart, and reveal that the uncertainty asymptotically approaches zero as we move toward the outside edge. Hence; it is my assertion that the consequence of errors in the load standard are most relevant and arguably critical for measurements of an impedance at or near Z0.

In an analogous manner, I might even argue that reactance uncertainties may have even less influence on measurements of DUTs exhibiting a real part less of less than Z0; since Zero reactance is established at all three calibration points.

In a practical sense, and given that even DIY calibration standards of high quality are not difficult to manufacture; it would appear that frequency accuracy and the precise definition of the reference plane are perhaps the most sensitive, and thus the most critical calibration parameters to be controlled. Ironically; uncertainties in those parameters diminish as impedance approaches Z0. What also becomes evident from these assertions is that the quality of the standards with respect to establishing the measurement reference plane increases as frequency increases.

--
73

Gary, N3GO

Erik;

My bad...I incorrectly stated that zero reactance is established at all three calibration points. Everything goes to infinity at the right edge of the chart. :-)

--
73

Gary, N3GO

Garry,

Thanks, I may have formulated unclear but what you state is what I meant.
Uncertainties in M act as "error bars" making it uncertain where you are in the graph, Uncertainties in the calibration standards cause left/right shifts/compression/decompression in the positioning of the graph
--
NanoVNA Wiki: /g/nanovna-users/wiki/home
NanoVNA Files: /g/nanovna-users/files
Erik, PD0EK

#83 : On the Doubtfulness

Hello,

Allow us, please, to announce that, as it seems, we may just found the deep
source of doubtfulness and in the following way : we thought that we had to
think historically, that is with terms of the time all this measurement adventure
begun, that is with the available accuracy of the calculations -rather than
computations- of that time.

Therefore, also allow us, please, to announce that having already in hand the
last, fully proved, "new" formulation of this "one-port" method of computation
of S-parameters of (reciprocal) two-ports, we focus our next research steps in
this very direction : on the comparison of these "one-port" computation results
with the "classic" one of "two-port" measurement ones.

Sincerely,

gin&pez@arg

:83#

@ Erik, PD0EK
10 December 2019 - /g/nanovna-users/message/8105

Dear Erik,

Thank you very much indeed for your continuing interest in our work !

However, since we are not sure at all what would you expect from us
regarding your Work contained in your three links you gave to us,
we don't want to jeopardize any related comment, which will be
considered as inappropriate by a possibly biassed member of this
group, and thus to give him the chance to start a nonsensical dispute
on matters definitely belonging in the subjective sphere of personal
habits and/or tastes.

With our kind regards,

gin&pez@arg

Gin&pez
Thanks for the reply.no need for any action from you side.
Garry already help me to understand better

--
NanoVNA Wiki: /g/nanovna-users/wiki/home
NanoVNA Files: /g/nanovna-users/files
Erik, PD0EK

#84: On the Virtuality of the "Measurement Port"

Hello,

Allow us, please, to inform you that since in our sow we see the
"Measurement Port" facupov as the Virtual Port of the irreversible,
non-reciprocal, two-port V2P [1], at least in the case of the basic
HP 8502A Transmission/Reflection Test Set [2], we just uploaded
a rather big (2,752 pixels width X 2,060 pixels height), and rather
clean, figure of its equivalent circuit of some version of it [3], at:



After that, we hope it would be crystal clear the objective fact that
facupov this device is * N O T * a TWO-PORT at all, but it is the
FOUR-PORT Network : w

[RF INPUT] - [TEST] - [INCIDENT] - [REFLECTED].

Therefore, also allow us, please, to inform you that, about 25 twenty-
-five years ago, we started our research on this very [anyVNA] subject,
by expressing -at least in the "Low Frequencies"- the shown Four-Port
as an effective "Error" Two-Port - after a long sequence of assumptions
and approximations, of course.

Sincerely,

gin&pez@arg

REFERENCES

[1] #77: On the current explanation of full one-port "error" model
in our sow - facupov, as always - with an Application to the
Measurements of Two-Port Devices :
11 November 2019 - /g/nanovna-users/message/6798

[2] archive.org,HP: 8502A :

[3] archive.org, HP: 8502A, p. 5/6 :

:84#

#85: On the Formation of a Virtual Port

Hello,

Allow us, please, to somehow explain the formation of a Virtual Port facupov,
in our sow.

Well, since we can always introduce the "reflection" relation:

(beta) = (gamma) . (alpha)

between the output ("reflected") and input ("incident") signals at one and
the * s a m e * r e a l * port, or equivalently : one and the same real port
defines a relation involving the signals "reflected from" and "incident to" it
-
e.g. in ||05| g :: 1.b = g.a1 || and ||07| G :: 1.b = G.a || at:
of:
#82' : On The Two-Port Sine Qua Non Practical Application - Source and Load
11 December 2019 - /g/nanovna-users/message/8147
-
we thought that we would also consider a -somehow inverse to the above-
definition by which the signals at two * d i f f e r e n t * ports, e.g. to the
[REFLECTED] and [INCIDENT] ports of HP8502A
-
#84: On the Virtuality of the "Measurement Port"
15 December 2019 - /g/nanovna-users/message/8225
-
could define one and the same * V i r t u a l * -non-real- Measurement Port.

By the way, also allow us, please, to strongly re-suggest, to the interested
member of this group, the fundamental, sine qua non, paper on the subject
of the S-parameters (of this Virtual Two-Port V2P, in our sow) named by
Richard H. Hackborn as "errors" in its Work:

"An Automatic Network Analyzer System", Microwave Journal, May 1968, p.46
#37 : The [LeastVNA] - 7 October 2019 - /g/nanovna-users/message/4250

Unfortunately, this paper did not openly appear on the Internet, at least at the
time we looked for it, that is exactly one year before, on 14.12.2018, so we also
suggest to look at a nearby Library, e.g. we found it at the Library of TUV at the
bookshelf : .

Anyway, we already gave an excerpt of this valuable paper -for fair use, of course- at:

#15 : 26 September 2019 : /g/nanovna-users/message/3147

Sincerely,

gin&pez@arg

:85#

GIN& PEZ;

Do your assertions in: #84: On the Virtuality of the "Measurement Port"

signal that you are abandoning your pursuit of a two port model of a “LeastVNA”, or is it simply a statement that such a model would have no meaning in an adaptive (reflection/transmission test set) environment?

--
73

Gary, N3GO

@Gary O'Neil, N3GO
15 December 2019 - /g/nanovna-users/message/8238

Dear Gary,

Not at all. Would you read, please, our related message:
#85: On the Formation of a Virtual Port
15 December 2019 - /g/nanovna-users/message/8237
?

Anyway, the fact is that we are looking now for the * l i m i t s * of this
model, because we already have interesting experimental evidences
on this very subject - * v e r y * interesting indeed, we promised you.

Kind regards,

gin&pez@arg

2 - @Gary O'Neil, N3GO
15 December 2019 - /g/nanovna-users/message/8238

Hello again,

We are terribly sorry but we forgot to emphasize enough that a model
such this one is totally unavoidable, because of the technique this
very measurement unit uses.

Regards,

gin&pez@arg

Thank you again GIN&PEZ;

This is both an interesting and exciting journey of discovery and understanding for me. Your diligence and persistence, along with the availability and convenience of modern mathematical tools like Maxima, are managing to win at least one follower of your work. :-)

It is most interesting that this new two port model appears to implicate a savings in hardware as well as computational efficiency.

I am looking forward to “testing” the algorithm with my limited resources for this, and attempting to formulate ideas for non-symetric 2-port devices to flip and compare for example S11 with S22 when the DUT is reversed.

FACUPOV, I suspect that the indirect S22 measurement is going to yield a most controversial result when pitted against its direct measurement. Also FACUPOV, equivalence to the latter is easily achieved by simply flipping the DUT, repeating the test, and acknowledging the additional set of uncertainty introduced by that action.

I anticipate that the uncertainty in S21 and S12 will be reduced, but a similar controversy may arise over differences in S12 results.

I will maintain sensitivity to clues of the aforementioned controversies as I evaluate and compare 2-port measurements.

--
73

Gary, N3GO

Dear Gary,

Well, allow us, please, to underline what we already said in:

#83 : On the Doubtfulness - 13 December 2019:
/g/nanovna-users/message/8173

that is : it is just a "new" -but careful- formulation which generalizes
not only the aforementioned paper by Hackborn, but also the idea
expressed in the following paper by W.P. Wheless, Jr. and C.S.
Wheless:

"Two-Port Network Specification of Baluns for NEC Analysis
and Other Applications", 1996-03, 12th Annual Review of
Progress in Applied Computational Electromagnetics at the
Naval Postgraduate School, Monterey, CA, March 18-22, 1996,
Conference, pp 69-74, PDF pp 96-101:



plus, once more, as it seems it has its practical limitations of:

/g/nanovna-users/message/8239
/g/nanovna-users/message/8240

which were already implied at:

#83 : On the Doubtfulness - 13 December 2019:
/g/nanovna-users/message/8173

obviously due to the facts already mentioned at section (9) of:

#73': On the sine qua non Core Uncertainty of AnyVNA - incl. NanoVNA - System
6 November 2019 - /g/nanovna-users/message/6529

Anyway, we will see.

Sincerely,

gin&pez@arg

ann : we just finished the experimental comparison - the results verified
our predictions for two constructed two-ports - #83 : On the Doubtfulness -
13 December 2019 - /g/nanovna-users/message/8173

#86: On the Results of Measuring Two-Ports Using Only [NanoVNA] Channel [CH0]

Hello,

Allow us, please, to announce that, in the process of preparing the presentation
of our results on Measuring Two-Ports Using Only [NanoVNA] Channel [CH0]
and regarding the values involved, we just realized in our sow the following
simple facts - always facupov, of course, as usual :

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

(0) All values are expressed as rational numbers of finite length, but we can
divide them to three 3 different sets of different origin and different accuracy:

(1) The set of nominal values of the three 3 Standards S, L, O, as they are
given by their manufacturers : { -1, 0, +1 }. These numbers are exact.

(2) The set of 4 measured values : { s, l, o, g }, as they are provided by
[NanoVNA] in use. These numbers are of fixed accuracy.

(3) The sets of finally computed values : either { S12S21, S22, G } or {G}.
Nowadays, these numbers may are of arbitrary accuracy defined by The
Common User.

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

Sincerely,

gin&pez@arg

:86#

#86': UPGRADE : On the Results of Measuring Two-Ports Using Only [NanoVNA]
Channel [CH0] or a [LeastVNA].
-
#86: On the Results of Measuring Two-Ports Using Only [NanoVNA] Channel [CH0]:
16 December 2019 - /g/nanovna-users/message/8275

Hello,

Allow us, please, to announce that just we also additionally realized, in our sow,
the following simple facts, always facupov, of course, and thus we just upgraded
our previous division of the values involved in "Measuring Two-Ports Using Only
[NanoVNA] Channel [CH0]" and now : "or a [LeastVNA]", as follows:

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

(0) All values are expressed as (complex) (couples of) rational numbers of finite
length, but we can divide them to three 3 different sets, according to their different
origin, form, and precision :

(1) The set of nominal values of the three 3 Standards S, L, O, as they are given
by their manufacturer in the usual form of { -1, 0, +1 }. These numbers are exact.

(2) The set of 4 measured values : { s, l, o, g }, in the form provided by the
manufacturer of [NanoVNA], his current version of the updated firmware, or the
[LeastVNA] in use. These numbers are of fixed precision.

(3) The set of finally computed values, that is either the { S12S21, S22, G }
or just the {G} alone. The form of these numbers, as well as their precision,
which nowadays may be arbitrarily high and limited only by the available
application, computer memory, and run time, are defined by The Common User.

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

Sincerely,

gin&pez@arg

:86'#

@Oristo - 4 November 2019 - /g/nanovna-users/message/6439

Hello,

Allow us, please, to thank you at last for your most motivating us comments,
regarding the relative values of s and o, as well as that one of l values,
because it is only now, after the verification of our last research findings,
we are feeling able to recognize the significance of these remarks made
by you.

Thank you.

Sincerely,

gin&pez@arg

GIN & PEZ;

Congratulations on your success reported in Post 8255 (#82).

Were the equations in posts 7272 (#78 twice corrected) & 7657 (#80) the ones used to perform your verification?

--
73

Gary, N3GO