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errors of "error" models

 

#80: [S]-parameters from [Z]-parameters
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#78'': #78' was re-corrected
20 November 2019 : https://www.op4.eu/code/s2p.png

Hello,

Allow us, please, to inform you that in the preparation of the
presentation of the measurements of S-parameters of a 2-port
network using the [LeastVNA] only, we had to re-produce
-from the very beginning- the needed mathematical expressions of
S-parameters in terms of Z-parameters, which we just uploaded at:

https://www.op4.eu/code/z2s.png

Sincerely,

gin&pez@arg

:80#

Gary O'Neil
 

Hello again GIN & PEZ;

If you don’t mind, can you please post again your complete and current set of equations, and present them in a black on white format more conducive to printing. The format you have been using is a terribly inefficient use of ink/toner resources. I can take the extra steps to do an image conversion locally; but having the reverse image to begin with will make it much easier to print out a hard copy that I can work with.

--
73

Gary, N3GO

 

@Gary O'Neil, N3GO - 2 December 2019
https://groups.io/g/nanovna-users/message/7680

Dear Gary,

It is very nice, indeed, to hear from you again !

Well, regarding your specific request, allow us, please, to suggest you to try:

[Windows][Start][Accessories][Paint][Image][Invert Colors]

Best regards,

gin&pez@arg

Gary O'Neil
 

Dear GIN&PEZ;

The process you describe is the one I have been using, and it works just fine. It is just an annoying and unnecessary extra step in the printing process. I still have to walk over to my XYL’s office to get my copy from the printer. :-)

--
73

Gary, N3G

 

#81: On the Physical Expression of Two-Port S-Parameters

Hello,

Allow us, please, to announce that in our sow and facupov
we just expressed physically (that is in a way similar to that
of the Measurement of Ratio of Quantities, which were
introduced by others * and are constantly used since then)
the S11, S12*S21, S22 parameters of a two-port network
in terms only of the VNA reflection measurements of
(S, L, O) loads, with Standard Nominal Values (-1, 0, +1)
respectively, and we uploaded our results at:

https://www.op4.eu/code/hurhkamen.gin.pez.arg.cc.by.4.0.2019.png

Sincerely,

gin&pez@arg

* https://www.op4.eu/code/Hellenes.The.Eight.gin.pez.arg.cc.by.4.0.2019.png

:81#

 

#81': update : on the physical expression of two-port s-parameters
#81 - 8 December 2019 - https://groups.io/g/nanovna-users/message/7962

Hello,

We just uploaded a substantially updated improved proof at:

https://www.op4.eu/code/hurhkamen.gin.pez.arg.cc.by.4.0.2019.png

Sincerely,

gin&pez@arg

:81'#

Gary O'Neil
 

Hello again GIN&PEZ



--
73

Gary, N3GO

Gary O'Neil
 

Hello again GIN&PEZ

I would like to continuing following your work, but I think you are expecting much mind reading on my part for me to meet that objective. I am able to infer some information from your one port equations and the context of this thread; and I can infer some from the variables used and the general form of several of the equations. As presented however, I am forced to make assumptions that are misleading at best, and incorrect at worst. You need to provide some textual guidance in the form of variable definitions with assignments void of ambiguity, such as the numbers 0 and 1, and the letters O and L. A starting point with a reference baseline set of measurements that are (or will be) required to complete the calculations should be established before the onset of your derivations.

The textual content need not be verbose, but it needs to be clear and unambiguous, precede your equations, and ideally it follows the process regarded as the scientific method.

Is there a message in the timeline listing of the Mathematicians/Philosophers of the Classical and Hellenistic periods; or was this appended to serve as a statement of how you would describe a model of your SOW? :-)

--
73

Gary, N3GO

 

@ Gary O'Neil, N3GO - 8 December 2019
https://groups.io/g/nanovna-users/message/8024

Dear Gary,

Once again, we thank you for your time.

You are right. Yes, this is indeed an endless, multidisciplinary, research
and one of its objectives is to bridge the gap between the now and the
past. Yes, we tried to see the fundamental ideas of quantities and their
ratio measurements in our sow, particularly in the two-port network case.
Well, this is not at all a simple task as it may sounds, because it has to
do with elementary concepts lying on the historical boundaries between
science and philosophy. Anyway, after many years of returning attempts,
we discovered yesterday that we had to restore the "multiplicative balance"
in the two basic, well-known, linear equations, that is instead e.g. of the
mathematical: b1=S11a1+S12a2, the "physical" one: 1.b1=S11.a1+S12.a2.
That was all.

Finally, yes, we also know that you are also absolutely right at all of the
rest matters you rise, including the badly shaped o, O, 0, 1 and l of MS
Courier New font and especially in this particular size. For that last one,
we will try to re-use the font of our choice: Liberation Mono, in an
appropriate size. of course. As of the above matters, unfortunately enough,
we have to invoke, once again, our permanent excuse : in our sow, this is
a research in progress and thus we have to find time to answer all of them.
We are terribly sorry for the inconvenience caused. Please, accept our apologies.

Best regards,

gin&pez@arg

Gary O'Neil
 

GIN&PEZ;

You are in excellent company. The Romans thought they could avert the zero issue altogether by not using it at all. They must have realized that the number 1 was going to be a problem when they ran out of fingers too. :-)

Is the number 2 the only numerical character used in your proof? I think I can differentiate the zero’s without ambiguity; I’m only uncertain of the ones and lower case L’s. Can I assume all are lower case L’s, and all as being measured Load values?

--
73

Gary, N3GO

 

@ Gary O'Neil, N3GO - 9 December 2019
https://groups.io/g/nanovna-users/message/8059

Dear Gary,

No, there is not only the numeral two. There are a lot of ones and small Ls.

But, could you wait a little, please? We will try to improve the appearance of
the text, by using Liberation Mono of appropriate size or whatever else font,
sometime later and we hope that we would finish after two or three hours, at
most.

Best regards,

gin&pez@arg

 

#81" : update : on the physical expression of two-port s-parameters
REF: 9 December 2019 - https://groups.io/g/nanovna-users/message/8065
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#81' : update : on the physical expression of two-port s-parameters
8 December 2019 - https://groups.io/g/nanovna-users/message/8013
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Well, regarding o, O, 0, 1 and l appearance : after numerous trials-and-errors,
we dropped the use of [Liberation Mono] and use [Bitstream Vera Sans Mono],
[Bold], [16], [Release: 1.10]:

https://www.op4.eu/code/hurhkamen.gin.pez.arg.cc.by.4.0.2019.png

Gary O'Neil
 

GIN&PEZ

This looks much better thank you; but please don’t feel rushed on my behalf. I acknowledge that this is a works in progress, and I am working through this in my leisure... a luxury of being retired, but not a legitimate excuse from doing my chores. :-)

--
73

Gary, N3GO

erik@...
 

I'm still trying to understand what you are publishing.
Am I correct your model as published in the white on black picture is a one port model like this
http://athome.kaashoek.com/public/nanoVNA/One%20port.PNG
and you describe how to determine the model using 3 known DUT's as in this
http://athome.kaashoek.com/public/nanoVNA/Calibration.PNG
Where you still have to solve the three equations but as I am laizy I use Maxima leading to this result:
http://athome.kaashoek.com/public/nanoVNA/Maxima.PNG
Or am I completely failing to grasp what you are trying to convey?

--
NanoVNA Wiki: https://groups.io/g/nanovna-users/wiki/home
NanoVNA Files: https://groups.io/g/nanovna-users/files
Erik, PD0EK

Gary O'Neil
 

Eric;

It might be helpful to review msg #6670. GIN&PEZ presents the derivation of the G-mini equation which is the one-port measurement model, which they summarize in msg #6798.

That one port model, based on an embedded S parameter matrix consisting of an (s, o, l, and DUT) terminated LeastVNA (virtual) reflection port, was then rearranged, then presented, and subsequently revised (corrected) in msg #7272 as a derivation, of a two port indirect measurement model that relies only on the single one port set of reflection measurements... not the independent S11, S22, and thru measurements in common use today.

An important component of their work is that all uncertainties are included in the calculations, and the s, o, l standards used are all considered nominal values. Regions of uncertainty are derived from the results but are defined independently, as a graphical mapping surrounding each measurement based on easily defined real boundaries.

This is my understanding to this point subject to forthcoming corrections by GIN&PEZ.

I have not yet studied the uncertainty derivations in detail, but the concept appears to be sound. I have independently coded the G-mini equation, and have found it to be spot on in agreement with the corrected output results of 3 independent analyzers; the NanoVNA, an N2PK VNA, and an AQRP VIA of similar architecture to the NanoVNA.

I personally find it helpful to return to and review previous posts periodically as I begin to sense that I am gaining in my understanding. I find the communications becomes more clear and it often exposes important details I missed altogether. The process does take a lot of additional effort on my part, but I find it beneficial in areas that the language fails to translate precisely.

I hope you find at least some part of this to be helpful.

--
73

Gary, N3GO

erik@...
 

Thanks, this helps.

As I understand now: they determine the embedded port parameters by using the equivalent of a one-port calibration with 3 known terminations, then express the embedded port parameters in the response measured for these 3 terminations, thus allowing the identification of regions of uncertainties in these measurements so these can be translated into uncertainties of the embedded port parameters (the uncertainty derivations) and this gives the uncertainty of the measurements done with the one port VNA?


--
NanoVNA Wiki: https://groups.io/g/nanovna-users/wiki/home
NanoVNA Files: https://groups.io/g/nanovna-users/files
Erik, PD0EK

 

#82 : On The Two-Port Sine Qua Non Practical Application - Source and Load
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REF: #81" : update : on the physical expression of two-port s-parameters
10 December 2019 - https://groups.io/g/nanovna-users/message/8076

Hello,

Allow us, please, to announce that we just finished our work on this subject and
uploaded the updated results at the very same address:

https://www.op4.eu/code/hurhkamen.gin.pez.arg.cc.by.4.0.2019.png

Also allow us, please, to say that in our sow, the virtue of this formulation lies
on that : facupov, we are not able to see any simpler way to express it more
completely other than this one - well, at least currently.

Sincerely,

gin&pez@arg

:82#

Gary O'Neil
 

Hello again Erik;

I think you are close but not quite precise in your understanding. Or possibly I’m not yet precise in my own. :-)

All uncertainties are embedded in the model as they are uncertain entities that exist in any measurement. There is no attempt here to sort out the uncertainties, much less in any precise manner. The equations are only a compact (minimized) set required to compute the one and/or two port results while attempting to not degrade the integrity of the calculations resulting from mathematical manipulation.

Measurement accuracy is influenced by the known inaccuracies of the standards used, but not defined by them. The true accuracy in the measurement is bounded by the collective contributions of all uncertainties in the measurement, and not simply (and incorrectly) allocated the preciseness of the standards alone.

The uncertainties in the results achieved by the equations are acknowledged; but addressed as an independent and separate but parallel computational process. This is described in terms of a mechanical (graphical) construction of the bounded limits of regions and intervals surrounding each data point independently. The limits used in describing the uncertainty boundaries are user defined, easily or conveniently determined, and are as precise as the user determines to be justifiable. The construction process is illustrated in the animated videos posted in msg # 7235, and articulated in detail in the series of 5 white papers posted at the beginning of this thread. I have only skimmed over these to date, but I believe them to be complete as presented.

I believe the equations derived thus far in this thread are intended to stand on their own as maximally efficient algorithms for both one and two port S-parameter measurements.

The Uncertainty boundary calculations are a second proposed contribution that attempts to bound the region about each measured value to the most relevant and unavoidable real constraints that have the potential of modulating the measurements away from their true and precisely accurate values. These results would be the ones used to define design margins needed to specify limits of guaranteed performance.

My expectation is to discover that the use of expensive characterized standards versus a well designed and fabricated set of nominal standards contribute only minimally toward the achievement of maximally accurate VNA measurements. At the very least, I anticipate this learning exercise to provide clarity with respect to the sensitivity of uncertainties that can be defined and user constrained or controlled.

This has not been a fast paced learning process as much of the material is quite new to me, and I offer my description of this for your consideration in your own pursuit of understanding. On any aspect other than the derivation and verification of the G-min equation, I remain a student of this process.

--
73

Gary, N3GO

erik@...
 

Gary,

Indeed, the model is precise, and its uncertainty is only based on uncertainty in the measurement of the 3 calibration standards and (this is not stated in their formula's but I assume the extent to which the standards are known . It is stated that G = -1,0,+1 but how about uncertainties in these? Not calibration set is perfect.)
This model allows the analysis of the impact of each uncertainty separate so you can compare calibration standard uncertainty with measurement uncertainty impact.
The derived equations are as far as I can see (but I am no expert) the same as what you get when you ask Maxima to solve the 3 calibration equations for G = -1,0,+1 . Or have they been able to get a additional level of complexity reduction?
Do you already understand to what extent the uncertainty boundary calculations are different from a differential analysis w.r.t o,s and l? Any higher order terms included?
Very interested to see the real test case data. With a very well balanced HW bridge a VNA will get almost perfect o,s and l data and that will imply the calibration uncertainties and measurement uncertainties both have a lineair impact going through a mobius transform.
--
NanoVNA Wiki: https://groups.io/g/nanovna-users/wiki/home
NanoVNA Files: https://groups.io/g/nanovna-users/files
Erik, PD0EK

 

#82' : On The Two-Port Sine Qua Non Practical Application - Source and Load
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REF : 11 December 2019 - https://groups.io/g/nanovna-users/message/8136

Hello,

Allow us, please, to announce that we just uploaded an updated version at:

https://www.op4.eu/code/hurhkamen.gin.pez.arg.cc.by.4.0.2019.png

with slight modifications and added * e x p l a n a t i o n s * on the text.

Sincerely,

gin&pez@arg

:82'