errors of "error" models
We just uploaded the current version:
Allow us, please, to we report that in order to be adequately
prepared to estimate the uncertainty in NanoVNA
measurements using complex differential error regions
and real differential error intervals, that is to attempt for the
first time scientific measurements using NanoVNA with the
only available method we know and with the currently
available software tools, we need, in addition to a correctly
working version of the interpreted foss [maxima-cas] to run
the /f/l/o/s/s/ [derdei.mc], a foss compiled language to we
be able to independently cross-verify the computation
results, and as a such one we intend to use for now the
Also, allow us, please, to we report that in a correctly working
operating system [wxp64p&sp2] we know that the following
versions of these two languages are respectively the last
ones which are correctly working under the 32-bit emulation
mode of an AMD x86-64 cpu:
We just uploaded the currently available version of /F/L/O/S/S/ Maxima code:
as well as, the currently available version of its documentation:
for the Uncertainty Estimation of Full One-Port VNA Measurements.
Next to come : the currently available version of /F/L/O/S/S/ FORTRAN code.
We just uploaded the currently available version of /F/L/O/S/S/ FORTRAN code:
Check the functionality of the program, please, by using the included text files :
[INPUT.TXT] : 101 Frequencies etc, and:
[SH.SC] : Short,
[LD.LD] : Load,
[OP.OC] : Open, and
[ME.ME] : AUT
which are the real raw measurements, collected by using an HP 8505A VNA
Automatic Network Analyzer System in CW mode under HP-IB control, from
a deliberately roughly constructed UHF Ground-Plane Antenna, which was also
deliberately roughly installed just outside and in the immediate vicinity of the
metal walls of the Anechoic Chamber in our past Antennas Laboratory, in order
to produce as much as possible anomalies in the results of Rho and Zeta,
as well as of their computed uncertainties both of complex and real value,
in terms of 101 frequency steps.
Next to come : numerous related references
PS Also, take a look, please, at the related discussion "on the comparisons":
Here are the references - for a few wrongly shaped pdfs you may use,
please, a "secure" removal tool - e.g. the freeware :
 Total Differential Errors in One-Port Network Analyzer Measurements with
Application to Antenna Impedance:
 Measurement Uncertainty in Network Analyzers: Differential Error Analysis
of Error Models Part 1: Full One-Port Calibration:
 Measurement Uncertainty in Network Analyzers: Differential Error Analysis of
Error Models Part 2: Full Two-Port Calibration:
 S-Parameter Uncertainties in Network Analyzer Measurements with
Application to Antenna Patterns:
 Measurement Uncertainty in Network Analyzers: Differential Error
Analysis of Error Models Part 3: Short One-Port Calibration - Comparison:
 Measurement Uncertainty in Network Analyzers: Differential Error
Analysis of Error Models Part 4: Non-Zero Length Through in Full
Two-Port SLOT Calibration:
 Measurement Uncertainty in Network Analyzers: Differential Error
DE Analysis of Error Models Part 5: Step-by-Step Graphical
Construction of Complex DE Regions and Real DE Intervals:
Allow us, please, to insist staying on the subject by transferring
and repeating here the contents of the following messages,
in order to somehow protect -if not save- them [*]
- - - - -
4 : on the comparison - https://groups.io/g/nanovna-users/message/2913
Allow us, please, to point out that to be possible to the slightest a comparison
between measurements regarding nanovna and/or vna, these measurements
should be accompanied by an estimation of their uncertainty, as well as by a
clearly stated way of its calculation.
- - - - -
5 : Re: on the comparison - https://groups.io/g/nanovna-users/message/2943
We both thank you very much all of you for your most valuable comments !
We gladly feel that we find a sound ground for a fruitful discussion, as we hope.
Well, we don't mean to offend you but, in our humble opinion, the whole story of
hp "error" models is just a myth serving the powerful advertisement, so, we don't
believe at all that this matter is due to any lack of knowledge or of ability among
Radio Amateurs, while, in direct contrast to that, the pioneered Work of whom is
usually exploited by patentees.
Anyway, we just ask you now to be patient enough and give us the chance to present
(1) the fortran code by which we estimate the errors of the aforementioned "errors",
in full one-port vna measurements (see, please, the related "discussion" ), as well as
(2) sometime later, the way in which we calculate the errors of the corresponding
"errors" in full two-port vna measurements.
Finally, we just mention that in the case of nanovna we just took a look at the mathematical expressions included there and we have a feeling -but notice, please, NOT a proof yet-
that the "error" model(s) used in the original nanovna code are missing some terms which
are present in the original "error" model(s). And this is the reason that we already asked:
"if is there any certain knowledge available regarding the specific error model(s) that
NanoVNA uses" 
--but unfortunately without any response yet--so, we did not be able to comment our
vna-nanovna comparison results ,
and by the way: after we followed, almost fully, the suggestions given in the Excellent
Work of Larry Rothman .
 errors of "error" models
Saturday, September 21, 2019 04:10
 error model(s)
Wednesday, September 18, 2019 00:24
 vna ~ nanovna : (r,x) comparative results but no comments
Tuesday, September 17, 2019 02:31
 Re: List of NanoVNA Console Commands
Sunday, September 15, 2019 15:23
- - - - -
6 : Re: on the comparison - https://groups.io/g/nanovna-users/message/2968
Allow us, please, to summarize briefly:
(0) The measurement uncertainty is error-bounds of the
(1) If a measurement does not involve mathematical expressions
then someone can choose the statistical way he likes to
mathematically estimate|compute a subjective uncertainty .
(2) If a measurement involves known mathematical expressions
then either there is or there is not -up to now- a known, unique,
mathematical way, that is a way solely based on these
mathematical expressions alone, to estimate|compute an
(3) A vna measurement involves known mathematical expressions
and after more than ten 10 years there are now five 5 known
mathematical ways to estimate|compute a unique objective
uncertainty, each one for each of the five 5 "error" models considered
(by intermediately estimate|compute the errors of these "errors"),
as well as new one(s), the sixth 6th (or more), shall be added
as soon as the "error" model(s) of the NanoVNA will be revealed.
(4) These "errors" of "error" models are just historical names of
parameters mathematically expressed in terms to what is widely
known today collectively as "S-parameters" and thus these are
not error bounds - they are not uncertainties of the measurement.
[ which -unfortunately enough, but not unexpectedly in almost any
[ suffering public discussion- were interfered elsewhere, as usually,
[ that is using the well-known technique of the coordinated barrage
[ of disorienting, non-answering, non-participating, non-discussing
[ cries - that is, once more : business, as usual
As I am not scientifically trained I have great difficulty to follow your posts and to understand what it is you ask.
- Are you merely sharing knowledge on error models applicable to VNA? Great, need some help on how we can use your knowledge to understand the limitations of our own measurements
- Do you invite only those with a solid scientific background to participate in an performance evaluation of the nanoVNA? Excellent, let the experts join and deliver a solid foundation to understand the limitations of nanoVNA performance
- Do you want the wider group to participate? If so, in what way? How to contribute?
Please help me to understand.
Allow us, please, to inform the interested reader
and/or contributor that we shall copy -"just in
case"- sometime later, all of our messages from
here to out there:
I admire and appreciate your persistence, as well your desire to stay on topic. I suspect this discussion is far above most on this list... myself included. There may be a few whose attention you have not yet captured, but whose support and insight may prove worthwhile when they realize the extent and focus of your work.
Your posts have been difficult to follow, but not impossible, and I’ve tried to dig a bit into your questions to see if there are any I can answer.
Some questions first:
1) Are you proposing your DERDEI software (algorithms) with “uncharacterized” standards as an alternative to using error coefficient polynomials that rely on “characterized” standards?
2) Are you proposing your DERDEI software (algorithms) with “characterized” standards as an enhancement to existing calibration processes as a means to establish boundaries on residual post calibration uncertainties?
3) Are you proposing a tertiary algorithm to be used as a means of fairly comparing the hardware performance of two independent VNA platforms; such as when making like measurements of an identical device on two completely independent VNA’s but under otherwise exacting conditions?
3) Are you in search of Beta testers of your DERDEI program using NanoVNA raw data, corrected post calibration data using uncharacterized standards, or corrected post calibration data using traceable characterized standards?
4) In your example INPUT.TXT file, the fourth input (AUT) is assumed to be Antenna Under Test. Are these the measurements of the UHF ground plane antenna in the described anechoic chamber environment described?
5) Is the purpose of the INPUT.TXT file intended for our evaluation and comments, or as a test file to verify your software is correctly installed and functional?
6) What do you want/need from users on this list in our response to you on this software? Most on this list lack VNA experience, and most DO NOT have characterized SOL or SOLT standards.
To answer your early question as to what is used in the NanoVNA, my “guess” would confirm your suspicion of missing terms in the calibration routine. There are no provisions for the input of calibration error coefficients of a user’s unique set of standards. Therefore; calibration terms embedded in the firmware of the NanoVNA would at best have no meaning, and at worst introduce error uncertainties of their own. I do not however have any knowledge of how calibration is achieved, or uncertainties defined... other than to say they are declared to be zero as this is generally acceptable to most amateur enthusiasts.
There are however two sources you may want to review if you haven’t done so already.
The hardware and software is open source, and derived from the efforts of edy555 in Japan. The NanoVNA is feature rich, but the product is restricted to the processors on chip resources, and thus memory limited...likely insufficient to accommodate supporting more sophisticated error correction algorithms.
NanoVNA Saver is an Open Source GUI supporting a PC connected NanoVNA that has made provisions for incorporating calibration coefficients for the standards in use in the calibration routine employed by that program, presumably using the NanoVNA’s raw data. It is written in Python and should be straight forward to analyze. It’s author Rune Broberg would the source to question the algorithms he employs.
You commented: “Well, we don't mean to offend you but, in our humble opinion, the whole story of
hp "error" models is just a myth serving the powerful advertisement.” While not intended to sound offensive, this likely did raise a few hackles. :-) Your use of the term myth suggests you may be slightly mis-informed.
HP, R & S, and others have a competing interest in growing the RF industry. There is no question that marketing among them is highly competitive as well. To their market however; capability, repeatability, stability, and accuracy are unquenchable demands, and the key parameters used to differentiate one vendor from another. Mythical error models would yield failed products by their customer base, and as such their business wouldn’t thrive. That said; the quest for absolute accuracy will continue until everybody is certain, and in unanimous agreement, that absolute accuracy has been achieved. :-)
I wish I could help you more, but this is likely my best effort toward your cause. Perhaps it will seed further discussion of your proposal, or the comments of others; as it appears to have merit for consideration.
You stated your efforts are Open Source, and have provided good resource links to launch and evaluate your software. Is there an online forum corroborating your efforts?
Allow us, please, to point out that:
The notion of error bounds (in the plural, since
they are two -implicitly, but definitely real
numbers, which are the two estimated|
|computed real numbers, which are lower than-
and greater than- the real number that expresses
the (unavoidably real) measurement of any
(unavoidably real) quantity,
looses its meaning in the case of any "complex"
("existing" by agreement) quantity, that is one
which is expressed by complex numbers,
because the notion of the ordering : lower|
|greater than- does not make any sense between
Therefore, we need to somehow extend this bound
notion in the case of (once again : by agreement)
Thank you very much for your kind interest on our Work!
We much appreciate that.
Especially, the most encouraging guess also made by you
about "missing terms". Very interesting indeed! Thank you,
Now, regarding your questions included at:
we would like to ask you first to tell us, please, if you tried
our software, that is if you already compiled and run the
FORTRAN REGION and then the MAXIMA DERDEI, to see
its rich, multiple-output graphics.
Hello again YZA;
I have not yet attempted to install the relevant software and math engine required to compile and run your Fortran code, and it would take some effort on my part (or any evaluator not programatically versed or equipped) to work through that process. Before investing the effort to do so, I am attempting to understand the goals and objectives of your work, and if or how it might benefit users of the NanoVNA, and the VNA community overall.
The principal utility and benefit of the NanoVNA is it's size and portability. To that end, it is limited in its available reserve of stand alone computational resources. Additionally; most users on this forum are not motivated to invest in high quality (accurately characterized) calibration standards that cost many times the price of the device itself. System requirements of the evaluator(s) need to be clearly defined.
The software you describe would, by necessity, require PC connectivity, and operates on data files collected by the NanoVNA and ported to your software for statistical analysis in order to derive the error bounded plots shown in your documentation. There are sophisticated VNA users in this group that might find great interest in your work if the goals, objectives, system requirements, output results, and the utility and benefit of those results were clearly presented such that they could be easily and clearly understood in the context of how they might enhance the quality of the NanoVNA measurements. Those users are likely a minority. There may be an even smaller subset of this group that may simply have an academic interest in your work.
I think your documentation may be sufficient for those motivated to dig into the details of your algorithms; given that there is a clear benefit for investing in that effort. What type of support are you requesting from this group? What dictates the need to distribute Fortran code? Can it not be compiled and distributed as a stand alone executable, and a readme.txt file outlining the detailed feedback content you desire?
@Gary O'Neil :
And thank you, once more, for your most
valuable contributions !
(1) regarding the objective requirement
for a distribution of the REGION executable,
allow us, please, to notice the useless result
of such an action, because, once again, this
file is not a standalone program but it constitutes
just the one part of this two-part /F/L/O/S/S/, and
(2) regarding the subjective concerns you most
reasonably expressed about your time, also
allow us, please, to notice that since the personal
taste is the decisive criterion that governs humans'
choices, and since the expediencies of any kind
were never dictated our acts, we are not be able
to the slightest to suggest you what to do in order
to meditate these worries of you.
Finally, since we mostly respect your efforts and
your time you spent to take a look at our humble
work, allow us, please, to conclude our communication
by thanking you, once again, very much!
First of all, allow us, please, to express, on the occasion,
our deep respect for your impressive Work with NanoVna.
Next, allow us, please, to inform you that just after the
message including the preliminaries of the uncertainty:
 : https://groups.io/g/nanovna-users/message/2968
we took into account your clear call for understanding
and thus we started a sequence of very short messages
on this subject, beginning with:
 : https://groups.io/g/nanovna-users/message/3043
Finally, allow us, please, to comment that, in our humble
opinion, regarding 'Understanding', there are the following
types of human beings, according their personal tastes:
(1) Those who don't want to understand, and those who want
to understand, but when they don't understand then, according
to their judging abilities, they put constantly the blame:
(2) on the others,
(3) on themselves, and
(4) either on the others or on themselves, according to the state
of their progress in the Knowledge
Keep up the Good Work !
@Reginald Beardsley via Groups.Io :
Allow us, please, to point out that frankly we are not
sure if the messages on this very topic, as well as,
the references especially included at:
 : https://groups.io/g/nanovna-users/message/2984
cover to the slightest your expressed interests, so,
let us know, please, accordingly, taking into account
that this is the current state of published research
on this subject, excluding some papers under
preparation in order to be published in our small
Once again, thank you very much for your interest
in our work !
Allow us, please, to inform you that we just
uploaded the following two, very rare, references:
 Richard H. Hackborn, "An Automatic Network
Analyzer System", Microwave Journal, May 1968, p.47 :
 Paul Schmitz, "Vector Measurements of High
Frequency Networks", HP 5958-0387, 5481, 1989, p.3-9 :
which, unfortunately enough, justify fully the writings at :
although, some honorable members of this forum
considered them as outrageous allegations of the
Allow us, please, to inform you that, after:
 : https://groups.io/g/nanovna-users/message/3147
we just uploaded our well-formed mathematical expressions
of full-one port vna measurements [*] :
which--due to their apparent symmetries, as well as to their
arrangement--we consider them as the most economical and
appropriate ones for programming them in any computer
language - either having the complex data type internally or not.
17 : From A Common User's Point Of View
Allow us, please, for the sake of completeness of
an appropriate preparation of a presentation for the
Estimation of the -sine qua non- Core of the Measurement
Uncertainty that Exists in *A N Y * VNA System, regardless
of what it really is, a VNA or a NanoVNA, facupov : that is
like that very one of ours, to also include here the initial
findings by us:
| Subject: vna ~ nanovna : (r,x) comparative results but no comments
| Sent: Tuesday, September 17, 2019 02:31
| To: email@example.com
| From: yin.oe3zgn.sv7dmc-pez.oe3zzp.sv7bax-arg firstname.lastname@example.org
| 1 one-port box + adapter - initial version:
| 2 one-port box + adapter - modified version:
| 3 one-port box + adapter - modified version:
| black : vna system
| red : nanovna + 31 mm adapter
| blue : nanovna - 31 mm adapter mathematically
| r : https://www.op4.eu/fora/nanovna-users/20190917/R-box-nanoVNA-RedBlue.png
| x : https://www.op4.eu/fora/nanovna-users/20190917/X-box-nanoVNA-RedBlue.png
0 : https://groups.io/g/nanovna-users/message/2521
Dr. David Kirkby from Kirkby Microwave Ltd <drkirkby@...>
On Fri, 27 Sep 2019 at 12:33, yza <yzaVNA@gmail.com> wrote:
17 : From A Common User's Point Of View
Maybe if you wrote a document on this, including adequate references, much
like a scientific paper, we could follow you. But you have made endless
posts, at least one of which has incomplete definitions of the equations,
it is almost impossible for anyone to follow you.
I am sure what you have is interesting, and some will be able to follow you
- perhaps not myself as my mathematics is not very good. But the way the
information is presented makes it impossible to follow.
One of things that is important is the phase difference between the offset
male and offset short standards. This will obviously be 180 degrees at low
frequency, but will depart from this as frequency is increased. I have seen
calibration kits assembled from inappropriate parts where the phases
difference drops to zero at one frequency. It’s obviously impossible to
calibrate then. But if one standard has a phase able of 0 degrees, and the
other 10 degrees, the calibration will be poor.
The whole issue is far from simple, but the way you are presenting the
information makes it difficult for anybody to follow you.
Dr. David Kirkby,
Kirkby Microwave Ltd,
Telephone 01621-680100./ +44 1621 680100
Registered in England & Wales, company number 08914892.
Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT, United