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# 113 : Non-Zero Length Through in Full Two-Port SLOT Calibration

Abstract

The most accurate full two-port calibration of a VNA Vector Network Analyzer requires a Direct or Zero–Length Through connection. However, it is not uncommon at all to have one or two cables and a DUT Device Under Test with incompatible connectors, either of different type or of the same type/sex, which enforce then the use of some kind of barrel or adapter. Thus, in this paper, we study these cases of Indirect or Non-Zero Length Through, we estimate the effects of such connections on the measurement uncertainty by using our theory of Differential Error Regions and Intervals DERs/DEIs, and we evaluate our resulting method by applying it in practice to a built two–port network, which was measured against frequency with a SLOT calibrated VNA extended by two lengthy cables.

Measurement Uncertainty in Network Analyzers: Differential Error Analysis of Error Models Part 4: Non-Zero Length Through in Full Two-Port SLOT Calibration

September 2016

- - - - -

Hello.

We just uploaded to ResearchGate the missing Full-Text of 4th Paper in order to also complete there this Series of 6 Papers:



Sincerely,

gin&pez@arg

: #113

#112 : [ANN] : Project : A C version of [REGION]

Hello.

In order to produce a C version of [REGION] we will try -for the first time- to use f2c:



Sincerely,

gin&pez@arg

: #112

#111 : Two Original Presentations at ANAMET, NPL, UK - The Automatic Network Analyser METrology Club, NPL National Physical Laboratory, United Kingdom

Hello.

In order to present more of the available past resources on this matter, we just uploaded at ResearchGate two of our original online presentations to the attendees of ANAMET Club Meetings:

"Building Complex Differential Error Regions", 30th ANAMET Club Meeting, NPL National Physical Laboratory, Teddington, UK, 24/10/2008:


and

"Complex DERs in Non-Zero Length Thru VNA Measurements", 32nd ANAMET Club Meeting, NPL National Physical Laboratory, Teddington, UK, 16/10/2009:


Sincerely,

gin&pez@arg

: #111

#110 : The Complete Documentation of the Software

"Measurement Uncertainty in Network Analyzers: Differential Error DE Analysis of Error Models Part 6: FLOSS - Software Tools"

Abstract

Two software tools were developed to compute and illustrate the uncertainty estimation of one-port VNA measurements using Complex Differential Error Regions, DERs, and their corresponding Differential Error Intervals, DEIs, in polar and rectangular form. The first tool, [REGION], was written in Open Watcom FORTRAN F77 Compiler as a Command Line Interface for calculations and is the programming realization of the graphical DER construction presented by the authors in the previous part of this series. The second tool, [DERDEI], was written in Maxima and is used as a Graphical User Interface for illustrations. Both of them were written with these Open, Free and under continuous support software development systems, in order to be publicly available, since the corresponding previously written and used by the authors programs demand the proprietary Mathematica application. The presented tools were tested with our VNA system measurement data but they can be easily used with any other VNA data ensuring that the text files have the same, specifically defined, format, valid under SLO calibration for one-port measurements. In order to demonstrate our method a number of selected experimental results along with some extreme cases of DERs and their DEIs, under particular circumstances, are also presented. The developed software tools are available on the Internet as FLOSS Free Libre Open Source Software.

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Hello.

At last, we just completed this work and uploaded it at:



Sincerely,

gin&pez@arg

: #110

#109 : reply to a newcomer
=
| From: "** ***" <*@gmail.com>
| Sent: Thursday, September 03, 2020 08:43
| Subject: Re: S-Parameter Uncertainties in Network Analyzer Measurements
=
| no, I am not aware of this discussion. anyway thanks for share that link.
-
errors of "error" models : /g/nanovna-users/topic/34237712
-
| I would like to understand the One-Port Error Model and Calibration
| (One-Port, 3-Term Error Model).
| I`m using the attached file
-
[ Network Analyzer Error Models and Calibration Methods by Doug Rytting ]
-
| Do you know how it works? see page 11/43 (pdf).
=
| To: "** ***" <*@gmail.com>
| Sent: Thursday, September 03, 2020 15:51
=

Dear Mr. ***,

Yes, of course we are aware in our group of Doug's papers.

Well, it is a pity that you don't want to follow the suggested
discussion. Because, it was only after the intensive thinking
enforced by the demands of our participation in this very
discussion that our point of view, regarding the kind of these
measurements, was finally made absolutely clear.

Anyway, we could theoretically conclude from this discussion
the following essentials:

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

(0) We can adopt a so-called by us "virtual"-real two-port
S-parameter "error" model, that is one consisting of a
Virtual-Measurement "Port": one that you can't see it as
really existing around, in order to connect a cable to it, and
the other, indeed a really existing one, just because you can
see it and connect a cable to it: the familiar (Under)Test Port.

(1) To arrive at this model you have * u n a v o i d a b l y *
begin with the real four-port consisting of the familiar Ports:
Input, Incident, Reflected, and (Under) Test - once again:
"real", because you can really see its four real ports and
connect cables to them.

(2) As usual, you have to write down the familiar four linear
S-parameter equations for this four-port and then -after some,
rather lengthy indeed, mathematical manipulation- to form
just one equation relating those familiar g and G ratios of
signal-samples of Reflected-to-Incident waves -g for the
Virtual-Measurement Port and G for the Real-(Under)Test Port.

(3) This equation involves 3 parameters and express the
g-Measurement in terms of G-(Under)Test, but since it is also
an invertible equation, you can also express the desired
G-(Under)Test, that is of an Unknown Load, in terms of
g-Measurement that is of the Known Network Analyzer
Readings you can see, also write down and/or collect,
as G = G(g).

(4) The involved 3 parameters, which are complicated
expressions of the four-port S-parameters mentioned above,
are those well-known (HP) "errors" - although unfortunately
enough: widely-non-understandable until now.

(5) Well, after all that said, not only here but especially in
the aforementioned discussion -currently with 292 messages-
it is also an unavoidable conclusion that for many years until now,
Doug and his colleagues at HP, also produced, under various
additional assumptions, more-or-less approximate equations
G ~= G(g) for the multi-ports of more than four ports they
considered.

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

That is all.

Sincerely yours,

Nikolitsa Giannopoulou
Petros Zimourtopoulos
ARG IAOI NFI
Antennas Research Group-Informal Association of Individuals-No Finance Involved-Austria-EU
:#109

#108 : A Proposed Pre-Virtual 2-Port of NanoVNA-0.6.0
Hello,
Allow us, please, to propose--FACUPOV in our SOW--the following 4-port as
- - - - - - - - - - - - - (c) gin&pez@arg (cc-by-4.0) 2019 : start - - - - - - - - - - -
the Pre-Virtual 2-Port of NanoVNA-0.6.0:

- - - - - - - - - - - - - finish : (c) gin&pez@arg (cc-by-4.0) 2019 - - - - - - - - - - -
Sincerely,
gin&pez@arg
REFERENCE
#92.2 : Our General Picture of [TheLeastVNA] - Update 2:
1 January 2020 - /g/nanovna-users/message/9026
:108#

#107': On the Missing Terms in NanoVNA firmware - ERRATUM

Dear Erik,

Thank you very much indeed for your valuable comment,
since you forced us to recheck the related code.

No, we can not explain that, simply because we erroneously
noticed this absence.

We are terribly sorry for the inconvenience.
Please accept our apologies.

Hence, we withdrawn this proposition:


Best regards,

gin&pez@arg

:107'#

Can you explain why they are needed given the current content of eterm_calc_er?

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

#107 : On the Missing Terms in NanoVNA firmware

Hello,

Allow us, please, to propose the following modifications remarked by "//" :



Sincerely,

yin&pez@arg

REFERENCES

[I] : errors in "error" models :
[#08] : 25.09.2019 : /g/nanovna-users/message/3004
[#11] : 25.09.2019 : /g/nanovna-users/message/3049
[#11]' : 25.09.2019 : /g/nanovna-users/message/3041, by Gary O'Neil, N3GO
[#15] : 26.09.2019 : /g/nanovna-users/message/3147

[II] : error model(s) : 18.09.2019 : /g/nanovna-users/message/2553 :
REF [2] :

On Tue, 7 Jan 2020 at 22:17, John Ackermann N8UR <jra@...> wrote:

Gary, just a guess (I'm not a VNA designer) but it might be because it's
easier to design and characterize an "absolute" (open or short) with
nominally infinite impedance than something that needs to match some
arbitrary value. And how would you choose the arbitrary values?
Different users have different requirements.

I think, but am not sure, that using arbitrary values also would prevent
any pretense at corrected measurements beyond those arbitrary values.
When your limits are infinity, nothing stands in your way. :-)

73,
John

You can certainly perform a calibration with arbitrary values - all the
electronic calibration units do this - they can't generate anywhere near
perfect opens and shorts using electronic switches.

Best accuracy occurs when the standards are as different as possible. In
principle, you could calibrate with 1.0, 1.0001 and 1.00002 ohms. But such
a calibration would be very unstable. The open and short have the greatest
phase difference that it is possible to make.

They are also the easiest to characterise, as you can determine their
properties from physical measurements and EM simulation, whereas you can't
do that with resistors or capacitors.

You can also calibrate with three shorts or three opens if you want. I have
done it with 3 shorts myself, but it not suitable for use over a wide range
of frequencies. If you look at the attached PDF, of a 110 GHz Keysight
85059A calibration and verification kit, you will see the opens and loads
are only rated for use to 50 GHz. Between 50 and 110 GHz, you use multiple
shorts. There are 4 different ones in the kit.

Dave

There is also a physical explanation why the imperfections of SOL standards are described (of parameterized) in a certain way.
The connection from the VNA goes through the connector (which has a certain characteristics impedance into S, O or L.
The connector contains a center conductor, a dielectric and the outer solid metal wall. The characteristic impedance of the connector (and the cable if being used) depends on the size of the center conductor, the thickness of the dielectric (and its dielectric constant) and the outer wall. NOw as long as this continues the impedance stays characteristic. So what does a S, O and L do?
It makes a transition to a new impedance (0, infinite and Z0 for the perfect Short, Open and Load).
But this transition is difficult to make perfect.
The simplest is the Short. You stop the dielectric at a well defined place (called the "reference plane") and make a massive metal (solder or some other metal) connection between the central conductor and the outer wall. But as the connection is not perfect it could have a bit of induction and therefore the imperfections of the short are often modeled as the fixed induction (H) in series with the Short. The induction of the short can be modeled (e.g calculated from the physical characteristics), measured as described in the last document I shared, or "compared" to a known golden standard Short (and yes, even the kilo has to start somewhere)
So the inductive terms used to describe the short are there because they are actually present in the short!!!! They are not "invented" to compensate for imperfections. They describe in as few parameters possible the actual impedance of the short.

The Open is also fairly easy to make at a well defined place (called the "reference plane" ) by stopping the center conductor, the dielectric and the outer wall. Of course you will immediately understand this can never be a perfect "Open", yes, at zero Hz the impedance will be huge (infinite?) but there is a tiny capacity because the center conductor and the outer wall still can "see" each other through the air as the dielectric constant of air is not zero. So this imperfection is calculating from a physical model and specified as capacitance because that is what is actually making the "Open" not perfect.

For the "Load" you have to replace the metal of the Short with some material with a certain resistance to create exactly the right resistance which is easy at zero Hz but from the physical reality you can easily understand there is possibly some inductance (the resistance material has a certain "length" to cover from center conductor to outer wall) or capacitance (the resistor has some "depth" and you no longer have the characteristic impedance of Z0 so there is some extra capacitance.

As a small amount of parallel capacitance has about the same impact as some extra length the capacitive imperfections are sometimes described as shifts of the reference plane.

So in one sentence: The parameters used to model the real impedance of the calibration loads are chosen to match real physical imperfections present in the calibration loads

Now your question related to "real high frequencies". As you can understand extra capacitance has more impact at higher frequencies so that is why you see sometimes calibration loads that deviate substantial at very high frequencies from their perfect impedance at zero Hertz.
This is not a problem but it is reality!!! and as long as you use the real impedance of the calibration loads as (O,S,L) in the G formula there is no problem as the G formula will still be able to calculate G from the measured g, the measured s,o,l and the real impedances S,O and L.
Now what will happens if you calibrate the VNA using the real OSL and the measure one of the calibration standards? You get O, S and L with all their deviations from perfections, which you do not care about because they have no impact on your measurement.
Example. If you have a load with a fringe C you see a resistance with a small C, which may become VERY visible at very high frequencies, even if it is small.

In the documents I added you can see there are many more ways to calibrate out and compensate the internal imperfections of the VNA using various (imperfect) calibration standards and complicated measurement "tricks"
This implies you can physically model and precision manufacture calibration stands as "gold" standards (like with the meter, defined from the speed of light and the second) with impedances calculated from these model and then build a metronomy chain to the much more imperfect calibration standards we normal people use.

Sorry for the long post, I got carried away.....
--
NanoVNA Wiki: /g/nanovna-users/wiki/home
NanoVNA Files: /g/nanovna-users/files
Erik, PD0EK

Hi Gary,

Regarding fringe capacitance, HP states that fringe capacitance can have an effect on measurement accuracy above about 300 MHz.

This should explain “why” knowing fringe capacitance is important. (And I hope it is already clear why you need to accurately know your standads’ Gammas).

By the way, different types of standards will have different values of fringe capacitance. The Gammas of different Opens aren’t simply a difference in “length change”.

Finally, I would like to add...

Someone once told me that it took HP 10 years to develop VNA error correction. If true, that would have been a tremendous amount of effort by a group of very talented scientists and engineers.

I’m just a retired engineer with a tangential interest in VNA’s. I won’t have the answers to all your questions, but I’ll try to answer what I can.

Best regards,

Jeff, k6jca

And here is another introduction. Read section 2.1.3
This document from 1990 also mentions the ratio of cross ratios and describes various different approaches to calibration next to the well known SOLT

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

Attached document should give some answers

The impedance model of the calibration load represents the actual impedance of the load either as it is calculated from theoretical modelling or from measurements like in attached document.

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

Interesting.....

My question still doesn't seem to be getting through... Yet it remains a simple one. :-) Let me try this again.

Question: What justifies characterizing the calibration standards?
Answer: Because it improves measurement accuracy.

Question: How does it do that?
Answer: It makes post calibration measurements of the standards plot with the profile of the standards and not plot as though the standards were perfect.

Question: How does doing this make the measurements more accurate?
Answer: Because HP says characterization of the standards improves accuracy, everybody agrees, this is the way it's always been done, and it actually works.

Question: How much more accurate are the measurements after calibrating with the characterized standards?
Answer: Close to absolute.

Question: How do you know the measurements are close to absolutely accurate?
Answer: Because they were characterized by a certified test lab, who provides us with the correction coefficients.

Question: Does the certification lab provide a tolerance on the accuracy of the coefficients they give you?
Answer: I don't know... Probably.

Question: So you are confident that your results are as accurate as you can make them?
Answer: Yes.

Question: Why?
Answer: Whatever do you mean???

Question: Isn't there some degree of uncertainty remaining?
Answer: Well sure...

Question: How much?
Answer: I don't know, but I know its not very much once I've calibrated appropriately with my Characterized calibration standards.

Question: What impedance does the open circuit standard represent?
Answer: Oh I don't know, but it's pretty high... maybe a few k ohms.

Question: I think I read something around 50 femptoFarads being used to compensate for the fringing capacitance of the open standard as a typical correction. Does that sound about right?
Answer: Yeah! I might have heard or read something like that. It's a very small number.

Question: I'll say... but 50 femptoFarads is about 32 ohms at 100 GHz. If the the open circuit impedance drops to 32 ohms, How far does that move the dot?
Answer: I don't know, but it isn't very far?

Question: But it shows that it has a noticeable span on the display. Why is that?
Answer: Because it probably moves that far after it's been calibrated. The open circuit might be offset by the connector length... and it only happens at really high frequencies. In the GHz range maybe.

Question: I'm guessing it's an unavoidable shunt capacitance and maybe there's some angular displacement in play also?
Answer: Probably... Maybe... It has to be something, or else it would be just a dot.

Question; So that isn't an error in the calibration?
Answer: No... It shows that it has been calibrated because it's displaying what the open circuit really looks like.

Question: Then the open circuit doesn't look like a real open circuit?
Answer: Correct. It's not possible to make a perfect open circuit.

Question: So I've been told... That's about as close to an open circuit as we can manufacture though am I right?
Answer: I think so.

Question: Then why isn't the standard used to represent a precise open circuit after calibration? Isn't this a real open circuit in the real world?
Answer: Because then it wouldn't be accurate, and not all open circuits are the same. They might be at a slightly different offset.

Question: That's still just a length change though correct.
Answer: Yes, but now we can measure it and use the data to measure others like it.

Question: You can't manufacture a precise open circuit, but you need to measure them accurately?
Answer: Correct.

Question: Why?
Answer: Huh?

Question: Why? What's the point? How does it manifest its value?

--
73

Gary, N3GO

Hi Gary,

Great questions. I have no idea what the answers are. But Erik’s and John’s replies seem reasonable.

Perhaps Dr. Kirby might know.

Best regards,

Jeff

Gary, just a guess (I'm not a VNA designer) but it might be because it's
easier to design and characterize an "absolute" (open or short) with
nominally infinite impedance than something that needs to match some
arbitrary value. And how would you choose the arbitrary values?
Different users have different requirements.

I think, but am not sure, that using arbitrary values also would prevent
any pretense at corrected measurements beyond those arbitrary values.
When your limits are infinity, nothing stands in your way. :-)

73,
John
----

Could it be because these are most easy to manufacture? A short and an open?

--
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Erik, PD0EK

Hi again Jeff;

I believe I now sufficiently understand the technical aspects of the discussions in this thread to forego the wizardry behind the pursuit of high accuracy. it appears sufficiently sound.

On that happy note… I will state my one remaining question succinctly. Why the obsession over accuracy at the the two most unstable phase regions of highest Q and unreachable limits of infinity and zero?

A reasonable and credible answer will be a bounded tolerance of impedance or phase in those regions, and an estimate of the consequence of exceeding the tolerance boundaries.

I will reiterate… There is nothing wrong with how this is treated what is being done or the rationale behind the obsession. The only question is simply... Why?

--
73

Gary, N3GO

Hi Gary,

I just wanted to make that I answered your question as to why a Short and an Open are not plotted at -1 and +1 after calibration. (The short answer is: because their actual Gammas do not equal -1 and +1.)

As to the math, don't be daunted! It is more straight-forward than you might think. Keep in mind:

1. The basic formula for one-port error correction is based upon the one-port signal-flow graph.
2. Deriving an equation from a signal-flow graph might seem awkward, but there are a number of sites on the web that will give you the rules (if I could do it, I'm sure you can, too).
3. The result will be an equation that, after rearranging, will give you an actual Gamma in terms of a measured gamma and three error terms.
4. But you cannot use this equation to find an actual Gamma until the three error terms are known.
5. To find these error terms, you first make three S11 (Gamma) measurements, each measurement is of a device with a *known* Gamma (thus you need 3 devices of different known Gammas).
6. For each measurement, plug the measured Gamma and the "known" Gamma into the equation derived in step 3, above. This will give you three equations with three unknowns.
7. Solving for the unknowns (i.e. the errors) is linear algebra.

Best regards,

- Jeff, k6jca