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Jeff, Erik, and John;

Thank you all for your patience with me on this. I at least feel comfortable with what I think I understand so far.

Once again I failed to express myself correctly and used the word devices in lieu of system. My bad... It inspired an answer to a question I wasn't asking. :-) I apologize for that and genuinely appreciate your (Jeff) response. That issue aside, I don't have any issues with your explanations, and they remain consistent with my understanding. My problem lies in following the math behind all of this to confirm or enhance my understanding of how calibration accuracy is assured. All signs point to this being done correctly, the results achieved are as desired, and the reasoning is rational. I'm not trying to be or to sound critical here... and at the risk of again inaccurately expressing myself, I'm not looking for cook book summary descriptions. The math is involved and challenging for an ole' timer to follow before losing concentration and falling asleep, and being new at the game of scrutinizing VNA performance to this level of detail makes it all the more daunting. I've resisted trying to figure out signal flow diagrams, but I sense learning how to use them may be less tedious than to continue trying to crawl through the equations and running spreadsheet examples. Learning is one of the perks of retirement though... and its all fun. :-)

Thanks again guys.

--
73

Gary, N3GO

Not claiming I am competent to do this I would like to try to summarize in limited amount of words what this thread has provided

It adds value for VNA measurement, due to its internal transform, to understand the impact of the magnitude of measurement errors (such as noise) or not well characterized calibration standards on the calculated values, in particular to understand the impact pending the position on the Smith chart. (referring to the DERR part of the communication)
It is possible to formulate an elegant, rather compact formula to calculate G solely based on g,s,o,l,S,O and L
It is possible and it makes sense to compare 1 port (S11) measurement performance of two VNA's measuring the same load if these have been calibrated using the same calibration standards and approach (this is regardless if this has been done using SOL or any other calibration approach, the use includes the utilization of the description of the used calibration standards, either as perfect, parameter modeled or data based) as the results of these measurements should be equal.
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Erik, PD0EK

On Sun, Jan 5, 2020 at 08:04 PM, Gary O'Neil wrote:
Hi Gary,

I don't know if I can answer your questions, but let me start with the last ones...

This brings up yet another question. If the devices are "measured and
remembered" as the math clearly dictates, what would cause a short and an open
(defined as such) to appear anywhere other than the locations -1 and 1 without
biasing the algorithm to place them differently? If they are intentionally
placed at a different location, what is the justification for doing so, since
this would seem to create a need to compensate for the induced post
calibration offset errors ?

First, it isn't the "devices" that are "measured and remembered", it is the "system errors" that are measured and remembered, so that their effect on measurements can be compensated for. (These "system errors" are separate from any characterized imperfections the Standards might have.)

The Standards are the means by which the system errors are determined. These standards are assumed to be perfect and without error, but not perfect in the sense that the short's reflection coefficient is -1+j0 or the open's equal to +1+j0. Rather, they are considered perfect in the sense that their electrical attributes (delay, loss, parasitic effects) have been accurately characterized and are known to the VNA system. In other words, perfect, yet imperfect.

If one of these "perfect yet imperfect" standards is then measured on the VNA, prior to the VNA's calibration, the position of its Reflection Coefficient, plotted on the Smith Chart, will be quite different from what it should be. This difference is due to the VNA's "system" errors".

There are three system errors associated with one-port (i.e. S11) measurements. Thus, to determine what these three errors are, three different "known" standards are used, creating three equations with three unknowns, those unknowns being the unknown system errors. These equations are then solved, and the unknown errors become known.

(For more on this, see here: )

Now that these three errors are known, they can be compensated-for (i.e. corrected) in future measurements. And if I now take one of my "perfect yet imperfect" standards and measure it on the VNA, the VNA should now accurately place its Reflection Coefficient on the Smith Chart.

But should it be placed at -1+j0 or 1+j0?

Let's say that this standard is a Short standard, and let's say there is some inherent, yet well characterized, delay within the short itself, between the actual implementation of the short and the calibration reference plane (that lies within the short's connector). The VNA should not plot this short at -1+j0, but should instead plot the short at the point on the Smith Chart that represents the *actual* impedance of the Short at its reference plane, which is *not* -1+j0 (because the delay will cause rotation). Dr. Kirby's example is a good illustration of this concept.

Let's take another example: the Open standard. These standards have some amount of fringe capacitance, and so let's assume that our Open has some fringe capacitance but no delay.

Now, after our calibration procedure, let's say we were measuring an unknown capacitor that, by coincidence, had *exactly* the same amount of capacitance as the fringe capacitance of the Open. Would we want this capacitor to be plotted at +1+j0? Or would we want it to be plotted at some point, not 1+j0 , that represents the actual Reflection Coefficient for that capacitance?

We would want it to be accurately plotted at the point representing the value of the capacitance. And since, in this example, there is no difference between my "Open" standard and the capacitance I later measured, if I then measured my Open standard on the VNA, its Reflection Coefficient should also appear at that same point on the Smith Chart as my unknown capacitor, not at 1+j0.

I hope the above explanation helps answer your two questions. Please let me know if I've been confusing or not clear. And then, once we get through this concept, we can tackle your other questions.

Best regards,

- Jeff, k6jca

P.S. it is rare for a standard to have zero delay from its reference plane. APC-7 standards, being sexless, have 0 delay, but almost all other standards have some sort of non-zero delay and thus, when measured, should not appear at -1+j0 or 1+j0. So almost all open or short standards, when plotted, should plot rotated from -1+j0 or 1+j0.

I hesitate to jump into this, but...

The "correction coefficients" that professional VNAs apply to compensate for, e.g., fringing capacitance in the opens, are not just electrical measurements of selected components.? Things like fringing capacitance are not flaws in the standards, but inevitable results of the physical realization of the electrical concept of an "open".

The coefficients do not come from electrical measurement of some "gold" standard.? Instead, they are derived from the physical characteristics of the standards, which are manufactured with extremely tight mechanical tolerances.?? From these characteristics the coefficients can be determined by using fundamental equations like the capacitance formula more accurately than is possible by electrical measurements.? (And of course they are sanity-checked electrically as well.)?

So, the coefficients are not really correcting for "imperfections", but are instead acknowledging at a fundamental level the properties of physical objects, to improve the mathematical models of those objects being used in the correction equations.

John
----

Hi Jeff;

Per my post:
@ Gary O'Neil - /g/nanovna-users/message/9184

I don't find any source of disagreement in your posts:
@ Jeff Anderson - /g/nanovna-users/message/9178
@ Jeff Anderson - /g/nanovna-users/message/9181

I will also confess that I overstated a Hackborn quote which modified its more accurate interpretation. He didn't dismiss anything, but rather makes the statement that all of the errors and uncertainties in the system are measured and remembered.

By that inexcusable but excellent example of my inability to make and defend my point; I will attempt instead to understand your understanding of the process, and search for where the two will hopefully converge.

After several reads and re-reads of your and Erik's posts; I think you two may be on the same page. Your post, and another by Dr. Kirby:
@ Dr. Kirby - /g/nanovna-users/message/9183

hint at a possible disconnect in "my" understanding, which may be linked to a vagueness in the use of jargon, or more pathetically, my lack of understanding of the jargon in use.

The way I am interpreting your posts, I see the use of the terms calibration, characterization, and correction. You also identify the noise and imperfect characterizations of the standards as not being corrected by the error correction process.... referring to a Hand quote.

You also make reference to HP and Keysight quotes... both of which I agree with as being correct. To my point; any statement that the "accuracy" of something (anything) used for the purpose of improving the accuracy of the measurement must itself be accurate cannot be argued. It is made true by the way it is stated and/or presented.

Clearly there is no argument that even with the highest of quality in the standards, at some upper limit of frequency, the manufacture of standards sets to the exacting dimensional tolerances required to guarantee that the reference plane remains constant becomes unachievable, significant rotational errors occur and corrections for the known and well defined imperfections are needed in the calibration in order to make meaningfully accurate measurements.

So my lack of understanding seems to lie in the question being what's the point of attempting to model imperfect standards of uncertain accuracy, and using that model to corrupt the ability of the algorithm to accurately measure and remember all of the system errors and uncertainties with uncertain guesses at what the ones that are measured have been characterized to be? Are not the errors that manifest themselves as problematic, only problematic because they result from differences in the location of their respective reference planes? the uncertainties of the parasitic reactance properties associated with each of the standards are measurable, and thus they will be "measured and remembered". As such, they are all present and accounted for in the calibration. Characterization of the standard reference plane location (degrees per GHz) would seem to be a more precise and accurate manner to compensate (not calibrate) for their respective rotational offsets without compromising the integrity of the calibration algorithm. After that; how precise does the rotational compensation need to be in order to sufficiently orient the regions of infinity to the VNA user such they are presented with the most accurate measurement the VNA is capable of providing?

This brings up yet another question. If the devices are "measured and remembered" as the math clearly dictates, what would cause a short and an open (defined as such) to appear anywhere other than the locations -1 and 1 without biasing the algorithm to place them differently? If they are intentionally placed at a different location, what is the justification for doing so, since this would seem to create a need to compensate for the induced post calibration offset errors ?


--
73

Gary, N3GO

Hello again Erik;

@ Erik... - /g/nanovna-users/message/9167

@ Erik... - /g/nanovna-users/message/9166

@ Jeff Anderson - /g/nanovna-users/message/9158


I attempted a response to the above referenced posts, but terminated it because I find nothing in your comments, nor Jeff's that I take issue with. Your most recent post describing modification of the NanoVNA's bridge to accommodate different choices for Z0 in fact convinces me that you do have sufficient insight to grasp the point they have been trying to make; and neither they nor myself have been successful at communicating it.

What there research provides, and where the focus needs to be pointed is not the measurements themselves, nor how the measurements are made, nor whether or not the user desires to obtain or otherwise characterize the standards used for calibration in order to obtain ultimate measurement accuracy.

The research they've done does however provide the tools and insight needed to evaluate and challenge the value and utility of performing such a task. In the reflection coefficient regions of -1 and 1, independent of noise and dynamic range, the computed results are no more or no less precise, or accurate; nor is there any impact on the uncertainty in the measurements; since both fall at or very near the regional limits of infinity where magnitudes of error in the computed impedance values can occur without consequence in an application, no noticable relocation of the plotted response. Rotational errors result from incorrectly identifying the location of the reference plane, and these can be easily identified and compensated for.

The purpose of the experiment of using the gross difference in calibration loads was not intended to highlight the VNA's utility, but rather to demonstrate that even gross errors in load calibration (4:1 and 10:1), do not make the measured results any more or less accurate, so long as the value at Z0 is well defined.

As regards using the VNA at a Z0 of 5k, your comments are spot on... Hence; I know you fully understand this point. It may however remain quite usable in spite of the increase in noise floor, but accuracy in the measurements will be no more or no less impaired as dictated by the accuracy of the load standard definition, and the tolerable uncertainty of the increase in noise.

For example when calibrated with 500 ohms, my 50 ohm standard resolved to 4.7 to 4.95 ohms without averaging. Considering this is a measurement made in 10:1 mismatch environment using an uncharacterized load standard of nominal value, this is a respectable tolerance; and one I would consider quite adequate for most applications that I would consider.

Consider also that any standard used at any frequency intended to serve as a zero ohms "standard" is quite likely closer to or, at the very least, as close as any product manufactured with the intention of zero ohms being a measurement region of great scrutiny or interest. Of course the same consideration would apply to the open standard definition as well.

Consider also that purchasing well characterized standard sets places your confidence in the uncertain but much improved accuracy of your results in the uncertain but reliable judgement of a third party, at a necessary but painful increase in cost; while allowing you to maintain the same degree of uncertainty in the accuracy of your measurements that you started with... at minimal risk.

--
73

Gary, N3GO

On Sun, 5 Jan 2020 at 21:58, Jeff Anderson <jca1955@...> wrote:

In other words, do NOT use (-1,1,0) as your SOL characterizations.
Instead, use the standards' actual characterizations.


- Jeff, k6jca

I just see your comment, and since I happened to have a VNA calibrated, I
stuck an Agilent short from an 85052B 26.5 GHz 3.5 mm calibration kit on
the test port via a special adapter needed for this. As you can see on the
Smith Chart, the arc starts at the far left (short) and is becoming close
to the right (an open) by 7 GHz.

The VNA was only calibrated to 7 GHz and I could not be bothered to
calibrate it again, but the phase at 7 GHz is about 19 degrees, so I expect
by 8 GHz or so the phase would be a text-book “open” despite it would read
zero ohms if measured on a multimeter.

Dave



--
Dr. David Kirkby,
Kirkby Microwave Ltd,
drkirkby@...

Telephone 01621-680100./ +44 1621 680100

Registered in England & Wales, company number 08914892.
Registered office:
Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT, United
Kingdom

On Sun, Jan 5, 2020 at 11:28 AM, Jeff Anderson wrote:

. (And B. P. Hand recognizes this in the Feb 1970 issue of the HP Journal when
he states that imperfect characterizations of the standards are one of the
sources of error.)

A slight clarification -- Hand was referring to errors that were *not* corrected with the error correction process. Noise is one of those errors. Imperfect characterizations of the standards are another. []


Here are some other quotes regarding the importance of the accurate characterization of standards...

From HP's 8753D User's Guide [], Page 6-50: "When you use a measurement calibration, the dynamic range and accuracy of the measurement are limited only by system noise and stability, connector repeatability, and the accuracy to which the characteristics of the calibration standards are known."

Note that last clause: "the accuracy to which the characteristics of the calibration standards are known." In other words, the more accurately known the characteristics of the standards used for the calibration process are, the more accurate will be the measurements.


From Keysight, "Specifying Calibration Standards and Kits for Keysight Vector Network Analyzers []: "The accuracy of subsequent device measurements depends on the accuracy and stability of the test equipment, the accuracy of the calibration standard model, and the calibration method used in conjunction with the error correction model."

Note that "the accuracy of the calibration standard model" is one of the factors determining the accuracy of measurements.


From Mini-circuits App Note AN49-017 []: "Approximating SOL standards by their canonical/ideal reflection coefficients will undoubtedly incur significant inaccuracies in phase measurements as the phase cannot be treated as static due to the ‘line’ in the transmission line model"

In other words, do NOT use (-1,1,0) as your SOL characterizations. Instead, use the standards' actual characterizations.


- Jeff, k6jca

On Sat, Jan 4, 2020 at 10:11 PM, Gary O'Neil wrote:

Hi Gary,

"It is unbelievably incredible that, since its
invention, so much emphasis has been placed on VNA calibration with maximized
precision, when it contributes more to errors and uncertainty in the results
than enhance accuracy."

For the vast majority of VNAs, the above statement is simply *not* true. In fact, for *any* VNA (or VNA Software, such as NanoVNA-Saver) that allows you to define the impedance and delay characteristics of the SOL standards, improving the (verifiable) accuracy of these characteristics then programming those characteristics into the VNA will enhance the accuracy of the final result.

A description of the VNA hardware used for one port impedance measurements.
...
Three port terminations are identified as sufficient to represent a short
circuit (zero ohms), and open circuit (infinity ohms), and a load standard (Z0
+/-j0 ohms). These devices are measured and plotted on the display at the
locations representing the reflection coefficient values they are intended to
represent (-1 +/-j0, 0 +/-j0, and 1 +/-j0 which also represent the complex
real impedance locations of 0, Z0, and infinity ohms respectively).
Note that these points are plotted as precise and ideal

Not true for the vast majority of VNA's or VNA software that allow the user to input the non-ideal characteristics of the standards.

After calibration, the S and O points are not plotted as "ideal" (i.e. -1, 1), but instead plotted per their *actual* impedance and/or delay. For example, a "short" that has been characterized to have delay will not plot as a point but as an clockwise arc on the unit circle, starting at 9 o'clock.

(The "L" standard, being the 50 ohm load, is a special case and plotted as a point at the center, but this is because, by convention, the typical VNA Load Standard is assumed to have the same resistance as the system's characteristic impedance, e.g. 50 ohms, which is why it is important to have the Load standard be as close to 50 ohms as possible, unless your particular VNA (or VNA software) allows you to set this to a different value).

The requirement for precision calibration standards correction was dismissed
when the automatic network analyzer system was first described in 1968, but
ignored until now. Perhaps that really is a bit of an absurdity. :-)

Are you saying that the requirement for precision calibration standards, as part of the correction process, was *dismissed* in '68? If so, I believe this is not correct.

HP (with its employees Hackborn, Hand, Rytting, and others) created a VNA error-correction technique that, by measuring a VNA's errors using SOL standards with **precisely known characteristics**, can give accurate S11 measurement results. And the more accurately the standards' characterizations are defined to be, the more accurate will be the calculation of the inherent VNA system errors, resulting in more precise results, after these errors have been corrected out of the measurement. The requirement for precisely-defined calibration standards was *never* dismissed. (And B. P. Hand recognizes this in the Feb 1970 issue of the HP Journal when he states that imperfect characterizations of the standards are one of the sources of error.)

The simple fact is -- assuming you can program into your VNA the known electrical characteristics of your standards (delay, loss, Z, etc.), then the more precisely you can define these characteristics to be, the more accurate will be your final results.

For those VNA's that do *not* allow one to input the physical characteristics of your standards (e.g. the NanoVNA running stand-alone), the user should try to ensure that the characteristics of the standards used for calibration are as close to the internal definitions used by that VNA . For the NanoVNA this is an open with no delay and fringe capacitance of 50 fF, the short is a perfect short, and the load is a perfect 50 ohm load. Or use external software (e.g. NanoVNA-Saver) that allows the user to enter into the software the actual characteristics of the standards.

- Jeff, k6jca

Many VNA's use a wheatstone bridge (few use V/I measurement). A wheatstone bridge has a design Z0 for which it provides most sensitivity. Z=(R-Ro)/(R+Ro)
This graph shows the output of the bridge depending on R for a R0 =50ohm.

As most RF systems are designed with a Z0 of 50 ohm the VNA designers chose to balance their bridge at Ro=50 ohm to provide most sensitivity around 50ohm
So yes, you can calibrate with a different load but you do not gain anything as the bridge is used in a less sensitive area. This can be easily verified by trying to calibrate with a Ro=5kOhm. YOu will observe more noise.
What you should do (if the VNA allows) is to replace the internal bridge reference R0 with a different value to regain sensitivity at the new Ro and than calibrate with a load of the new Ro.
This is why people have been asking for how to use the nanoVNA with an external bridge where it is possible to replace the reference R0 with a different impedance.



--
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Erik, PD0EK

On Sat, Jan 4, 2020 at 10:11 PM, Gary O'Neil wrote:

Three port terminations are identified as sufficient to represent a short
circuit (zero ohms), and open circuit (infinity ohms), and a load standard (Z0
+/-j0 ohms). These devices are measured and plotted on the display at the
locations representing the reflection coefficient values they are intended to
represent (-1 +/-j0, 0 +/-j0, and 1 +/-j0

Gary,

The point Jef wants to make is that above statement is NOT true for well characterized but non perfect calibration standards. The characterization (polynome) will describe where for instance the "open" should be seen on the smith chart. The same is true for the load. Adding a first characterization in the form of a small constant C makes the load move away from 0+j0 at higher frequencies. So the characterization of the calibration standard is not there to fix them at -1 +/-j0, 0 +/-j0, and 1 +/-j0 but to have the actual impedance reflected

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

GIN&PEZ, Erik, Jeff, et al;

Absurd and it's derivatives is probably not the most descriptive of the points being made. Consider this a trigger word that translates with emotional overtones. As all of us are aware, emotions can rapidly remove us from reason, and terminate useful and credible dialog. That said, absurd is an excellent choice, but only to those who have been following this thread in great detail, and contextually understand the word choice.

To those who aren't quite up to speed on where this project has arrived, it roughly translates to: "It is unbelieveably incredible that, since its invention, so much emphasis has been placed on VNA calibration with maximized precision, when it contributes more to errors and uncertainty in the results than enhance accuracy."

I have devised a simple VNA hardware description and one-port experiment that I think will demonstrate and illuminate the implications of this project, and reveals how the VNA relates to any user... at least in a one port environment The object of the experiment is to give readers an intuitve sense of what has been revealed in this thread; and provide sufficient understanding of the results to motivate them to challenge their current beliefs. It takes effort to follow the details sufficiently to comprehend its implications, and then study and defend the logic, reasoning, explanations, and conclusions that follow.

For much of this to make sense though, selectively challenging points of interest and comparing it with what the reader may already know and/or believe, may only serve to confuse and make the task of understanding difficult.

A descripton of the VNA hardware used for one port impedance measurements.

The common user views the VNA as a Smith Chart; a circle which represents the Mobius mapping of the complex plane from zero to Infinity centered at Z0 and often (not always) normalized to 1 +/-j 0 ohm.
By definition; maximum power is absorbed by the load when the load is equal to the characteristic impedance of the source (sometimes normalized to 1 +/- j0) . No power is reflected, the reflection coefficient is zero, and this minimum reflected power condition (measured as zero voltage) is displayed at the exact center of the chart.
A calibration process is required to establish the center of the chart as representing the characteristic impedance of the system, and to restrain all values of reflection coefficient to within the unit circle.
Three port terminations are identified as sufficient to represent a short circuit (zero ohms), and open circuit (infinity ohms), and a load standard (Z0 +/-j0 ohms). These devices are measured and plotted on the display at the locations representing the reflection coefficient values they are intended to represent (-1 +/-j0, 0 +/-j0, and 1 +/-j0 which also represent the complex real impedance locations of 0, Z0, and infinity ohms respectively).
Note that these points are plotted as precise and ideal, and as with the Smith Chart, these points being identified is sufficient to plot the entire complex impedance domain from 0 to infinity centered on the characteristic impedance of the measurement system.


An illustrative experiment of the power and utility of the VNA, and the unnecessary constraints of other than nominal valued measurement standards.

Augment your set current of SOL standards with two additional resistive loads of reasonably equivalent quality. I chose 200 and 500 ohms for my experiment.

1) Perform a normal calibration of your VNA. Observe where the Short, Load, and Open appear to verify your calibration was successful. Measure and record the value of your two newly created loads.

2) Recalibrate your VNA using one of the new loads as the load standard (e.g. 200 ohms). Observe where the Short, Load, and Open appear to verify your calibration was successful. Measure and record the value of your two remaining loads.

3) Repeat step 2 using the last of the two new loads.

Do not be concerned with what you observe during this experiment. You will become informed. All calibrations will result in the load always being in the center.

*

The following is what I expected to observe and my measurements were in agreement with this:

A) For test case 1, using my current set of standards, I measured the anticipated values of 200 and 500 ohms real as displayed on the NanoVNA.

B) For test case 2, using my 200 ohm load as the calibration standard, I measured 12.5 ohms real for my original 50 ohm calibration standard, and 125 ohms real for the 500 ohm load.

C) For test case 3, using my 500 ohm load as the calibration standard, I measured 5 ohms real for my original 50 ohm calibration standard, and 20 ohms real for the 200 ohm load.

Notice that my A results are the correct values of the newly constructed loads... This is because the NanoVNA firmware assumes my measurements were made in a 50 ohm measurement environment and scaled the display for Z0 accordingly.

In my B measurements, the NanoVNA makes the same assumptions about Z0. This is a fixed value in the firmware. However this wasn't the environment I calibrated the system to measure. I defined Z0 for my measurement to be 200 ohms, but the NanoVNA displays its results based on its Z0 assumption of 50 ohms.

Corrrecting my B results by an appropriate scaling factor of 200/50 = 4, I simply multiply the NanoVNA readings by 4 and this becomes 4 * 12.5 = 50 ohms and 4 * 125 = 500 ohms, thus my displayed results are as expected.

In the same manner, multiplying the results in my C measurements by the Z0 scaling factor of 500/50 = 10, my measured results become 10 * 5 = 50 ohms and 10 * 20 = 200 ohms, and the displayed are again as expected.

Probe around your NanoVNA while performing this experiment. You will make some obvious but unsuspecting observations. For example the VSWR of the 500 ohm load is 10:1 when calibrated in a 50 ohm measurement environment, but when calibrated in a 500 ohm measurement environment, the SWR is 1:1 and flat across frequency, and the 50 ohm calibration standard is 10:1 and flat across frequency.

So what does all of this mean from a common user's point of view (FACUPOV)?

The VNA is exposed as nothing more than a complex ratiometer. It displays the ratio of a reflected wave to a transmitted wave. This is of course the definition of the reflection coefficient. This is also the condition displayed graphically on a Smith Chart.

Measurement accuracy is strictly defined by the accuracy in which the ratio can be resolved, and the known/characterized/accepted true value of the reference to which it is compared (user defined as ZO).

Errors and uncertainties are measured, remembered and not introduced into the results... e.g. the uncertainty of using measurement hardware having a dramatically mismatched (10:1) Z0 source impedance is transparent in the measurements.

Amateur radio operators are resourceful creative and inventive creatures. It won't take long for us to realize that we can calibrate our instruments in any arbitrary impedance of our fancy, moving the results closer to the center of the Smith Chart where its displayed behaviour is expanded and made more optimally visible and easier to analyze.

Most intriguing about this project is that through all of the work that has been put into bringing these new perspectives to our attention, nothing needs to change in either hardware nor software; although opportunities to make it more efficient have been revealed along the way.

The requirement for precision calibration standards correction was dismissed when the automatic network analyzer system was first described in 1968, but ignored until now. Perhaps that really is a bit of an absurdity. :-)

--
73

Gary, N3GO

On Sat, Jan 4, 2020 at 03:55 PM, gin&pez@arg wrote:

Hi gin&pez:

After that said, also allow us, please, to consider now that our way to use
this mathematical model, that is * w i t h o u t * the introduction of additional mathematical
expressions, is by this very fact the most simple way to confront with this really existing issue
- which by way, it also covers the non-default operation of your VNA - simply because our way
covers the measurements by * a n y * VNA.

What additional mathematical expressions are you referring to?

If this is your mathematical model:

G = (S*(L-O)*(g*s+l*o)+L*(O-S)*(g*l+o*s)+O*(S-L)*(g*o+s*l))/
((L-O)*(g*s+l*o)+ (O-S)*(g*l+o*s) + (S-L)*(g*o+s*l))

Then, to create *accurate* representations of S. O. and L, you must derive the values of S, O, and L in a similar fashion to how they are derived for any other VNA that uses the standard 3-error-term one-port calibration technique. Are these SOL calculations the additional mathematical expressions you are referring to?

And at this very point also allow us, please, to emphatically declare that we
don't find anything erroneous in our point of view, that is the one From A Common User
Point of View FACUPOV, since we already looked ahead to exclude VNA cases in which this
default operation it is not their default. Our claim still holds for all those
still existing VNAs which do consider by default such an Absurdness.

Finally, allow us, please, to also emphatically say that * I F * after all
that provisions of your VNA, the unknown load value is still * c o m p u t e d * using the
expressions which are consequences of this very net linear S-parameter model,
* T H E N * you have not get rid off the Core Uncertainty of the Measurement still existing :
(a) in your Standards,
as well as (b) in the inaccuracy of your VNA readings.

My apologies, I do not understand the point you are trying to get across with the above two paragraphs.

So perhaps it would be better if I state my point-of-view:

Your equation (which is very elegant, congratulations!):
G = (S*(L-O)*(g*s+l*o)+L*(O-S)*(g*l+o*s)+O*(S-L)*(g*o+s*l))/
((L-O)*(g*s+l*o)+ (O-S)*(g*l+o*s) + (S-L)*(g*o+s*l)),
is, at its essence, a function of G in terms of 7 variables, those variables being: s, o, l, S, O, L, and g.

The well-known 3-term error model for one-port calibration consists of 4 equations (equations 1, 5, 6, and 7 here: )
Note that when equations 5, 6, and 7 are inserted into equation 1, the result is a function of G in terms of 7 variables. And those seven variables are the same as your equations's seven variables: s, o, l, S, O, L, and g.

If you then assign values to s, o, l, S, O, L, and g, and solve either your equation or the equations that represent the 3-term error model, you will get the *same* answer for G.
See: /g/nanovna-users/message/8569

So -- we have the same input variables, and we have the same result. This implies, to me, that your equation and the equations representing the 3-term error model are functionally equivalent. My guess is, some smart person (not me) could take the equations that represent the 3-term error model and manipulate them so that the resulting equation is equivalent to your equation.

When you mention "expressions which are consequences of this very net linear S-parameter model", and then you state that, because of this S-parameter model, "you have not get rid off the Core Uncertainty of the Measurement still existing : (a) in your Standards, as well as (b) in the inaccuracy of your VNA readings", I become confused. Are you stating that the 3-term error model has uncertainties and inaccuracies that your equation does not have?

I'll point out again -- both your equation and the 3-term error model use exactly the same variables, and both generate exactly the same result when values are substituted for those variables.

Therefore, to my mind, both your equation and the 3-term error model's equations must have exactly the same uncertainties and inaccuracies.

Anyway, after all that said, may we ask you now, please:

- Do you ever wondered why your VNA still leaves this Absurdness available to
its user ?

My apologies, gin&pez, but I do not know what absurdity you are referring to.

- Do you ever wondered how its measurement is finally extracted to be
presented to the user ?

If you are asking me if I know how my VNA calculates S11, the answer is yes.

Best regards,

- Jeff, k6jca

#106": More On The Fourth Load VNA Trick

@Jeff Anderson - 4 January 2020 - /g/nanovna-users/message/9158

Dear Jeff,

Thank you very much for your most valuable information, by which you declare that
your VNA introduces, to the linear S-parameter equations model, * a d d i t i o n a l *
mathematical expressions, by which it tries to express the "physical impairments"
of the Standards.

This simply means to us that your particular VNA recognizes the most obvious fact:

"The Names of the Standards - that is their Nominal Values (-1, 0, 1) in accordance to
(S, L, O) order - do not express their values".

Thank you very much, indeed !

Because, this is exactly what we are trying to say in this Group from the very beginning.

After that said, also allow us, please, to consider now that our way to use this mathematical
model, that is * w i t h o u t * the introduction of additional mathematical expressions, is by
this very fact the most simple way to confront with this really existing issue - which by way,
it also covers the non-default operation of your VNA - simply because our way covers
the measurements by * a n y * VNA.

And at this very point also allow us, please, to emphatically declare that we don't find
anything erroneous in our point of view, that is the one From A Common User Point of
View FACUPOV, since we already looked ahead to exclude VNA cases in which this
default operation it is not their default. Our claim still holds for all those still existing
VNAs which do consider by default such an Absurdness.

Finally, allow us, please, to also emphatically say that * I F * after all that provisions of
your VNA, the unknown load value is still * c o m p u t e d * using the expressions which
are consequences of this very net linear S-parameter model, * T H E N * you have not
get rid off the Core Uncertainty of the Measurement still existing : (a) in your Standards,
as well as (b) in the inaccuracy of your VNA readings.

And it is still there, because it is * i n s e p a r a b l y * associated * w i t h * the
mathematical model in use itself.

That's all the crystal clear truth.

Anyway, after all that said, may we ask you now, please:

- Do you ever wondered why your VNA still leaves this Absurdness available to its user ?

- Do you ever wondered how its measurement is finally extracted to be presented to the user ?

With our best regards,

gin&pez@arg

On Sat, Jan 4, 2020 at 01:33 PM, gin&pez@arg wrote:

Hi gin&pez

"
Therefore, the Absurdness does not belong to us,
but to VNA itself, because:

(a) It considers by default that all the Standards
of the Whole World are identical and they have
values equal to those of their Names, that is of
their Nominal Values (-1,0,+1), and

Thank you for the clarification.

I am curious why you make this claim (a), because, in my experience, it is not correct. I offer as evidence any number of VNAs (or VNA software) that allow the user to characterize the three standards in terms of their actual physical characteristics (delay, loss, mismatch, and actual impedances (e.g. as a function of fringe capacitance, etc.).

For example, my 8753C does not "consider by default" that the Reflection Coefficients of any SOL standards are (-1, 1, 0). It actually considers *all* standards to have physical impairments that keep them from being the ideal (-1,1,0). And the only way to make the VNA use Reflection Coefficients that are (-1,1,0) is to go through the rather painful process of manually setting to zero (via the 8753C's menu system) each of the impairments for each of the SOL standards that have been pre-programmed (by HP) into the VNA.

"
Does it have an enough crystal clear meaning now?

It is much clearer! Many thanks.

- Jeff, k6jca

@Gary O’Neil, N3GO
/g/nanovna-users/message/9132

Dear Gary,

Well, allow us, please, to remind you that we would not arrive at this
- most spectacular, indeed ! - conclusion, if you did not insist to ask
all those questions, while the only thing we asked from you it was to
be staying tuned...

Kind regards,

gin&pez@arg

#106': On The Fourth Load VNA Trick

@Jeff Anderson - 4 January 2020
/g/nanovna-users/message/9153

Hello,

Thank you very much for interest in our work,
and especially for quoting this excerpt by us,
as well as for the opportunity you are giving
to us to improve it !

Well, we presume that you are not following
this thread from its very beginning. So, let us
try our best to reshape this excerpt, as follows:

"
Therefore, the Absurdness does not belong to us,
but to VNA itself, because:

(a) It considers by default that all the Standards
of the Whole World are identical and they have
values equal to those of their Names, that is of
their Nominal Values (-1,0,+1), and

(b) It handles these Standard values in the very
same way we use them, that is : with linear
S-parameter equations.
"
Does it have an enough crystal clear meaning now?

Sincerely,

gin&pez@arg

#106':

@Gary
Can you help me to understand the reply from g&p?

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

On Sat, Jan 4, 2020 at 11:51 AM, gin&pez@arg wrote:

Therefore, it not our absurdness the fact that VNA considers by default that
it is enough for it not only to consider All the Standards of This Whole World as
identically having values equal to those of their Names, that their
Nominal Values (-1,0,+1), but in addition to that Absurdness to handle them
in this very same frame of our SOW : with linear S-parameter equations...

gin&pez,

Please forgive me, but your writing style, in my opinion, contains much too much extraneous "verbiage," and it is difficult for me (and probably others) to wade through the unnecessary words and sentiments in an attempt to glean the actual point you are trying to communicate. Trimming your sentences and paragraphs down to the essentials would greatly help you to express your points.

For example, what is the point you are trying to communicate in the paragraph I have quoted, above? Are you saying that all VNA's consider their SOL standards to have Reflection Coefficients of (-1, 1, 0), irrespective of the actual Reflection Coefficients of those standards?

Or are you saying something else? If it is "something else," then could you please explain your point in a clear and concise fashion?

Thank you,

- Jeff, k6jca

#106: On The Fourth Load VNA Trick

@Erik, PD0EK - 4 January 2020 - /g/nanovna-users/message/9131

Dear Erik,

We would like to thank you very much because you revealed at last your Subjective
World. Now, there is a chance to understand each other just on the basis of logical
reasoning, of course.

Well, we already openly set the crystal clear limits of our SOW regarding the kind
of "VNA Measurements" : linear S-parameter equations and their consequences;
nothing more-nothing less, but exactly all of this. All that can be logically concluded
and reasonably described within these very limits - which, by the way, you already
accepted too by proposing to us that picture (alas, still self-contradictory) you are
hosting at your website.

That's all. Crystal clear.

Therefore, it not our absurdness the fact that VNA considers by default that it is enough
for it not only to consider All the Standards of This Whole World as identically having
values equal to those of their Names, that their Nominal Values (-1,0,+1), but in addition
to that Absurdness to handle them in this very same frame of our SOW : with linear
S-parameter equations...

Start at last putting the blame - if you think that is really one such - to where it is belong
exactly, that is to:

The Fourth Load VNA Trick

which comes from that Much Bigger than our Small Objective World SOW, that is from
The Objective World of Linear S-Parameter Equations. And remember, please, that we
didn't invented this World, we simply present what are the unavoidable logical consequences
for anyone who would adopted it, as a whole of course and not by selecting only those parts
of it who thinks he likes because he finds them as most convenient for his purposes - that is
to form a Subjective World instead of an Objective one.

Kind regards,

gin&pez@arg

#106: