errors of "error" models
erik@...
On Tue, Nov 5, 2019 at 05:48 AM, gin&pez@arg wrote:
Dear gin&pez@arg How are you sure the errors to be corrected are larger than the uncertainty in your measurement. e.g. you are not trying to correct an already (almost) perfect VNA?  Erik, PD0EK


#73 :
erik@...  5 November 2019 : https://groups.io/g/nanovnausers/message/6495 Dear Erik, Thank you very much indeed for your interest in our work and also for the chance you give us to explain it always facupov, of course further ! Therefore, regarding your specific question: "How are you sure the errors to be corrected are larger than the uncertainty in your measurement. e.g. you are not trying to correct an already (almost) perfect VNA?" allow us, please, to definitely clear without any doubt that in our sow [#24], [#34] we are only * c u r r e n t l y * sure for the following  but we hope to excuse us because, maybe unfortunately enough, we selected to explain all that using purposely a greatly emphatical language:       (c) gin&pez@arg (ccby4.0) 2019 : start       (0) "A perfect VNA" is an object of the * i m p e r f e c t * world of mathematics (1) "An already (almost) perfect VNA" may be an object in other subjective worlds  we don't know, but we are ready to include it in our sow, as soon as we will be provided by the specific quantitative data of its existence (2) "The Least VNA" is simply AnyVNA that is used as a Reflectometer or Impedance Meter in terms of frequency of OnePort devices using the wellknown ("standard", 'Standard' or Standard) set of three 3 loads {S, L, O}, all with known nominal values given respectively, not at all by us but by their manufacturers, as the socalled "{1, 0, +1}" or whatever similar [ but loosely, because this may be result in a * B I G * source of misunderstanding [ since this "set of values" is in fact the one of the couples of values: [ [ { ( 1 , 180 ) , (0 , undefined ) , ( 1 , 0 ) } [ [ in terms of their ( modulus , argument ) ordered [  [ that is in order to avoid to mess up the things, the modulus value has always to [ appear first, after the opening left parenthesis and before the separating comma, [ and then the second argument value to appear before the closing right parenthesis [  [ pairs or couples of values although a last apt, as usual comment made by our Fellow in Knowledge Garry O' Neil, N3GO [1], forced us to already think a possible reconsideration of this definition in the direction of an even more simplification; always facupov, of course (3) "The LeastVNA measured Impedance" is * I N * F A C T * an * I N D I R E C T * "measurement", that is a * C A L C U L A T E D * or * C O M P U T E D * result, just an * O U T P U T * of the welldefined * M A T H E M A T I C A L * function expressed by the wellknown * F O R M U L A * [#52]: https://www.op4.eu/code/Gmini.c.gza.cc.by.4.0.2019.png in terms of the measurements of these * T H R E E * loads, made * D I R E C T L Y * using that * A N Y * V N A * (4) Obviously this is an * I N S E P A R A B L Y * A S S O C I A T E D * to * A N Y * * V N A * mathematical expression, a socalled "(mathematical) model", of this very instance LeastVNA of that AnyVNA. (5) We did * N O T * invent this relation [#52]: https://www.op4.eu/code/Gmini.c.gza.cc.by.4.0.2019.png We just simplified the given one [#16]: https://www.op4.eu/code/ccby4.0gzainvnaparams.png  as perhaps they did that others before us, although we don't know if something that really happened. This is easily verified by anyone who would like to use simple, highschool algebra on these expressions, by ignoring their complex "nature" and substituting: (i) g, G in Hellenic gamma, Gamma (ii) 1, 0, 1 in A, B, C, and (iii) s, l, o in a, b, c, respectively, and proceeding with the resulting eliminations. That's all. (6) Now, since the 8 = 3 x 2 + 1 x 2 measurements s, l, o, and g, were indicated by our VNA to us with a * F I N I T E *, * L I M I T E D * * A C C U R A C Y * of just * T H R E E * 3 *, or * F O U R * 4 * at most, decimal * D * I * G * I * T * S *, it was extremely natural in our sow to ask ourselves : HOW BIG WILL BE THE EFFECT IN THE UNAVOIDABLY * C O M P U T E D * IMPEDANCE, IF WE WOULD TAKE INTO ACCOUNT THAT *J U S T * O N L Y * O N E *, THE LAST ONE, DIGIT OF THESE FOUR MEASURED VALUES WAS IN DOUBT ? THAT IS AS IT HAPPENS IN ANY OTHER MEASUREMENT, BY ANY OTHER INSTRUMENT, SO WHY NOT WITH THOSE BY AnyVNA OR OUR VNA ? That's all.. And, once again, definitely this has nothing to do with the perfectness or imperfectness of AnyVNA itself. But, this definitely has to do with the unavoidably finite number of reliable digits used by AnyVNA to indicate its measurements. And this finite number of reliable digits in these four 4 measurements is only JUST ONE source of error in the finally COMPUTED indirect "measurement". (8) We emphasized in the above the COMPUTED character of the indirect "measurement" because, if this INDIRECT "measurement" was a usual DIRECT measurement, all the doubt would unavoidably restrict to just a few, perhaps even only the last one, of its resulted digits  but, unfortunately enough, this is not the case here. (9) Also, and in addition to all that, the range of measured values (small, less than one 1 in modulus), as well as the particular form of the unavoidable mathematical expression (ratio of differences of small, less than one 1, in modulus values) FORCED us to attempt such a research  and it would be the GREATEST of OMISSIONS by us, if we did not act in this way, as long as we declared ourselves not only as "researchers" but in addition as "scientific" ones... (10) After all that said, we think that we are ready to answer your question as follows:  We are NOT interested to correct our "measurement" in fact one of our VNA itself  We are NOT interested if the errors to be corrected in fact ones of our VNA itself are larger than the uncertainty in our "measurement" in fact in the computed indirect "measurement" of our VNA itself  We are only * c u r r e n t l y * s u r e * that our method of estimation of the above inaccuracy errors, which * U N A V O I D A B L Y * C O N T R I B U T E * to the ENTIRE "MEASUREMENT" UNCERTAINTY of our two VNA systems  that is either of our VNA or of our * N a n o V N A *, * P L U S * our THREE Standards and just in this, the simplest of all the possible cases, also "currently the simplest", after our reservation (2) above, that is after Garry O' Neil's comment  We are * c u r r e n t l y * s u r e * that our method of estimation of all the errors we are currently in place to recognize as REALLY EXISTING in AnyVNA measurements, that is the above Inaccuracy Errors PLUS those definitely larger than these Uncertainty Errors given to our three 3 Standards by their manufacturers, all together count 8 + 3 x 2 = 14, contribute UNAVOIDABLY to the ENTIRE "MEASUREMENT" UNCERTAINTY of our two VNA systems And this is the reason we call them : "The Uncertainty Core"  at least of our two VNA and NanoVNA Systems  In conclusion: * UNCERTAINTY * LESS * THAN* THAT * IS * ENTIRELY * IMPOSSIBLE * in AnyVNA SYSTEM and at least in its LeastVNA application  fullStop.    end : (c) gin&pez@arg (ccby4.0) 2019           * You * Have * Been * Warned * REFERENCES [1] Gary O'Neil , N3GO  4 November 2019 : https://groups.io/g/nanovnausers/message/6432 [#16] : 27 September 2019 : https://groups.io/g/nanovnausers/message/3161 https://www.op4.eu/code/ccby4.0gzainvnaparams.png [#24] : The Main Frame of a Possible Communication  1 October 2019: https://groups.io/g/nanovnausers/message/3649 [#34] : Trying to Limit the Misunderstanding up to its Removal  5 October 2019: https://groups.io/g/nanovnausers/message/4108 [#52] : Update : The compact SLO formula for [AnyVNA]  17 October 2019: https://groups.io/g/nanovnausers/message/5100 https://www.op4.eu/code/Gmini.c.gza.cc.by.4.0.2019.png With our Best of Regards, 73 Nikolitsa, OE3ZGN/SV7DMC and Petros, OE3ZZP/SV7BAX : 73#


#73': On the sine qua non Core Uncertainty of AnyVNA  incl. NanoVNA  System
(the message #73 is withdrawn mainly because its conclusion is too weak) erik@...  5 November 2019 : https://groups.io/g/nanovnausers/message/6495 Dear Erik, Thank you very much indeed for your interest in our work and also for the chance you give us to explain it always facupov, of course further ! Therefore, regarding your specific question: "How are you sure the errors to be corrected are larger than the uncertainty in your measurement. e.g. you are not trying to correct an already (almost) perfect VNA?" allow us, please, to definitely clear without any doubt that in our sow [#24], [#34] we are only * c u r r e n t l y * sure for the following  but we hope to excuse us because, maybe unfortunately enough, we selected to explain all that using purposely a greatly emphatical language:       (c) gin&pez@arg (ccby4.0) 2019 : start       (0) "A perfect VNA" is an object of the * i m p e r f e c t * world of mathematics (1) "An already (almost) perfect VNA" may be an object in other subjective worlds  we don't know, but we are ready to include it in our sow, as soon as we will be provided by the specific quantitative data of its existence (2) "The Least VNA" is simply AnyVNA that is used as a Reflectometer or Impedance Meter in terms of frequency of OnePort devices using the wellknown ("standard", 'Standard' or Standard) set of three 3 loads {S, L, O}, all with known nominal values given respectively, not at all by us but by their manufacturers, as the socalled "{1, 0, +1}" or whatever similar [ but loosely, because this may be result in a * B I G * source of misunderstanding [ since this "set of values" is in fact the one of the couples of values: [ [ { ( 1 , 180 ) , (0 , undefined ) , ( 1 , 0 ) } [ [ in terms of their ( modulus , argument ) ordered [  [ that is in order to avoid to mess up the things, the modulus value has always to [ appear first, after the opening left parenthesis and before the separating comma, [ and then the second argument value to appear before the closing right parenthesis [  [ pairs or couples of values although a last apt, as usual comment made by our Fellow in Knowledge Garry O' Neil, N3GO [1], forced us to already think a possible reconsideration of this definition in the direction of an even more simplification; always facupov, of course (3) "The LeastVNA measured Impedance" is * I N * F A C T * an * I N D I R E C T * "measurement", that is a * C A L C U L A T E D * or * C O M P U T E D * result, just an * O U T P U T * of the welldefined * M A T H E M A T I C A L * function expressed by the wellknown * F O R M U L A * [#52]: https://www.op4.eu/code/Gmini.c.gza.cc.by.4.0.2019.png in terms of the measurements of these * T H R E E * loads, made * D I R E C T L Y * using that * A N Y * V N A * (4) Obviously this is an * I N S E P A R A B L Y * A S S O C I A T E D * to * A N Y * * V N A * mathematical expression, a socalled "(mathematical) model", of this very instance LeastVNA of that AnyVNA. (5) We did * N O T * invent this relation [#52]: https://www.op4.eu/code/Gmini.c.gza.cc.by.4.0.2019.png We just simplified the given one [#16]: https://www.op4.eu/code/ccby4.0gzainvnaparams.png  as, perhaps, they did that others before us, although we don't know if something that was really happened. This is easily verified by anyone who would like to use simple, highschool algebra on these expressions, by ignoring their complex "nature" and substituting: (i) g, G in Hellenic gamma, Gamma (ii) 1, 0, 1 in A, B, C, and (iii) s, l, o in a, b, c, respectively, and proceeding with the resulting eliminations. That's all. (6) Now, since the 8 = 3 x 2 + 1 x 2 measurements s, l, o, and g, were indicated by our VNA to us with a * F I N I T E *, * L I M I T E D * * A C C U R A C Y * of just * T H R E E * 3 *, or * F O U R * 4 * at most, decimal * D * I * G * I * T * S *, it was extremely natural in our sow to ask ourselves : HOW BIG WILL BE THE EFFECT IN THE UNAVOIDABLY * C O M P U T E D * IMPEDANCE, IF WE WOULD TAKE INTO ACCOUNT THAT *J U S T * O N L Y * O N E *, THE LAST ONE, DIGIT OF THESE FOUR MEASURED VALUES WAS IN DOUBT ? THAT IS AS IT HAPPENS IN ANY OTHER MEASUREMENT, BY ANY OTHER INSTRUMENT, SO WHY NOT WITH THOSE BY AnyVNA OR OUR VNA ? That's all.. And, once again, definitely this has nothing to do with the perfectness or imperfectness of AnyVNA itself. But, this definitely has to do with the unavoidably finite number of reliable digits used by AnyVNA to indicate its measurements. And this finite number of reliable digits in these four 4 measurements is only JUST ONE source of error in the finally COMPUTED indirect "measurement". (8) We emphasized in the above the COMPUTED character of the indirect "measurement" because, if this INDIRECT "measurement" was a usual DIRECT measurement, all the doubt would unavoidably restrict to just a few, perhaps even only the last one, of its resulted digits  but, unfortunately enough, this is not the case here. (9) Also, and in addition to all that, the range of measured values (small, less than one 1 in modulus), as well as the particular form of the unavoidable mathematical expression (ratio of differences of small, less than one 1, in modulus values) FORCED us to attempt such a research  and it would be the GREATEST of OMISSIONS by us, if we did not act in this way, as long as we declared ourselves not only as "researchers" but in addition as "scientific" ones... (10) After all that said, we think that we are ready to answer your question as follows:  We are NOT interested to correct our "measurement" in fact one of our VNA itself  We are NOT interested if the errors to be corrected in fact ones of our VNA itself are larger than the uncertainty in our "measurement" in fact in the computed indirect "measurement" of our VNA itself  We are only * c u r r e n t l y * s u r e * about our currently in use method of estimation of the above inaccuracy errors, which * U N A V O I D A B L Y * C O N T R I B U T E * to the ENTIRE "MEASUREMENT" UNCERTAINTY of our two VNA systems  that is either of our VNA or of our * N a n o V N A *, * P L U S * our THREE Standards in just this, the simplest of all the possible uses of these (also currently "the simplest" use, after our reservation (2) above, that is after Garry O' Neil's comment  We are * c u r r e n t l y * s u r e * about our currently in use general method of estimation of all the errors we are currently in place to recognize as REALLY EXISTING in AnyVNA measurements, that is (a) the above Inaccuracy Errors, PLUS (b) those, definitely larger than these, Uncertainty Errors given to our three 3 Standards by their manufacturers  all together count to finding 28 (real) numbers at most, by taking into account that all these are in general (real) intervals with two 2 endpoint numbers, a lower and an upper one, so that 2 x (8 + 3 x 2) = 2 x 14 = 28  contribute UNAVOIDABLY to the ENTIRE "MEASUREMENT" UNCERTAINTY at least of our two VNA systems, if nobody's else. And this is the reason we call this component of the entire uncertainty: "The sine qua non Core Uncertainty of AnyVNA  incl. NanoVNA  System" In conclusion: We are currently sure for that: Facupov, * UNCERTAINTY * LOWER * THAN* THIS * CORE * UNCERTAINTY * * IS * ENTIRELY * IMPOSSIBLE * in AnyVNA  incl. NanoVNA  SYSTEM under its LeastVNA application, as well as, We are currently sure for that: Our current method of estimation of this Core Uncertainty is the only known one as an objectively existing one, even as an object of just our sow  that is it has a deterministic character  for more than ten years now. Others may have their own methods of estimation of other types of uncertainty components, as objects of their subjective worlds  that is they have a statistical character. However, facupov, currently we are definitely not interested either on those uncertainty components or on their estimating methods  fullstop.    end : (c) gin&pez@arg (ccby4.0) 2019           * You * Have * Been * Warned * REFERENCES [1] Gary O'Neil , N3GO  4 November 2019 : https://groups.io/g/nanovnausers/message/6432 [#16] : 27 September 2019 : https://groups.io/g/nanovnausers/message/3161 https://www.op4.eu/code/ccby4.0gzainvnaparams.png [#24] : The Main Frame of a Possible Communication  1 October 2019: https://groups.io/g/nanovnausers/message/3649 [#34] : Trying to Limit the Misunderstanding up to its Removal  5 October 2019: https://groups.io/g/nanovnausers/message/4108 [#52] : Update : The compact SLO formula for [AnyVNA]  17 October 2019: https://groups.io/g/nanovnausers/message/5100 https://www.op4.eu/code/Gmini.c.gza.cc.by.4.0.2019.png With the Best of our Regards, 73 Nikolitsa, OE3ZGN/SV7DMC and Petros, OE3ZZP/SV7BAX :73'#


Gary O'Neil
Thank you GIN & PEZ
 73 Gary, N3GO


Gary O'Neil
Thank you GIN & PEZ;
Your post #6529 #73': On the sine qua non Core Uncertainty of AnyVNA  incl. NanoVNA  System (the message #73 is withdrawn mainly because its conclusion is too weak) Seems to add significant clarity to my understanding of your project overall; I will attempt a concise summary of my understanding, and seek your confirmation on this, or clearly illuminate those components of thought where I am in error. The One port LeastVNA equation: https://www.op4.eu/code/Gmini.c.gza.cc.by.4.0.2019.png [#52] Is a reduced (oneport) expression derived from the full (two port) set of equations https://www.op4.eu/code/ccby4.0gzainvnaparams.png [#16] and neither of these are new, but are based on the prior works of perhaps many. The unique property of [#52], (and [#16] as well) is that they describe calibrations of any VNA using just the nominal measurements of the SOL standards, and any nominal DUT measurements from which the desired DUT parameters are then computed. An additional unique (and most important property) of the equations is that they do not attempt to correct for any source of uncertainty bias. Correction parameters are intentionally ommitted. [#16], and [#52] as a subset, are declared the Core equations for any VNA calibration, and define the variables, and computational requirements common to any VNA (All VNA's) for the following reasons: 1) The measurements are performed identically for any VNA 2) The quanity of measurements and computations are identical for any VNA 3) ALL measurement uncertainties that are not common to ALL VNA's are excluded from the computations and results. 4) The equations enable measurements made on any VNA calibrated as a "system" to be compared equally without bias. All known unavoidable uncertainties are common to all VNAs, and are absorbed equally and identically into the calibration as the overall uncertainty of the measurement system itself. The Core uncertainty is defined as the unavoidable deterioration of computational precision created when multiplying and dividing by indeterminately large and small quantities, the accumulation of roundoff and truncation errors, and the unavoidable number of mathematical operations required to arrive at a computed final result. The Core uncertainty, is a computational artifact, that is objectively deterministic, and defines the UNAVOIDABLE MINIMUM boundaries of uncertainty in any VNA, that can not be improved through the use of higher precision equipment or components. This is the objective of the DERDEI software currrently in the form of a FORTRAN calculator and wxMaxima plotting utility. In other words... Sine qua non F(Any)CUPOV. :) 73 Gary, N3GO  73 Gary, N3GO


erik@...
Dear GIN & PEZ
I must, unknowingly, have asked a very wrong question. Apologies for that. The reason for asking was the simplification to the formula G=m/s I was assuming, probably very wrong, that any simplification is based on the absence of impact of the factors that are being ignored. You are able to calculate the uncertainty of the measurement so I was merely interested how the factors being ignored where in magnitude of impact compared to the magnitude of uncertainty of the measurement. But if this is a stupid question please ignore it and do not spend any time to reply, only state: This is a stupid question.  Erik, PD0EK


Gary O'Neil
Hi Erik;
I was raised to believe that there is no such thing as a stupid question, but after several decades of not being exposed to the light, I discovered that there are actually many... All of them are the ones that never get asked. :) From my perspective at least, the question you asked was a brilliant one, as evidenced by the response it solicited. It is a struggle for me to capture much of the understanding I'm attempting to achieve through the many segmented and translated responses. Its only fair to assume that the reverse holds true for them as well. Their published documents on this are much better written English translations, but they don't stand on their own for all readers, and for those of us who have had limited if any exposure, are left with many unanswered questions. We ask questions to get smarter. Very often it is helpful to hear "You don't understand." If we fail to ask questions that solicit such a response, we might well go through our lives with the truly stupid notion that "We must be pretty smart."; while in fact we have no understanding at all. :) Sometimes I ask questions that I believe I know the answer to very well, to verify my understanding. I am a married man, so I have learned that just because I'm confident that I have all of the right answers; most of the time they are entirely incorrect. LOL!  73 Gary, N3GO


@Erik, PD0EK  6 November 2019:
https://groups.io/g/nanovnausers/message/6539 Dear Erik, This is not a stupid question. Best regards, gin&pez@arg PS More on that by Gary, N3GO  6 November 2019: https://groups.io/g/nanovnausers/message/6566


#74: The Virtual Port  "Revealing" the Most Confusing "Secrets" of "Error" Models
Hello, Allow us, please, to "reveal" that:       (c) gin&pez@arg (ccby4.0) 2019 : start       In our sow, every "error" model has at least one real load port and at least one virtual measurement port.    end : (c) gin&pez@arg (ccby4.0) 2019           Would you, please, think about it ? Sincerely, gin&pez@arg :74#


#75: A Mechanical Production of the [LeastVNA] Description
Hello, Allow us, please, to inform you that we just uploaded a mechanical production of the [LeastVNA] description, at: https://www.op4.eu/code/GMINI20191109.MC.txt Sincerely, gin&pez@arg :75#


Gary O'Neil
GIN&PEZ@arg
Thank you for the derivation of the GMINI equation, based on the embedded solution set of four simultaneous equations (GABC) to resolve the embedded value of G based on the measurements of the standards used for S, O. and L. I think I am following the reasoning in your thesis, or at least I understand and agree with the derivation, and I agree that all of the uncertainties are embedded in the measurements. It has also given me an appreciation for Maxima. I don't believe it is a tool that my Algebra and Calculus Instructors would have permitted me to employ in my exams. :) 73 Gary, N3GO  73 Gary, N3GO


#76: The Big Three Free Software Tools Supporting The Independent Research
 @Gary O'Neil, N3GO  10 November 2019 : https://groups.io/g/nanovnausers/message/6711 Dear Gary, Thank you, since you are giving us the very rare chance nowadays to revise all that 10+ years old work, to see its weaknesses, to try once again to fill its gaps, to express new, improved, ideas  always facupov, about fundamental, considered as "wellknown" concepts, because, the Most Difficult Thing to Finally See is the Simplest One Standing in Front of You  and to improve further our skills regarding: The Big Three Free Software Tools Supporting The Independent Research we are still using by combining their Symbolical, Numerical, and Graphical abilities, that is respectively of: [Maxima], [Open Watcom], and [GnuPlot]. Thank you very much, indeed. Sincerely, gin&pez@arg :76#


#77: On the current explanation of full oneport "error" model
in our sow  facupov, as always  with an Application to the Measurements of TwoPort Devices Hello, Well, after the previous related messages, we think that we are now enough prepared to ask you to allow us, please, to attempt a presentation of the current explanation of the so called full oneport "error" model in our sow  facupov, as always.       (c) gin&pez@arg (ccby4.0) 2019 : start       In our sow, the full oneport "error" model is an Abstract or Virtual TwoPort V2P located inside [AnyVNA] (incl. [NanoVNA]) and having as its ports the Virtual Measurement Port VMP [#74] and the Real Load Port RLP. This V2P is obviously characterized by the [LeastVNA] description of Gmini: G = (gl)*(os)/[(go)*(sl)(gs)*(lo)] Therefore, using the above concepts, we can measure, indirectly  as in the case of oneport  : (a) either the S11, S12S21, and S22 parameters of any TwoPort Device appropriate to be connected by the one port of its two ports to the RLP of the V2P and/or (b) any unknown OnePort G' appropriate to be connected to the other port of this TwoPort Device, using this very same Gmini: G' = (g'l')*(o's')/[(g'o')*(s'l')(g's')*(l'o')]        end : (c) gin&pez@arg (ccby4.0) 2019       REFERENCE [#74] The Virtual Port  "Revealing" the Most Confusing "Secrets" of "Error" Models  7 November 2019 : https://groups.io/g/nanovnausers/message/6604 Sincerely, gin&pez@arg :77#


[ann] nexttocome : on the measurement of sparameters using the [LeastVNA] only


D.M.Kerns and R.W.Beatty : "An understanding of this introductory microwave
network analysis is essential to the serious worker in the ﬁeld of microwave measurements. In order to investigate errors in measurements, one must have in mind precisely what quantity is desired in the measurement. Basic definitions of these quantities involve both explicit and implicit assumptions which must be recognized. In addition a knowledge of these analytical tools should be helpful in understanding error analyses already performed by others and described in the literature.", Basic Theory of Wave guide Junctions and Introductory Microwave Network Analysis, Part 2, Introductory Microwave Network Analysis, 2.0.Introduction to Part 2, p.34, Paragraph 3, International Series of Monographs in Electromagnetic Waves, Editors: A. L. Cullen, V. A. Fock J. R. Wait, Volume 13, Pergamon Press Inc, First Edition, 1967.


#78: on the measurement of sparameters using the [LeastVNA] only
 12 November 2019  https://groups.io/g/nanovnausers/message/6912  Hello, Allow us, please, to inform you that we just uploaded the (indirect) "measurements" of S11, S12S21, S22 of an unknown 2port connected to the [LeastVNA], as well as the (indirect) "measurement" of GL of an unknown 1port connected to this 2port, at: https://www.op4.eu/code/s2p.png where: s, l, o and S, L, O are the [LeastVNA] measurements at the Virtual Port of [LeastVNA], when the SHORT, LOAD, OPEN "standards", 'standards', or Standards having Nominal Values 1, 0, +1 are connected at the Load Port of [LeastVNA] and at the Load Port of the connected 2port, respectively, while G is the [LeastVNA] measurement of the GL connected to the same Load Port of 2port. Notably, only oneport reflection measurements are involved. Sincerely, gin&pez@arg :78#


[ann] : [NanoVNA] ~ [LabVNA] comparison using a 2port


#78' : #78 was corrected : https://www.op4.eu/code/s2p.png
 #78: on the measurement of sparameters using the [LeastVNA] only 18 November 2019  https://groups.io/g/nanovnausers/message/7162


#79: Three AnimatedGIF/AVIs in Slow Motion Demonstrate,
StepbyStep, the Graphical Construction of Differential Error Regions Arising in the Measurements with [AnyVNA] Hello, Allow us, please, to inform you that 11 years ago we uploaded 3 AnimatedGIF/AVIs in slow motion demonstrating, StepbyStep, the graphical construction of the differential Error regions arising in the Measurements with [AnyVNA], at: 1/3 http://antennas.gr/anamet/30/ani/gif/ico.gif http://antennas.gr/anamet/30/ani/avi/ico.avi 2/3 http://antennas.gr/anamet/30/ani/gif/iico.gif http://antennas.gr/anamet/30/ani/avi/iico.avi 3/3 http://antennas.gr/anamet/30/ani/gif/iiio.gif http://antennas.gr/anamet/30/ani/avi/iiio.avi Sincerely, gin&pez@arg :79#


#78'' : #78' was recorrected : https://www.op4.eu/code/s2p.png
 #78' : #78 was corrected : https://www.op4.eu/code/s2p.png 19 November 2019  https://groups.io/g/nanovnausers/message/7185 #78: on the measurement of sparameters using the [LeastVNA] only 18 November 2019  https://groups.io/g/nanovnausers/message/7162  :78''#

