errors of "error" models
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#73 :
erik@... - 5 November 2019 : /g/nanovna-users/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 (cc-by-4.0) 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 One-Port devices using the well-known ("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 so-called "{-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 well-defined * M A T H E M A T I C A L * function expressed by the well-known * F O R M U L A * [#52]: 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 so-called "(mathematical) model", of this very instance LeastVNA of that AnyVNA. (5) We did * N O T * invent this relation [#52]: We just simplified the given one [#16]: - 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, high-school 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 (cc-by-4.0) 2019 - - - - - - - - - - * You * Have * Been * Warned * REFERENCES [1] Gary O'Neil , N3GO - 4 November 2019 : /g/nanovna-users/message/6432 [#16] : 27 September 2019 : /g/nanovna-users/message/3161 [#24] : The Main Frame of a Possible Communication - 1 October 2019: /g/nanovna-users/message/3649 [#34] : Trying to Limit the Misunderstanding up to its Removal - 5 October 2019: /g/nanovna-users/message/4108 [#52] : Update : The compact SLO formula for [AnyVNA] - 17 October 2019: /g/nanovna-users/message/5100 With our Best of Regards, 73 Nikolitsa, OE3ZGN/SV7DMC and Petros, OE3ZZP/SV7BAX : 73# |
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#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 : /g/nanovna-users/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 (cc-by-4.0) 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 One-Port devices using the well-known ("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 so-called "{-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 well-defined * M A T H E M A T I C A L * function expressed by the well-known * F O R M U L A * [#52]: 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 so-called "(mathematical) model", of this very instance LeastVNA of that AnyVNA. (5) We did * N O T * invent this relation [#52]: We just simplified the given one [#16]: - 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, high-school 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 end-point 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 (cc-by-4.0) 2019 - - - - - - - - - - * You * Have * Been * Warned * REFERENCES [1] Gary O'Neil , N3GO - 4 November 2019 : /g/nanovna-users/message/6432 [#16] : 27 September 2019 : /g/nanovna-users/message/3161 [#24] : The Main Frame of a Possible Communication - 1 October 2019: /g/nanovna-users/message/3649 [#34] : Trying to Limit the Misunderstanding up to its Removal - 5 October 2019: /g/nanovna-users/message/4108 [#52] : Update : The compact SLO formula for [AnyVNA] - 17 October 2019: /g/nanovna-users/message/5100 With the Best of our Regards, 73 Nikolitsa, OE3ZGN/SV7DMC and Petros, OE3ZZP/SV7BAX :73'# |
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@Erik, PD0EK - 6 November 2019:
/g/nanovna-users/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: /g/nanovna-users/message/6566 |
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#74: The Virtual Port - "Revealing" the Most Confusing "Secrets" of "Error" Models
Hello, Allow us, please, to "reveal" that: - - - - - - (c) gin&pez@arg (cc-by-4.0) 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 (cc-by-4.0) 2019 - - - - - - - - - - Would you, please, think about it ? Sincerely, gin&pez@arg :74# |
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#76: The Big Three Free Software Tools Supporting The Independent Research
- @Gary O'Neil, N3GO - 10 November 2019 : /g/nanovna-users/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 "well-known" 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# |
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#77: On the current explanation of full one-port "error" model
in our sow - facupov, as always - with an Application to the Measurements of Two-Port 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 one-port "error" model in our sow - facupov, as always. - - - - - - (c) gin&pez@arg (cc-by-4.0) 2019 : start - - - - - - In our sow, the full one-port "error" model is an Abstract or Virtual Two-Port 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 G-mini: G = (g-l)*(o-s)/[(g-o)*(s-l)-(g-s)*(l-o)] Therefore, using the above concepts, we can measure, indirectly - as in the case of one-port - : (a) either the S11, S12S21, and S22 parameters of any Two-Port Device appropriate to be connected by the one port of its two ports to the RLP of the V2P and/or (b) any unknown One-Port G' appropriate to be connected to the other port of this Two-Port Device, using this very same G-mini: G' = (g'-l')*(o'-s')/[(g'-o')*(s'-l')-(g'-s')*(l'-o')] - - - - - - - end : (c) gin&pez@arg (cc-by-4.0) 2019 - - - - - - REFERENCE [#74] The Virtual Port - "Revealing" the Most Confusing "Secrets" of "Error" Models - 7 November 2019 : /g/nanovna-users/message/6604 Sincerely, gin&pez@arg :77# |
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D.M.Kerns and R.W.Beatty : "An understanding of this introductory microwave
network analysis is essential to the serious worker in the ?eld 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. |
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#78: on the measurement of s-parameters using the [LeastVNA] only
- 12 November 2019 - /g/nanovna-users/message/6912 - Hello, Allow us, please, to inform you that we just uploaded the (indirect) "measurements" of S11, S12S21, S22 of an unknown 2-port connected to the [LeastVNA], as well as the (indirect) "measurement" of GL of an unknown 1-port connected to this 2-port, at: 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 2-port, respectively, while G is the [LeastVNA] measurement of the GL connected to the same Load Port of 2-port. Notably, only one-port reflection measurements are involved. Sincerely, gin&pez@arg :78# |
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#78' : #78 was corrected :
- #78: on the measurement of s-parameters using the [LeastVNA] only 18 November 2019 - /g/nanovna-users/message/7162 |
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#79: Three Animated-GIF/AVIs in Slow Motion Demonstrate,
Step-by-Step, 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 Animated-GIF/AVIs in slow motion demonstrating, Step-by-Step, the graphical construction of the differential Error regions arising in the Measurements with [AnyVNA], at: 1/3 2/3 3/3 Sincerely, gin&pez@arg :79# |
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#78'' : #78' was re-corrected :
- #78' : #78 was corrected : 19 November 2019 - /g/nanovna-users/message/7185 #78: on the measurement of s-parameters using the [LeastVNA] only 18 November 2019 - /g/nanovna-users/message/7162 - :78''# |
gin&pez@arg