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Jim,

Do you refer to John Taylor's "An Introduction to Error of Analysis"?
That's the text that I used in college, and the photo on the cover is so
great that I have a framed poster of it on a wall in my lab.

DaveD
KC0WJN


On Sun, Jan 26, 2025 at 15:40 Jim Lux via groups.io <jimlux=
[email protected]> wrote:

Probably not 12. :)

But really, let’s look at it.
Reflection coefficient is what? <0.005 or <0.0025?
Rho= (Z1-Z2)/(Z1+Z2)
So we’re looking at about 3 or 4 digits, which is pretty good.

The challenge would actually be the uncertainty in the connector mate.
About 25 years ago I was developing a noise source for calibrating a
precision receiver at 13.402 GHz. We wanted to measure the transmitted
power from the QuikSCAT satellite at a ground station to tenths, if not
hundredths of a dB, so the whole system was an exercise in driving
uncertainties down everywhere in the system.

We sent it off to NIST to test on their fancy calibration system (They
published a paper about it, along with some other sources). As I recall,
the mate/remate uncertainty (for lapped and pinned wr-62 waveguide) was
given as a few Kelvins out of 7000K for the source, and can fairly be
called state of the art. That’s about 4 digits, maybe 3.5. That’s power,
not voltage.

I’d say that anyone claiming a measurement uncertainty for an absolute RF
power measurement (which is what VNAs basically do) of better than 1E-4
(linear) is probably stretching. One can do more accurate relative
measurements, of course, particularly if the system doesn’t change (no
mate/demate).

So
A) the fact that we know some physical constants (Z0 of free space, speed
of light) to a lot of digits is a testament to some experimentalists
ingenuity and attention to details.
B) lots of digits is not worth worrying about in day to day, or even
unusual, applications.
C) Understanding uncertainty is important, even if you don’t do it in a
formalized way. (There is a whole book and standard on this, of course).

Just for folks contemplating pushing the limits - don’t forget things like
solid earth tides and relativistic corrections. (See project GREAT as a
demonstration of general relativity). In reality, just dealing with the
temperature cycling from the HVAC in your lab will be the dominant source
for a lot of things.

And pushing the limits on uncertainty can be fun.

On Jan 26, 2025, at 12:01, ww6x via groups.io <ww6x=

[email protected]> wrote:

?If one were to buy an HP 909C with ISO IEC 17025 Accredited

certification (about $400 total), how many guaranteed decimal places would
that have?

--
ww6x

On Sun, Jan 26, 2025, at 10:41 AM, Jim Lux via groups.io wrote:
Indeed. Well, that’s, what, 1 part in 1E12?
There are relatively few things one can measure to that kind of
precision. In the Radio Science world, they measure the round trip
delay of a radio signal to Jupiter and back to a bit better than that.
One can build/buy a device that gets 1E-12 Allan deviation for time
over, say, 1000 seconds. See the time-nuts mailing list.

Voltage (and current) are a bit tougher, if only because finding a
standard to calibrate against is hard. 24 bit ADCs and DACs are fairly
common, and achieve relative accuracies of maybe 2^22. That’s a 1E-7
kind of uncertainty. But finding absolute voltage references is tough -
there are semiconductor band-gap references that are maybe 1ppm (1E-6).
Doing better as a primary standard would be a Josephson junction which
turns voltage into frequency, which can be measured quite accurately,
but the need for 4K temperatures makes that challenging. (See Volt-Nuts
mailing list - there could be tricks to get better)

On Jan 26, 2025, at 09:15, ww6x via groups.io <ww6x=

[email protected]> wrote:

?The impedance of free space is Z? = 376.730313412(59) Ω. I, for one,

will not stand for any measurement with less accuracy.

--
ww6x

On Sun, Jan 26, 2025, at 9:00 AM, Jerry Stuckle wrote:

It is close enough for YOU. It is NOT close enough for everyone.

Measuring resistance to 4 or 5 digits is challenging with good repeatability. What’s the temperature coefficient of your unknown? What’s the tempco of your measurement system.

And of course, the DC resistance is related to, but not necessarily equal to, the RF impedance at other frequencies. That’s where the art of precision terminations is.

BTW, the specifications on things like terminations is more about the practical uncertainty of the manufacturing test set up. That’s why you see connectors specified as VSWR<1.03. In reality, they’re all a lot lower, but it’s a pain to measure in a manufacturing environment.

I suspect that other things in your VNA system would be larger contributors to uncertainty.
Mate/Demate is one of them. NanoVNAs don’t come with precision connectors like APC-7. And cable flex is another. Those $5000 cables for VNAs are partly because they’re reasonably phase stable with some amount of flex; and people still tape them down to the bench when making measurements on multiple UUTs.

There is a whole literature and annual conferences on precision RF measurements. People devote their entire life to eking out the next digit.

For anything above 1 GHz (radio astronomy), I use the SMA standards which
are rated to 20+ GHz. I have both the N and SMA HP cal kits.

Dave - W?LEV



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On Sun, Jan 26, 2025 at 8:32?PM Team-SIM SIM-Mode via groups.io <sim31_team=
[email protected]> wrote:

Hi WW6X

HP 909 coax terminaison seems to be garanteed to 50 +/- 0.2 Ohm from DC
to 2Ghz , and it costs more than twice NanoVNA's .
For HF band it should have better accuracy .
Some resistor meters can have at least 4 significant digits accuracy
which allow to compensate error by reference load function included on
DiSlord FW 1.2.40 example : 50-->50.3 Ohm around 0.6% correction

73's Nizar.

--

*Dave - W?LEV*


--
Dave - W?LEV

Probably not 12. :)

But really, let’s look at it.
Reflection coefficient is what? <0.005 or <0.0025?
Rho= (Z1-Z2)/(Z1+Z2)
So we’re looking at about 3 or 4 digits, which is pretty good.

The challenge would actually be the uncertainty in the connector mate.
About 25 years ago I was developing a noise source for calibrating a precision receiver at 13.402 GHz. We wanted to measure the transmitted power from the QuikSCAT satellite at a ground station to tenths, if not hundredths of a dB, so the whole system was an exercise in driving uncertainties down everywhere in the system.

We sent it off to NIST to test on their fancy calibration system (They published a paper about it, along with some other sources). As I recall, the mate/remate uncertainty (for lapped and pinned wr-62 waveguide) was given as a few Kelvins out of 7000K for the source, and can fairly be called state of the art. That’s about 4 digits, maybe 3.5. That’s power, not voltage.

I’d say that anyone claiming a measurement uncertainty for an absolute RF power measurement (which is what VNAs basically do) of better than 1E-4 (linear) is probably stretching. One can do more accurate relative measurements, of course, particularly if the system doesn’t change (no mate/demate).

So
A) the fact that we know some physical constants (Z0 of free space, speed of light) to a lot of digits is a testament to some experimentalists ingenuity and attention to details.
B) lots of digits is not worth worrying about in day to day, or even unusual, applications.
C) Understanding uncertainty is important, even if you don’t do it in a formalized way. (There is a whole book and standard on this, of course).

Just for folks contemplating pushing the limits - don’t forget things like solid earth tides and relativistic corrections. (See project GREAT as a demonstration of general relativity). In reality, just dealing with the temperature cycling from the HVAC in your lab will be the dominant source for a lot of things.

And pushing the limits on uncertainty can be fun.

Hi WW6X

HP 909 coax terminaison seems to be garanteed to 50 +/- 0.2 Ohm from DC to 2Ghz , and it costs more than twice NanoVNA's .
For HF band it should have better accuracy .
Some resistor meters can have at least 4 significant digits accuracy which allow to compensate error by reference load function included on DiSlord FW 1.2.40 example : 50-->50.3 Ohm around 0.6% correction

73's Nizar.

If one were to buy an HP 909C with ISO IEC 17025 Accredited certification (about $400 total), how many guaranteed decimal places would that have?

--
ww6x

?Indeed. Well, that’s, what, 1 part in 1E12?
There are relatively few things one can measure to that kind of precision. In the Radio Science world, they measure the round trip delay of a radio signal to Jupiter and back to a bit better than that.
One can build/buy a device that gets 1E-12 Allan deviation for time over, say, 1000 seconds. See the time-nuts mailing list.

Voltage (and current) are a bit tougher, if only because finding a standard to calibrate against is hard. 24 bit ADCs and DACs are fairly common, and achieve relative accuracies of maybe 2^22. That’s a 1E-7 kind of uncertainty. But finding absolute voltage references is tough - there are semiconductor band-gap references that are maybe 1ppm (1E-6). Doing better as a primary standard would be a Josephson junction which turns voltage into frequency, which can be measured quite accurately, but the need for 4K temperatures makes that challenging. (See Volt-Nuts mailing list - there could be tricks to get better)

The problem with that, of course, from a basic error analysis perspective,
is that any other values used in any equation using a value of Z? with 12
(or 14) significant figures will probably have many less than 12 (or 14)
significant figures and will dictate that the result of the calculation is
only valid with the number of significant figures of the number in the
equation with the lowest number of significant figures. This is basic
proper error propation practice.

A trivial example:
In the expression

n = Z?/2.0 = 188.365156706,

where Z? is written as 376.730313412,

Strictly speaking, the "6.730313412" part of
376.730313412 is meaningless, since the value of the numerator only has two
significant figures. But we would allow 377/2, giving 188 (or 188.5, where
the general practice of allowing one extra significant figure in the result
is used).

(Lol. I'm not sure if I expressed that as concisely or correctly as
possible).

DaveD
KC0WJN


On Sun, Jan 26, 2025 at 12:15 ww6x via groups.io <ww6x@...>
wrote:

The impedance of free space is Z? = 376.730313412(59) Ω. I, for one, will
not stand for any measurement with less accuracy.

--
ww6x

On Sun, Jan 26, 2025, at 9:00 AM, Jerry Stuckle wrote:

It is close enough for YOU. It is NOT close enough for everyone.

The impedance of free space is Z? = 376.730313412(59) Ω. I, for one, will not stand for any measurement with less accuracy.

--
ww6x

It is close enough for YOU. It is NOT close enough for everyone.

ER calibration allow compensate DUT impedance mismatch in S21 measurements
But on H4 not allow fix Port 2 impedance mismatch due to memory limits (need additional space)

On LiteVNA and V2 implemented full ER calibration
Also possible use external software like last NanoVNA-App or NanoVNA Saver (ER calibration used by default)

Hi Roger

I just test it by my H4 + V 1.2.40 and reference load change on Calibration submenu can take any time we want after or before calibration , so no care about when it's done , great facility to use it any time we want without need to calibrate again . Wonderfull .
but enhanced response option is still unknown for me , what can be ?

73's Nizar

Hi Roger

I appreciate a lot your simple accuracy improvement methode for who are interested , knowing that having a good accurate SMA 50 Ohm load will cost much more then all NanoVNA's prices in the market , compared of a free firmware refrence load calibration , I think its a great option added by Dislord to the sheap NanoVNA's, Thanks .
73s. Nizar

Hi Roger

Thanks for your methode clarification, using external good multimetre to measure on DC mode the refrence load value , i am agree also with Dave that simple DC resistor measurement by a digital multimeter is not so sure for all users and Dave gives some measurements examples with its three different DMM , but some specific resistor measurement instruments are accurate enought using 4 cables for accurate resistor measurement , it can be a good start point for an accurate calibration not needed for most users on this group..

Accurate measurements is olso a Hobby on it self, Hi Hi Hi , DiSlord firmware has added two different kind of reference load change the one on Display menu subitems that affect only graphics and some function displays as SWR ., Smith ... Thats one i have used for my 75 Ohm coaxial .. And a second one embedded on the Calibration Submenu , its what Roger use for more accurate impedance measurement, its also a great option added improve accuracy, Please Roger, just i am wondering if this reference load change 50 -->> 50.9 Ohm used for calibration, did should be set before calibration or no matter before or after ?

Dave thanks for your precious contribution as a moderator of this group and as an experienced RF man , as well as Roger , Stan , DiSlord and many others.
73s Nizar

Roger Need:

Sorry if I stomped on your toes. PLEASE continue reading.

What you don't know is I am also a professional EMC/RFI engineer with a lot
of time spent in RF/uW design and test and designing, building and
evaluating antennas. I've "usually" worked as an EE, but my degree is in
physics. I also have a good collection of professional RF/uW test
equipment to compare the NANOVNAs and TINYSAs to those instruments - they
compare embarrassingly well!

No this group is not all "amateurs", but many are. I see more and more
hams using the NANOVNAs and TINYSAs and asking for help on this and other
groups which ARE devoted to amateur, but.....we have a few non-hams and
lots of non-professionals in those groups as well. I salute those efforts
and I aim wherever I can to answer questions and help those who have never
used either of the two instruments. I've been at home with spectrum
analyzers and vector network analyzers (and a lot more!!) for over 40
years. I'm now retired at 78 YO. I have my own 8753C with S-Parameter
Test Set and all the SMA and type-N HP cal standards and most of the other
RF/uW test equipment to my back as I write.

My physics training probably motivated me to cite the three measurements of
the HP cal standard with three DMMs. The labs I took while in college
required error analysis and attention to significant figures. They also
required a course in the calculus of variations. It's in my blood.
Forgive me. That, along with proper abbreviations of all things RF and in
the other hard sciences.

All the groups to which I subscribe and contribute (helping others) have a
mix of hams, non-hams, and professionals (of which I am). So, please cut
us some slack..........PLEASE?

Forgive me. This email is far more pointed and critical than I usually
write. But, yes, I'm offended as a fellow moderator of this group.

Dave - W?LEV

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Virus-free.www.avg.com
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On Sat, Jan 25, 2025 at 6:38?PM Roger Need via groups.io <sailtamarack=
[email protected]> wrote:

On Sat, Jan 25, 2025 at 09:30 AM, W0LEV wrote:

Again, remember, we are "amateurs". We do not run a metrology lab (well,
maybe one or two of us might?). 50.86-ohms DC resistance is plenty good
enough.


The number of significant digits directly reflects what is displayed by
each of the DMMs. Which is correct? I SERIOUSLY doubt the differences
would be of ANY significance in amateur radio work!

Dave,

You are making a blanket statement when you say we are all "amateurs" here
or talk about "amateur radio" work. This is NOT an amateur radio group.
There are many of us in the group that are professional RF engineers or
technicians and we strive to get the best performance possible out of the
NanoVNA. If it were not for people like DiSlord (firmware), Zareth and
Rune ( NanoVNA Saver) and OneofEleven, Owen Duffy and DiSlord (NanoVNA app)
striving to squeeze the best accuracy and features from the NanoVNA we
would not have the exceptional device we are using today.

And some of us do own test equipment that can measure resistance to
several decimal places with digits that are significant.

So if you don't wish to achieve the best accuracy possible with the
device that is your choice but please enough with these
"we do not run a metrology lab" comments that you make from time to time.
It is discouraging and dismissive to those of us trying to show how the
NanoVNA can be used to its full potential.

Roger Need

--

*Dave - W?LEV*


--
Dave - W?LEV

I'll go with Dave, horseshoes, hand grenades, and nuclear bombs, close IS good enough for these devices AND our devices. AMEN

Mike C. Sand Mtn GA

On Sat, Jan 25, 2025 at 09:30 AM, W0LEV wrote:

Again, remember, we are "amateurs". We do not run a metrology lab (well,
maybe one or two of us might?). 50.86-ohms DC resistance is plenty good
enough.


The number of significant digits directly reflects what is displayed by
each of the DMMs. Which is correct? I SERIOUSLY doubt the differences
would be of ANY significance in amateur radio work!

Dave,

You are making a blanket statement when you say we are all "amateurs" here or talk about "amateur radio" work. This is NOT an amateur radio group. There are many of us in the group that are professional RF engineers or technicians and we strive to get the best performance possible out of the NanoVNA. If it were not for people like DiSlord (firmware), Zareth and Rune ( NanoVNA Saver) and OneofEleven, Owen Duffy and DiSlord (NanoVNA app) striving to squeeze the best accuracy and features from the NanoVNA we would not have the exceptional device we are using today.

And some of us do own test equipment that can measure resistance to several decimal places with digits that are significant.

So if you don't wish to achieve the best accuracy possible with the device that is your choice but please enough with these
"we do not run a metrology lab" comments that you make from time to time. It is discouraging and dismissive to those of us trying to show how the NanoVNA can be used to its full potential.

Roger Need

Again, remember, we are "amateurs". We do not run a metrology lab (well,
maybe one or two of us might?). 50.86-ohms DC resistance is plenty good
enough.

And consider the accuracy of the DMM with which you measured that 50-ohm
calibration source at 50.86-ohms. For example, I have three DMMs handy on
my electronic workbench. I measured one of my HP 909C type-N calibration
standards with each of those three DMMs. Here are the results:

1) 50.279 Ohms (an HP benchtop DMM)
2) 50.1 Ohms (an older Sperry DMM)
3) 50.2 Ohms (a "cheap" Harbor Freight DMM)

The number of significant digits directly reflects what is displayed by
each of the DMMs. Which is correct? I SERIOUSLY doubt the differences
would be of ANY significance in amateur radio work!

Dave - W?LEV

On Sat, Jan 25, 2025 at 4:59?PM Roger Need via groups.io <sailtamarack=
[email protected]> wrote:

The ability to enter the value of the load resistance is only used to
increase the accuracy of calibration. Small deviations from 50 ohms can
then be compensated for. The cal load supplied with my NanoVNA measured
50.86 ohms at DC so I used that as my entry.

I find this feature gives me more accurate impedance measurements but it
does not significantly affect SWR.

--

*Dave - W?LEV*


--
Dave - W?LEV

The ability to enter the value of the load resistance is only used to increase the accuracy of calibration. Small deviations from 50 ohms can then be compensated for. The cal load supplied with my NanoVNA measured 50.86 ohms at DC so I used that as my entry.

I find this feature gives me more accurate impedance measurements but it does not significantly affect SWR.

Hi

Roger , we can measure the real coaxial caracteristic impedance by DiSlord coax function with more accuracy then the commercial announced value for our specific portion of cable to be used example 77.7 Ohm instead of announced 75.0 Ohm , and then enter this value on the 50 --> Zc=77.7 reference change then we can mesure SWR , return loss .. ect on this portion of cable with more accuracy .

but please can you clarify us more how you can measure impedances with more accuracy with your new method ? it's a little bit confused for me . an example with screenshoots can help a lot, Thanks .

73's Nizar