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In an older post,(I now fail to find), Kurt explained it is possible to use, after calibration, a long high quality coax to test and improve the correction factors of the calibration standard.
So here I am trying to set this up (while learning GNU octave at the same time).
I calibrated and subsequently measured a 1 meter coax with both open and short at the end.
The blue lines give the magnitude over frequency (0.5 till 900MHz over 1020 points) of the long coax with both the open and short measurement (I assume the down angle is caused by energy absorption in the coax and thus linear and it should be a straight line) and the red lines give the angle variations (after correcting with a polyfit assuming a constant angle/Hz), again this should be a straight line
Next step would be to do a least squares fit using the C0,C1,C2 for open and L0,L1,L2 for short and the length of the short/open to get a perfect straight lines for the magnitudes and angles
I can share the octave scripts I have created thus far
Any feedback if this approach might work?????

Doing a manual optimization using
openC0=300e-15 F
openC1=-250e-24 F
did result in an reduction of the amplitude variations (blue lines, see attached picture)
Changing shortL0 seemed to have a similar impact as openC0 so I do not know how to reduce both amplitude and phase variations (red lines)

On Sun, 27 Oct 2019 at 15:34, <erik@...> wrote:

In an older post,(I now fail to find), Kurt explained it is possible to
use, after calibration, a long high quality coax to test and improve the
correction factors of the calibration standard.
So here I am trying to set this up (while learning GNU octave at the same
time).
I calibrated and subsequently measured a 1 meter coax with both open and
short at the end.
The blue lines give the magnitude over frequency (0.5 till 900MHz over
1020 points) of the long coax with both the open and short measurement (I
assume the down angle is caused by energy absorption in the coax and thus
linear and it should be a straight line) and the red lines give the angle
variations (after correcting with a polyfit assuming a constant angle/Hz),
again this should be a straight line
Next step would be to do a least squares fit using the C0,C1,C2 for open
and L0,L1,L2 for short and the length of the short/open to get a perfect
straight lines for the magnitudes and angles
I can share the octave scripts I have created thus far
Any feedback if this approach might work?????

You really don't need to worry about the inductance of a short. Neither my
20 GHz HP 8720D, nor the 40 GHz version, the 8722D, have the ability to
enter the coefficients of the inductance. So really it is a waste of time
on a 1 GHz VNA. It is true that home-built standards are likely to have
more inductance than professional ones, but in my experience at least, it
is unnecessary at 1 GHz.

The small inductance can be compensated for by a *slight* adjustment in the
offset delay of the short. If I look at the offset delay of the short of
the 85052B 3.5 mm cal kit on my 8720D, the value is* 31.798* ps (see
picture), with no ability to specify L0, L1, L2 and L3. If I look at the
Keysight website for the same kit



the offset delay is 31.785 ps, with values for L0, L1, L2 and L3. So
basically adding 0.013 ps to the delay is fine for a 20 GHz VNA with a
26.5 GHz cal kit.

For the 3.5 mm kit, the coefficients for male and female parts are the
same. For N cal kits, that is rarely the case.

I just checked the delays of the shorts for the 85054B 18 GHz N cal kit in
my VNA,

Female short 28.003 ps - Keysight website says 27.990 ps
Male short 63.106 ps - Keysight website says 63.070 ps.

So I would argue, just specifying an offset delay of the short is fine, and
there's no need to specify L0, L1, L2 and L3. Even if the user just takes
the data from the Keysight website, and does not adjust it at all, the
difference at 1 GHz is irrelevant.

I too need to learn Octave. I use Mathematica, but want to get away from
this proprietary stuff.

You don't say what values you are using for the delay at any point. Are you
considering that?

On Sun, 27 Oct 2019 at 16:02, <erik@...> wrote:

Doing a manual optimization using
openC0=300e-15 F
openC1=-250e-24 F
did result in an reduction of the amplitude variations (blue lines, see
attached picture)
Changing shortL0 seemed to have a similar impact as openC0 so I do not
know how to reduce both amplitude and phase variations (red lines)

Someone else (forget who), showed to my satisfaction at least, that there
was no need for anything beyond C0 for cal kits. He checked 3 kits I own

* 85054B 18 GHz N
* 85052B 26.5 GHz 3.5 mm
* 85050B 18 GHz APC7.

He used some Octave code which showed that for those cal kits at least,
there was no point having any more than C0, as the effects of C1, C2 and C3
are smaller than the uncertainties of the calibration kits.

Your value of 300 fF for C0 seems large. I would expect that to be below
100 fF for almost any kit.

I suspect you are ignoring the offset length, and trying to do it all with
a capacitance, which will not work.

Dave

On Sun, 27 Oct 2019 at 17:01, Dr. David Kirkby <
drkirkby@...> wrote:

On Sun, 27 Oct 2019 at 16:02, <erik@...> wrote:

Someone else (forget who), showed to my satisfaction at least, that there
was no need for anything beyond C0 for cal kits. He checked 3 kits I own

* 85054B 18 GHz N
* 85052B 26.5 GHz 3.5 mm
* 85050B 18 GHz APC7.

He used some Octave code which showed that for those cal kits at least,
there was no point having any more than C0, as the effects of C1, C2 and C3
are smaller than the uncertainties of the calibration kits.

I should have added, that there is possibly some point in including C0, C1,
C2 and C3 on homemade cal kits, but not inductance coefficients.

Did not yet try to optimize the delay. Will try
The low frequency phase wobble reduces substantially if I use loadR=50.7
Could that be the actual impedance of the coax? Or is that the value where the bridge is in balance?
I am using the default nanoVNA load for calibration and this is rather accurate

Well, the delays did not work as expected.
So I'l formulate my tuning question a bit more to the point.

The green line in attached picture shows the outcome of this formula "phase(S11open) - phase(S11short) - pi" of a 1 meter coax cable versus the frequency (0.5 till 900MHz)
The phase is unwrapped to avoid discontinuities.
The line should be flat on 0 independent of the frequency but it is not. 0 means the S11open and S11short are exactly opposite on the smith chart

What parameter of a generic VNA calibration set or bridge imperfection model will allow tuning away the green error at higher frequencies? So the parameter should have an increasing impact on phase errors on higher frequencies and not on amplitude or low frequency phase errors?

As you can see the tuning for the amplitude is progressing rather well. The blue lines show abs(S11open) and abs(S11short)

And I would be most happy if someone can explain how to modify global variables (without a "clear all") from a function as I fail to find how?????

Erik,

Did you take a look at what I did in the following post and the subsequent posts in that thread? This involved trying to fix a poor BNC short and open.

/g/nanovna-users/message/4963

I think this is related to your question.

--
Bryan, WA5VAH

In an older post,(I now fail to find), Kurt explained it is possible to use,
after calibration, a long high quality coax to test and improve the correction
factors of the calibration standard.

You may have read my interpretation (#3515) of page 3 in:


... which now states:
"Providing your short and open calibration standards are well defined (like the Rosenberger kit from SDR-KITS)
incl. the precise value of the load resistance (which is measured by SDR down to 0.01ohm accuracy)
there is only one source for fine tuning and that is the fringe C of the load which varies from one example to another."

.. and Kurt suggests tweaking that to minimize oscillations in
"a S11 dB trace with e.g. 0.2dB per division (the first red trace) which is oscillating across the frequency range"

I sort of confirmed that for myself, using 2m LMR-400..

On Sun, 27 Oct 2019 at 19:15, <erik@...> wrote:

Well, the delays did not work as expected.
So I'l formulate my tuning question a bit more to the point.

The green line in attached picture shows the outcome of this formula
"phase(S11open) - phase(S11short) - pi" of a 1 meter coax cable versus the
frequency (0.5 till 900MHz)
The phase is unwrapped to avoid discontinuities.
The line should be flat on 0 independent of the frequency but it is not. 0
means the S11open and S11short are exactly opposite on the smith chart

Why should phase of S11 open and S11 short be 180 degrees apart?

Are just leaving open a bit of coax, then adding a short to it? If so, the
phase difference will not be 180 degrees due to the fringing capacitance of
the cable. That phase difference will increase with frequency. That's well
all well-engineered calibration kits have the offset delay on the short a
bit longer than on the open.

Dave

Why should phase of S11 open and S11 short be 180 degrees apart?

180 degrees is a good first approximation

The manual optimization took way too much time so I learned how to do non-linear least squares multiparameter fit in Octave. The created Octave scripts are attached. Loaddata.m loads the uncalibrated datasets. optim.m runs the optimization to minimize the residue (residue.m) by repeating calibration (calib.m) with tuned parameters. Don't complain about my ineffective use of Octave. This is my second day of usage.
With every optimization pass the updated calibration correction parameters are used to do a S11 calibration at reference plane and then the S11 open/short/load of a 1 meter coax is corrected using the determined calibration
The initial run delivers the first picture. This is the 1 meter coax after calibration at reference plane with uncorrected calibration parameters.
The target is to get a S11 open/short of a 1 meter coax to behave well, e.g. the abs(S11) should decent linear with frequency starting at 1 (red and green lines)
The blue line is the abs(error) for that frequency and as you can see the error is suggesting there is a very systematic error somewhere
Then I spend considerable time to have Octave search for the best calibration model correction parameters and I finally settled for only two: OpenC0 and OpenC1 (see second picture). The Load and Short Length did not make any relevant difference.
As you can see the error at lower frequencies is not reduced and it is almost as if the original non-corrected S11 open/short rotate with an constant offset. because their abs error rotates with constant amplitude and speed
So now I am stuck. There must be a systematic error the causes most of the observer errors in the 1 meter coax measurement but this error can not be optimized out with the current model I am using.
Any suggestions of what I am doing wrong?

I'm used average for calibration and it works great. But it takes more time for measurement. So I upload firmware with average, calibrate it with disconnected USB cable and then upload normal firmware. With such kind of calibration I got much better calibration with no random spikes. :)

These are 1020 point measurements. There are no spikes nor noise

On Tue, 29 Oct 2019 at 18:28, <erik@...> wrote:

The manual optimization took way too much time so I learned how to do
non-linear least squares multiparameter fit in Octave. The created Octave
scripts are attached. Loaddata.m loads the uncalibrated datasets. optim.m
runs the optimization to minimize the residue (residue.m) by repeating
calibration (calib.m) with tuned parameters. Don't complain about my
ineffective use of Octave. This is my second day of usage

What is on the y-axis of your graphs?

There's absolutely no way that C0 should be as high as 500. Someone
recently showed for that Keysight kits, having just a delay and C0 was
sufficient at 1500 MHz or so. So forget C1 for one minute, and just worry
about

1) Get the offset delay right - assuming C0=C1=C2=C3=0
2) Optimise for a value of C0

Look at the values on the Keysight website



to give you some idea of the typical values of C0. There are tons of kits
there, so I will list the first 3 I have, but plus one with a smaller
connector.


*85050B 18 GHz APC7. *
This since is genderless, there is no male or female.
C0=90.4799

*85054B 18 GHz type N*

C0=89.939 (male open)
C0=104.13 (female open)

*85852B 26.5 GHz 3.5 mm, so closest to SMA. *

C0=49.433 for both male and female.

*85056A 50 GHz 2.4 mm (I don't have such a kit, but I will just list it, as
its a smaller than 3.5 mm connector)*

C0=29.722 (male open), 29.72 (female open)

Your coax could have quite a loss at the top end, which means a complex
value (by complex, I do mean real and imaginary) of characteristic
impedance.

You would be better with a length of RG401 (6.3 mm OD), but if not, the
cheaper RG402 (3.5 mm OD). Those would have lower loss than your RG58.

But you seem to be ignoring any offset delay, and without that being
somewhere near correct, it is pointless worrying and C0, C1, C2 or C3.

What is your calibration standard? Is it the standard male open supplied
with the NanoVNA? If so, I could give you some sensible starting values.

Dave

--
Dr David Kirkby Ph.D C.Eng MIET
Kirkby Microwave Ltd
Registered office: Stokes Hall Lodge, Burnham Rd, Althorne, CHELMSFORD,
Essex, CM3 6DT, United Kingdom.
Registered in England and Wales as company number 08914892

Tel 01621-680100 / +44 1621-680100

David

You are very right. C0 is only that high after the optimization because of other problems but I can not find them.....

On Tue, 29 Oct 2019 at 19:41, <erik@...> wrote:

David

You are very right. C0 is only that high after the optimization because of
other problems but I can not find them.....

What are you using as the calibration standard that you are trying to
optimise? Are you trying to optimise the male open supplied with the kit?
Or creating a female open by putting that open on the end of an adapter? If
you are, remember that adapter supplied with most kits is very poor. I have
not measured the delay of it, but I would guess around 50 ps.


--
Dr David Kirkby Ph.D C.Eng MIET
Kirkby Microwave Ltd
Registered office: Stokes Hall Lodge, Burnham Rd, Althorne, CHELMSFORD,
Essex, CM3 6DT, United Kingdom.
Registered in England and Wales as company number 08914892

Tel 01621-680100 / +44 1621-680100

The vertical scale is the abs of the measured s11. Zero to one. Red an green lines
The pink line is S11 open phase minus S11 short phase minus pi.
What would the offset delay do to the rotation of S11 open and short. Would it impact the phase or also the magnitude.
Would it be constant shift or frequency dependent?

On Tue, 29 Oct 2019 at 20:11, <erik@...> wrote:

The vertical scale is the abs of the measured s11. Zero to one. Red an
green lines
The pink line is S11 open phase minus S11 short phase minus pi.
What would the offset delay do to the rotation of S11 open and short.
Would it impact the phase or also the magnitude.
Would it be constant shift or frequency dependent?

Hi,
I need to go out, so don't have time to re-arrange all these equations into
the form you want, but hopefully it will get you started.

A section of transmission line with a vacuum dielectric causes a phase
shift phi of

phi = 2*Pi*L/lambda

where lambda is the wavelength (metres), and L the length (metres).

The wavelength lambda = c/f where f is the frequency in Hz, and c the
velocity of light in a vacuum.

so phi = 2*Pi*L*f/c

*So the phase shift is directly proportional to frequency, and directly
proportional to the length of the line. *

Some manufacturers of cal kits use a length (e.g. Rohde and Schwarz), and
others a delay (e.g. Keysight). They are related by the velocity of light
in *vacuum*, not air or the dielectric. That's the convention used - it is
obviously not realistic in practice.

The delay d (seconds) of that transmission line lf length L is L/c, where c
is the velocity of light in vacuum.
e.g. 30 ps is 8.9938 mm.

So the phase shift phi is proportional to frequency, and proportional to
the delay. Obviously you get phase wrapping too, but that's another issue.

If those don't make any sense, I would have screwed up somewhere.


--
Dr David Kirkby Ph.D C.Eng MIET
Kirkby Microwave Ltd
Registered office: Stokes Hall Lodge, Burnham Rd, Althorne, CHELMSFORD,
Essex, CM3 6DT, United Kingdom.
Registered in England and Wales as company number 08914892

Tel 01621-680100 / +44 1621-680100