On Mon, 23 Sep 2019 at 21:04, alan victor <avictor73@...> wrote:
Hello Reg,
I brought up this question of uncertainty in measurements several posts
ago. Although the calculation is not complicated, obtaining the parameters
to find the uncertainty boundaries is a task.
The easiest one to address is S11 and there are papers published by NIST
and the Automatic Radio Frequency Test Group (IEEE) that have addressed the
exact calculations. I'll see what I can find and can post.
I was unclear what the gentleman in this thread were requesting, but I
believe it is the same information required to calculate the uncertainty
error for any VNA measurement. For S11 this would include the directivity
errors, the reflection tracking errors and the source match errors. These
are exactly the three of the five elements posted by the NanoVNA after a
cal is complete for S11 only. Additional ones come into play for S21 cal.
Hence the measurement uncertainty in S11 is a function of these three
LINEAR values which we must obtain (somehow) from the NanoVNA architecture;
i.e. the bridge and the mixers.
Once these values are in hand, it is possible to find the difference
(error) between the measured S11 and the actual.
For S11 we would find that the difference between the measured and the
actual S11 or (S11M-S11A) is given by DELTA(S11) as follows:
DELTA(S11)=(S11M-S11A ) ~ D + TR * S11A + MS * S11A^2
D is the directivity errors, TR is the reflection tracking errors, MS is
the source match errors.
Hence, devices with small reflection coefficient, the D value is the
source of the major error. While the devices with large reflection
coefficient, source match is a most significant error.
This is a very terse answer to a subject that is well documented but not
easy to answer in a brief email.
Hope this sheds some light.
Alan
I don¡¯t have the mathematical abilities for this, but I don¡¯t think this
is an easy problem to address, as finding out the magnitude of the
different errors (eg source match, directivity errors etc) is not trivial
without some items that will cost more than a NanoVNA.
However, I do know some of the techniques used, the institutions doing
work in this area, as well as the name of a couple of helpful people who
maybe able to give advice. I will list these in the order I think of them,
rather than any more logical order.??
1) I am aware that the Swiss standards laboratory METAS is doing a lot of
work on VNA measurement uncertainty. They have a tool for this
Their algorithms are purchased. Google
VNA uncertainty METAS
2) There is also a lot of work on this area at the National Physical
Laboratory (NPL) In the UK.
Google
VNA uncertainty NPL
3) Although the first paper I found on this topic is about waveguide
calibration, so is not particularly relevant here, it does contain the
email address of the person leading this work at NPL, who is *Nick Ridler. *
I spoke to Nick at one of the Keysight meetings on THz measurements. He was
very helpful about what I asked him about. (As a side note, I recall being
quite impressed to see a piece of rectangular waveguide Nick bought along,
about 100 mm long, where the cross section of the waveguide is so small
that I thought it was a spec of dust. ???)
4) Precision airlines, which are lengths of transmission line, very close
to 50 ohms, are usually used for determining the error terms. The
techniques for this are well documented.
5) Airlines for 3.5 mm, which is physically compatible with SMA, are
readily available on eBay , (I have some myself as part of an HP 85053B VNA
verification kit). The 3.5 mm airlines tend to be quite short in length,
limiting their use to high frequencies.
5.5) In my opinion, for one interested in obtaining the best performance at
modest cost, it is best to test with APC7 connectors. They are very high
precision connectors, better than N or SMA, yet since they are not used
much nowadays, they can be found quite quite cheap.
6) 7 mm (APC7) airlines are readily available at modest prices on eBay.
They can easily be obtained at up to about 300 mm in length, but they still
cost more than a NanoVNA. Prices of these tend to vary dramatically, but if
one waits, one will find them for a few tens of dollars.
6.5) The best APC7 airlines don't have connectors on them, but are
supported by a test port at one end a short with a hole at the other end.
The centre conductor is stored in a via. These are often sold as ¡°tested¡±
on eBay, despite they have no centre conductor included, so are of no use.
Slightly inferior airlines have connectors on them and the centre conductor
can not be removed or lost. I would personally buy these, as the other type
are difficult to handle. I have them in one of my VNA verification kits,
These can be found at reasonable price on eBay, but often are missing a
floppy disk.l That makes them totally useless for their intended purpose,
as does the S/N of any part being different from that on the floppy disk.
If you see such a kit, you can tell the seller that, and can potentially
pick up a couple of airlines very cheaply.
7) A technique known as the T-checker,
can be used to verify the calibration accuracy of 2-port measurements. This
makes use of a mathematical property that relates the 9 S-parameters of a
lossless 3-port network. One of the ports is terminated in an arbitrary
impedance, the measurements made at the other two points, then a simple
scalar parameter is computed. *This is a very cheap technique to use*,
requiring nothing more than a coaxial T piece, but it only verifies the
calibration - it tells you nothing about the sources of error.
I am unaware of any standalone programs that can take a Touchstone file
around generate the T- check formula, but it would not be rocket science to
write one. M
8) Kurt Poulsen, who is a member of this group, has done a lot of work on
calibration kits using the software designed for use with the VNWA. Perhaps
Kurt can provide links to the relevant documents he had written.
9) Unfortunately the VNWA software is closed source, but there are open
source versions of tools like optimisers in high school
10) There¡¯s going to be some discontinuity between SMA & APC7 adapters due
to the change in diameter of the lines. That will be less of an issue with
N to APC7, as there is little change in the diameter of connectors.
11) The components for APC7 calibration kits are quite inexpensive, but
still higher than a NanoVNA. APC7 loads with return losses of almost 50 dB
can be found for a few tens of dollars.
12) APC7 open standards fail into 2 types
* The simplest is just a tube that acts as a waveguide beyond cutoff. The
basic problem with this design is that the fringe capacitance varies
depending on how far the collet protrudes beyond the reference plane which
is not well defined.
* More sophisticated opens have a piece of plastic that pushes the collet
flush with the reference plane. The plastic adds capacitance, but at least
one then has a well defined geometry.
That¡¯s all I can think of just now.
--
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
