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#44 : Answers

@Gary O'Neil - Sun, Oct 6, 2019 at 05:28 AM:
/g/nanovna-users/message/4169

- also any other interested reader and/or contributor -

Dear Gary,

Once again : We are terribly sorry for this delayed
reply. However, our excuses remain constantly the
same : hard work. Please, accept our apologies.

Anyway, as we promised, here are our answers to your
specific questions:

1
The [ANALYSE] Tool (Documentation : PDF 2/15) is an
application software that we developed in order to control
through HP-IB and synchronize the overall operation of
the following five 5 different instruments:

(1) An HP8505A VNA

(2) An HP8660C Synthesized Signal Generator for PLL

(3) An HP5340A Frequency Counter in order to achieve
100 Hz frequency accuracy

(4) A step-motor, extracted from a big printer, as well as
a motor controller, which we built to be used for antenna
radiation/pattern measurements, and

(5) the computer we used to collect the indications of both
magnitude/amplitude/modulo or what other name and the
phase/argument can be used for all of them.

Thus, it was indeed a software tool designed and developed
for our automatic VNA measurement system and it is of course
independent of the rest of our work for our definition of DERs
and DEIs, as well as their determination.

Nowadays we see that VNAs use different ways to communicate
with the user and to give their data. For example we took the
[NanoVNA] data with the [Putty] via the USB interface.

This is all the reasons of why we do not describe in details this tool.

2
The 4 files [SH.SC], [OP,OC], [LD.LD], and [ME.ME] are the four
4 needed measurements in 101 frequencies, from 600 to 1000 MHz,
with a 4 MHZ step, for a ground plane antenna, as we have already
mentioned. The first three 3 are for the calibration with the "known"
SLO "standards" and the last one is the measured indications of the
antenna. All these text files have the same simple format:

frequency [MHz] - magnitude [dB] - argument [degrees]

The number of digits used are what we have from our measurement
system. And since these files are text files we can easily change their
format.

And we indeed changed recently the frequency format, since the
frequency counter we have now available can not give us -at least for
the moment- the 100 Hz accuracy we had 10 years ago - only 10 KHz.

Note: All the measurements in all of our presentations in ANAMET
- Automatic Network Analzer Metrology Club of NPL - or in our papers
were taken in CW mode, while we haven't used yet our [NanoVNA]
in CW mode.

3
The so-called system "errors" (D,M,R) or (Ed, Es, Er)
or (D,S,R) or whatever else other name, are just intermediate
complex variables and that is why we do not included an
output file for them. But we could add one easily, of course,
if there is such a need.

4
The well-known full one-port "error" model was adopted,
and the well-known relation of the bilinear transformation
was used * w i t h o u t * any simplification or term
elimination. All the involved quantities are in the complex
plane.

5
The method of determining an uncertainty estimation
in the reflection coefficient of the full one-port DUT, or of
any other quantity or "quantity" that is dependent on the
reflection coefficient such as e.g. the input impedance,
is based on the usual total differential laws as we applied
them in this specific case of complex functions of many
complex variables.

6
As we already mentioned elsewhere in our messages to
the group:

In order to keep the relations general the capital letters
A,B,C was used for the three "standard" loads for the
calibration and the three small letters a,b,c for their
corresponding measurement indications. Thus for a SLO
calibration we have - once again:

A = S = -1 (magnitude 1, argument 180 degrees),

B = L = 0 (magnitude 0, argument undetermined), and

C = O = 1 (magnitude 1, argument 0 degrees).

For their uncertainty we have - once again :

S : -0.01 for magnitude, +/-2 degrees for argument,

O : -0.01 for magnitude, +/-2 degrees for argument, and

L : 0.029 for magnitude, none for the undetermined argument

For the measurement inaccuracies, we used for all the four
4 measurements s, l, o, m:

+/-1 digit of the LSD for both magnitude and argument
readings or indications.

Thus, the uncertainties of the "standard" loads and the
inaccuracies of the measurements are all in the complex plane.

7
The final estimated uncertainty for reflection coefficient
of the DUT is the Differential Error Region DER in the
complex plane for each frequency with the corresponding
Differential Error Intervals DEIs for real and imaginary parts
in the Cartesian form, as well as and the DEIs for the
magnitude and argument in the Polar form.

Maxima was used basically for that presentation in ANAMET
and especially for the DERs, since for the DEIs any program
that plot points and lines can be used. But the plotting of a
DER needs a special treatment in order to correctly combine
rather many straight lines and circular arcs and thus it is
more tedious to be drawn.

Details for the DERs and DEIs are given in our papers and
thhree ANAMET presentations.

Please, stay tuned !

Best regards,

73

nikolitsa oe3zgn|sv7dmc & petros oe3zzp|sv7bax @ arg iaoi nfi

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