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On Sat, Jan 4, 2020 at 03:55 PM, gin&pez@arg wrote:

Hi gin&pez:

After that said, also allow us, please, to consider now that our way to use
this mathematical model, that is * w i t h o u t * the introduction of additional mathematical
expressions, is by this very fact the most simple way to confront with this really existing issue
- which by way, it also covers the non-default operation of your VNA - simply because our way
covers the measurements by * a n y * VNA.

What additional mathematical expressions are you referring to?

If this is your mathematical model:

G = (S*(L-O)*(g*s+l*o)+L*(O-S)*(g*l+o*s)+O*(S-L)*(g*o+s*l))/
((L-O)*(g*s+l*o)+ (O-S)*(g*l+o*s) + (S-L)*(g*o+s*l))

Then, to create *accurate* representations of S. O. and L, you must derive the values of S, O, and L in a similar fashion to how they are derived for any other VNA that uses the standard 3-error-term one-port calibration technique. Are these SOL calculations the additional mathematical expressions you are referring to?

And at this very point also allow us, please, to emphatically declare that we
don't find anything erroneous in our point of view, that is the one From A Common User
Point of View FACUPOV, since we already looked ahead to exclude VNA cases in which this
default operation it is not their default. Our claim still holds for all those
still existing VNAs which do consider by default such an Absurdness.

Finally, allow us, please, to also emphatically say that * I F * after all
that provisions of your VNA, the unknown load value is still * c o m p u t e d * using the
expressions which are consequences of this very net linear S-parameter model,
* T H E N * you have not get rid off the Core Uncertainty of the Measurement still existing :
(a) in your Standards,
as well as (b) in the inaccuracy of your VNA readings.

My apologies, I do not understand the point you are trying to get across with the above two paragraphs.

So perhaps it would be better if I state my point-of-view:

Your equation (which is very elegant, congratulations!):
G = (S*(L-O)*(g*s+l*o)+L*(O-S)*(g*l+o*s)+O*(S-L)*(g*o+s*l))/
((L-O)*(g*s+l*o)+ (O-S)*(g*l+o*s) + (S-L)*(g*o+s*l)),
is, at its essence, a function of G in terms of 7 variables, those variables being: s, o, l, S, O, L, and g.

The well-known 3-term error model for one-port calibration consists of 4 equations (equations 1, 5, 6, and 7 here: )
Note that when equations 5, 6, and 7 are inserted into equation 1, the result is a function of G in terms of 7 variables. And those seven variables are the same as your equations's seven variables: s, o, l, S, O, L, and g.

If you then assign values to s, o, l, S, O, L, and g, and solve either your equation or the equations that represent the 3-term error model, you will get the *same* answer for G.
See: /g/nanovna-users/message/8569

So -- we have the same input variables, and we have the same result. This implies, to me, that your equation and the equations representing the 3-term error model are functionally equivalent. My guess is, some smart person (not me) could take the equations that represent the 3-term error model and manipulate them so that the resulting equation is equivalent to your equation.

When you mention "expressions which are consequences of this very net linear S-parameter model", and then you state that, because of this S-parameter model, "you have not get rid off the Core Uncertainty of the Measurement still existing : (a) in your Standards, as well as (b) in the inaccuracy of your VNA readings", I become confused. Are you stating that the 3-term error model has uncertainties and inaccuracies that your equation does not have?

I'll point out again -- both your equation and the 3-term error model use exactly the same variables, and both generate exactly the same result when values are substituted for those variables.

Therefore, to my mind, both your equation and the 3-term error model's equations must have exactly the same uncertainties and inaccuracies.

Anyway, after all that said, may we ask you now, please:

- Do you ever wondered why your VNA still leaves this Absurdness available to
its user ?

My apologies, gin&pez, but I do not know what absurdity you are referring to.

- Do you ever wondered how its measurement is finally extracted to be
presented to the user ?

If you are asking me if I know how my VNA calculates S11, the answer is yes.

Best regards,

- Jeff, k6jca