开云体育

23 : On the Uncertainties of the "Standards" - Part I

@ Jeff Anderson : /g/nanovna-users/message/3294

Hello,

Thank you very much for your most encouraging message !

We much appreciate your interest in our work - thank you.

We also thank you for your most valuable * s p e c i f i c *
inquiries regarding it, by which you give us the chance to
explain it, from a common user's point of view, facupov, as
we always try to do.

Regarding your first question:

JA : "... you mention that the S and O standards have 2
uncertainties each (while the load has 1 uncertainty).
How are you defining these uncertainties? "

- (c) gin&pez@arg (cc-by-4.0) 2019 : start -

allow us, please, to answer its last part as follows:

We are not defining the uncertainty of any "standard".

If the manufacturer of a "standard" is a decent one
then he defines its uncertainties, so we could reservedly
adopt it as a 'standard' and proceed in our measurements
with it.

A "standard" without uncertainties is nothing else than
a load with a nominal value, that is one named with a
value: e.g. a "standard" of 50 Ohm is just a load of which
its "true value" is somewhere near by 50 + j0 Ohm.

How much near by?

As much as it is defined by its manufacturer. If he did not
define how much it is, then we don't know how much.

In this, most reasonable way, we could reservedly adopt
as a 'standard' at DC any common resistor part on which
its manufacturer has put -usually by coded colors-
its nominal value in ohms and its tolerance as an
implicitly minus/plus percent of its nominal value in ohms,
that is : its nominal value and its uncertainty, e.g. as
47 Ohm and 10%, which results, instead of a single
"true value", in unaccountably many values, which they
lie between the lower value or bound of:

42.3 Ohm = - 10% x 47 + 47 Ohm = - 4.7 + 47 Ohm

and the upper value or bound of:

51.7 Ohm = 47 + 10% x 47 Ohm = 47 + 4.7 Ohm

or which they lie in the true closed interval of values

[ 42.3 , 51.7 ] Ohm

Therefore, allow us, please, to think that this example
is most than adequate to show the way in which the
Uncertainty is defined facupov for this resistor in DC:

This is exactly these two 2 values or two 2 errors in
the "true value" of 47 Ohm:

the lower error or value -4.7 Ohm and

the upper error or value of +4.7 Ohm

where, also notice that, please, in this case
these two 2 errors lie symmetrically to the
center value of 47 Ohm.

It is very important for our duty of supporting
the true -without putting it between double " "
or single quotation marks ' '- understanding
of our work to conclude the subject with this
"footnote":

This resistor can be also be considered as a
'standard' with a "true value" of 50 Ohm and
an uncertainty expressed by the two 2 error
bounds of -7.7 Ohm and +1.7 Ohm, for the
lower and upper ones, respectively, and
especially : non-symmetrically, simply because
its "true value" of 50 Ohm with its unsymmetrical
Uncertainty [ -7.7 , +1.7 ] Ohm results in exactly
the same invariant interval for the values of this
resistor : [ 42.3 , 51.7 ] Ohm, as it is defined by
the initial "true value" of 47 Ohm and its
symmetrical Uncertainty [ - 4.7 , + 4.7 ] Ohm.

Finally, a Warning Sign in capitals for the Common User:

THE DECENT MANUFACTURER HAS THE KINDNESS
TO SUPPLY THE UNCERTAINTY INFORMATION IN
ORDER TO BE USED BY THE COMMON USER

So, if either a "common user" feels happy or a Common
User feels unhappy when he ignores this uncertainty then
this is just another matter of taste - he has been warned.

- end : (c) gin&pez@arg (cc-by-4.0) 2019 -

Sincerely,

gin&pez@arg