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Re: Dimensions of my flat spiral coil



Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>

IN this context, sigma is the standard deviation of the measurement, a
standard statistical measure (it is the square root of the mean (average) of
the squared deviations from the mean of the measurements... a bit wordy, I
grant you...)  Compare for instance to the RMS (root mean square).  An
example...

Say you have 9 measurements..(I've contrived, mightily, to make the numbers
easy..)

51, 54, 55, 53, 54,  52, 58, 59, 57
The mean is 55.... (although, note, only one measurement actually at the
mean..)
The difference of each measurement from the mean is as follows:
-4, -1, 0, -2, -1,  -3, +3, +4,  +2
Square them...
16,1,0,4,1, 9,9,16,4
Take the mean
4.6667
Take the square root..
2.16
and that's the variance
(Before folks leap on me, I used the sum((X-mu)^2)/N not N-1 formulation....
for illustrative purposes, it's easier..)
I note that most scientific calculators and Excel can do all the grunt work
for you.. STDEV gives you standard deviation

Basically, if you're measurements have independent random errors that are
gaussian distributed (bell curve), which is a good starting assumption for
measurements (although, truncation (limited digits), has a uniform
distribution... slightly different), especially if your measurement is made
of the average( or sum) of lots of other measurements (This is called the
central limit theorem...).
Independent errors is important (systematic errors, like a dc bias, throw
all this off..)(independent errors are like noise.. just as likely to be
high as low, etc.)

Once you make that assumption, you know a lot about how likely the number
you measured is how close to what the real number is.  For instance, you
have a 68% chance that the real number is within 1 SD (1 sigma) of the
number you measured..  Example:  I measure a voltage as 5.2 volts, and my
measurement technique has a 1 sigma uncertainty of 0.25 volts.  I can assume
then, that the real voltage has a 68% chance of being somewhere between 4.95
and 5.45 volts. I also know that it has a 96% chance of being within 2 sigma
(0.5 V).  That is the actual voltage has a 96% chance of being between 4.7
and 5.7 volts.  A lot of times, the 2 sigma range is what is used when a
percentage uncertainty is given (in this case, for a 5V measurement, a 0.5V
uncertainty is 10%).

The same kind of thing applies to manufacturing tolerances... If I design a
circuit that can tolerate a 4 sigma variation in parameter value, then the
probability I'll get a part that is out of range for my circuit is pretty
darn small (<.0001).


Epsilon is something entirely different..(at least in this context).. It's
the dielectric constant or propagation constant, and has to do with the
electric fields in a medium.  The capacitance of a capacitor depends on the
epsilon of the dielectric (2.x for most plastics and oil, 10 for alumina, 81
for water) as well as plate size and spacing.  The epsilon of vacuum is
8.84E-12 Amp sec/Volt meter  (that's what accounts for the constant in the
standard capacitance formulae).

I have to confess that up until about 5 years ago, I was pretty casual about
measurement uncertainties (except back in college, when we got zapped for
"too many sig figs".. and then, the emphasis was more on calculation
uncertainty, not measurement uncertainty).  Then I wound up designing and
building a system to measure, very precisely, the RF power and frequency of
a microwave signal received from a satellite, and learned far more about
metrology and standards and references, and uncertainties, than I ever
dreamed were possible. (for what it's worth, we were measuring (estimating,
more properly) the power transmitted (at the satellite) to an accuracy of
0.05 dB, absolute, with a ground station).

Do a search for NIST and Measurement Uncertainty, and you'll find a really
great monograph that covers all this stuff in a fair amount of detail, and
is quite readable.  Anyone who is trying to measure things to better than,
say, 2-5%, should really read it..

I am truly thankful that building Tesla Coils is a 5-10% tolerance
endeavor!!!!

>
> Not that I can see.  Where can I quickly learn about sigma and epsilon?
> I've been seeing these terms a lot lately and I have no clue what they
mean.
>
>
> >... you can deliberately perturb the surroundings, and see how much of a
> difference it makes.  For instance, if you put a steel plate 2 feet away,
> and repeat the measurement, and it doesn't vary more than the measurement
> uncertainty, then you can kind of figure that you're insensitive to
> disturbances of that type.
>
> Great advice.  I'll do this with my next measurements.
>
> Dave
>
>
>