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Re: E-Tesla = Medhurst

Hi Bob,

At 01:40 PM 6/11/00 -0400, you wrote:
>Hi Terry.
>After a little more thought or was it a lot more thought.
>For a large parallel C the voltage a long the coil  approaches a linear
>function regardless of what the distribution is with out parallel C.  ie the
>current flowing in the distibuted intrinsic C hardly effects the voltage
>across the coil because the coil current is much higher than the intrinsic C
>Hence the additional current flowing in to the distributed intrinsic C is
>only a function of the voltage and C.  This is even true for low H/D (<0.25)
>with almost unity coupling (auto transformer action).
>Under such condition the distibuted intrinsic C can be refereed to one end
>by simple summing the  currents.  Because the currents are proportional to
>the voltage a voltage weighted intrinsic C is equal to a single C you must
>put in parallel with the coil to have the same total current flow that the
>distibuted intrinsic C had.
>Hence if you run E-Tesla with a linear voltage and on an isolated coil it
>will produce med C. This is a theoretically valid comparison and should
>correlate to approximately. 1% in C not F. A good test of the theory and

Ok.  I stripped out E-Tesla5.50 to put a linear voltage on the secondary
and stick it in free space and all that.  The program is at:

I then ran the program with a 200 grid on 10 inch diameter coil of various
lengths.  I then compared the results to Medhurst.

H/D	Cmed	C ET5 calc	Error %
10.0	1.32	1.2056		-8.66
9.0	1.22	1.1238		-7.89
8.0	1.12	1.0482		-6.41
7.0	1.01	0.96745		-4.21
6.0	0.92	0.88716		-3.57
5.0	0.81	0.80313		-0.85
4.5	0.77	0.75848		-1.50
4.0	0.72	0.71428		-0.79
3.5	0.67	0.66897		-0.15
3.0	0.61	0.62244		 2.04
2.5	0.56	0.57424		 2.54
2.0	0.5	0.52573		 5.15
1.5	0.47	0.4758		 1.23
1.0	0.46	0.42783		-6.99

The graph is at:

Note that both graphs have a bend at 5.0!?!  Must be something magical
happening at that point.  Below 5.0 Medhurst tracks very well until the
coils get really small.  I wonder if the error is him or us? :-)  ET5 looks
like two straight lines while the Medhurst graph is showing obvious signs
of a little experimental error.  The program did about 300 billion more
calculations than Medhurst did so it should be straight! :-))  I wonder if
I dare say that the computed numbers "may" be more accurate than Medhurst's
in the 2.5 to 5.0 range?

Looks like Bob is again right!!

>If you run it with a ground plain it will produce med C with a ground plain.
>But as Medhurst did not produce such a table you can not make any valid
>comparison.  The true C / TM equation is again theoretically valid for an
>isolated coil.
>When I say valid for..... I dont mean its not valid for other conditions it
>means only that I can only prove its valid for that condition/s.
>So E-Tesla can be said to be theoretically accurate for coils with
>approximately 1000 turns (low turn to turn C effects), for large top loads
>and with a ground plain sufficiently below the coil (at least several
>diameters)  that the inductance is valid.
>Note E-Tesla must include some  internal C (turn to turn C)  effects because
>the C is determined with a voltage profile as opposed to a unity profile
>(the correct way to calculate intrinsic C) then weighting the result with
>the voltage profile.   However as the  internal C has mostly internal
>current I don't know if it can be refereed to the one end and I don't if how
>you treat the internal coupled flux is valid or  correctly produces  a
>reffered C to one end.  That will require more thought but as I believe its
>a small effect I am not motivated to try. If you try it both ways and the
>answer (refereed C or med C) is significantly different then I will be
>motivated to try.
>Now what about the self resonant case.  When the only current flowing in the
>coil is due to the distributed intrinsic C both the voltage and current are
>not linear so the above method of referring the intrinsic C to one end is
>not valid.  A 5% to 10% error in F is  10% to 20% error in C or L.

I am working on such things to further increase accuracy...



>Regards Bob
>You can put this on the list if you think anybody else is interested