# E-Tesla = Medhurst

```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
current.

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

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
model.

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.

Regards Bob

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

-----Original Message-----
From: Terry Fritz <twftesla-at-uswest-dot-net>
Date: Sunday, June 11, 2000 12:20 AM
Subject: Re: Voltage profile on the secondary

>Hi Bob,
>
>At 10:54 PM 6/10/00 -0400, you wrote:
>>Hi Terry,
>>
>>Sorry I did not explain my self very well.  What I should have should have
>>said was:
>>I was using the assumption that the voltage distribution is a sine wave
but
>>then your measurments indicate this is a very poor assumption.  I was
hoping
>>modified so I could still use my assumption
>>
>>In the  infinite length constant C case I am certain its a sine wave.   It
>>cant be anything else in a linear system..
>>
>>The finite case depends on the distribution of the C and the decrease in
>>coupling  at the ends.  I dont know the distribution so I can not give an
>>
>>Its some time since I did mechanics at collage.  If I remember correctly
for
>>a thin ruler under its own weight the defection cubic because the angle is
>>parabolic due to the bending moment being the product of the mass and
>>distance.
>>
>>When you measured the coil was it above a ground plain or as isolated as
you
>>could get it?
>
>It was above a split foil ground plane.
>
>>
>>The key problem with your voltage weighted C is that there is no theory to
>>justify it (that I have seen).  This does not invalidate it but it makes
it
>>very weak.
>>
>
>I was hoping you could come up with that small detail ;-)))  I have not
>been able to find a good reason or a tie in to circuit theory to explain it
>yet either.  However, I have not seen any actual measurements to say it is
>wrong but the measurements do not support a sine profile...  I was
>pondering if the capacitance could be linking just like the mutual
>inductance in the coils and if that could somehow explain it.  However, I
>really have no idea why...
>
>Since the program works so well, there must be something to it.  The
>voltage profile is critical to getting the right answers.  Of course, I may
>have hit on some strange equivalent case.  The program also gives the
>Medhurst C instead of your true C to do all this.  I wonder if setting the
>voltages all to 1.0 and using the true C formula would work too?  I'll
>check into that.*
>
>Cheers,
>
>
> Terry
>
>* The frequencies seem to come out low but only by about 5-10%  Far closer
>than I expected.  Might be something to that...
>
>
>>Regards Bob
>>
>>
>>
>>
>>-----Original Message-----
>>From: Terry Fritz <twftesla-at-uswest-dot-net>
>>To: tesla-at-pupman-dot-com <tesla-at-pupman-dot-com>