# Re: (Fwd) Re: Formula for self C of a Coil (not Medhurst)

```Hi Malcolm and all,

Malcolm can you check what Medhurst assumes for the ground to coil
separation  and post it please.

>Original Poster: "Malcolm Watts" <malcolm.watts-at-wnp.ac.nz>
>
>Hi Robert,
>                I'm sure you will love what I'm about to say (maybe ;) :

I would not put it as strongly as that. I know circuit laws will prevail.
In fact you can use a lumped view of how a coil resonates to
show that Medhirst C is not the self C(true or sheet C) of the coil.

> I read about your low frequency measurement. One might call
>this the sheet capacitance of the coil. Problem is: the resonator is
>not a sheet of metal at the frequencies we are using it.

I prefer the term C or self C i.e the C you measure, just like the L
that you measure which is also distributed. It then has the same
definition as the C and L of the majority of other components.
I suggest med C for Medhursts C and res C for the C derived
from the L and Fr so they are distinguished from  the C you measure
with a LC bridge. This may help to avoid  confusion with the
equations.  However what we call it is not that  important just as
long as we agree on the terms and  definitions.

The object was a point check on the equation for the C. Previously
LC bridge measurements had been criticised due to the effect of L.
The C of the coil will be very close to the C of cylinder (hollow).

>Is the object of this exercise to model it from DC - light?

I offered a coupled transmission line model in response to a statement that
no transmission model could resonate at the correct frequency without
unrealistic large values of L and C.  So the initial object was to show that
was not correct. The object of my analysis was to show how the lumped
equation produces the right answer and the transmission line does not.
It turned out to be the other way round so the circuit laws are correct.

> What does Tx line modelling have to say about using such
>capacitance figures?

I don't understand this question.

> How are you going to distribute it?

I will differentiated the C equation wrt to length to obtain the
distribution function of C with length. Terry's program may provide
the same thing (if he mods it) and hence a cross check.
You also need the distribution function for L and coupling.
Incidentally looking at Medhurst C it appears to be for an isolated
coil so it will have large errors for typical coils.

>me that using such a figure makes the L/C ratio far less favourable
>than it already is. Can you really use a "lumped" inductance figure
>with any degree of validity in a Tx line model (we must now
>remember that it has capacitance distributed over it so perhaps it is
>just as "incorrect" as the sheet value of capacitance).

What I have suggested is using a distributed L and coupling that has a total
equal to the L of the coil.  ie If you measure the model L or C it will have
the same L and C as the real coil. The effect of the distribution is solved
either by the simulation model or the analysis

>That has been my feeling for years too but perhaps we are now
>heading into apples and oranges territory. For a long time I have
>regarded Medhurst's formula as a *useful recipe*, not a definitive
>work but again that presupposes that the coil is actually a solid cylinder
>at the frequencies of interest. One can see an immediate difficulty if
>one tries to use Fr to derive a value for Cself. Since Cself is distributed
>over inductance one is effectively trying to measure portions of it via
>portions of an inductance.............  This also throws into doubt the use
>of the
>energy equation *based on the use of Medhurst's Cs*  to derive a
>maximum figure for Vs. Perhaps it is overly optimistic?

Yes and no. If you use med C because its lower it will be optimistic but if
you use it in lumped model it will be pessimistic because in the real case
the voltage is distributed.
>
> What are we now to make of the capacitance of the top terminal?
>We know that it is part shielded by the coil itself and we also know that
>filling
>in a toroid makes virtually no difference to its capacitance (or at least
>to the coil
>operating frequency).
>. What do your transmission line models predict for
>output voltages and how do these compare with COE voltages for a
>lumped model *IF the resonator ends up with a fixed amount of
>energy in it in both cases*?.

I will let you know when I have a model and I find out what COE means.

You don't need a transmission line model.  just distribute the energy
according to the voltage profile between the distributed C and Top C.

Presumable if a transmission line model has the correct C and L it will
predict the correct V.  As you suggest there is a problem with the C between
the top load and coil.   However as the top load and the top of the coil are
at the same voltage the error will be small.
Using Terry's program (without a voltage profile) the accurate self C of
topload (normally assumed to be an isolated sphere) and the distributed coil
to topload C can be determined for any model or analysis.

Regards Bob

```