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

Hi Robert,
                 Sorry for the delay in replying.  I was going to do some 
measurements on one of my coils for you but as you'll see later in 
this post, I realized you would end up with the same figures you are 

> Original Poster: "Robert Jones" <alwynj48-at-earthlink-dot-net> 
> Hi Malcolm and all,
> Malcolm can you check what Medhurst assumes for the ground to coil
> separation  and post it please.

I think Antonio might have answered that one?  If not, I'll go through 
Medhurst's paper which I dug out last night. Actually - Bart says he 
has it online so you might want to access it directly.
> >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 was going to do exactly this for you but you'll see that it will not give 
you your expected result.

A method of measuring a parallel tuned circuit is to connect an AC 
current source across it, measure FR and then knowing L, calculate 
C.  So what I'd planned to do was connect such a source across a 
grounded resonator. But you can see that I will end up with the 
same result as Medhurst does.  Since a current source has an 
impedance hopefully much higher than that of the coil, you are 
essentially measuring the resonator with no loading on it. That to my 
mind would give the same result as base feeding it from a voltage 
source, yes?

> > 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.

Yes.  I think that in determining the true C of the resonator, it *must* 
be grounded at one end. To not do so is to turn it into a different 
animal. That is easily verified - its oscillatory mode changes.

       Aside - I think the device should be regarded as unique in its 
own right. It is not a uniform line and it is not a lumped circuit 
although it exhibits some properties of both. I think Bert put it well 
when spoke of the wave/particle conundrum. It is like trying to 
assign known models to a foreign object and hence the paradoxes 
> 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).

I think Antonio answered that when he explained that grounding the 
base shorts out the base - earth capacitance.

> >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.

I think that is in dispute. There is a distributed model that is 
something of a hybrid between lumped and Tx line that does work 
using the sum of the distributed capacitances and the sum of the 
distributed inductances. I have not found that an equal section 
artificial line works in this way. I built a number of lines to check 
this, each with different component graduations including equal L 
and C sections. The one that worked went something like this:

gnd - 100mH --- 50mH -- 25mH -- 12.5mH -- 6.25mH -- 3.125mH 
                   5pF        10pF      20pF       40pF         80pF       160pF

All lines I tried were seven section (h'ware limitations). This is the 
model that I submitted to the Corums for their consideration.
         However, I now think that this model is not valid as it would 
exhibit a phase shift of 90 degrees between the input and output 
voltages. ??   Reason - it lacks the turn-turn coupling of the real 

>  > What does Tx line modelling have to say about using such
> >capacitance figures?
> I don't understand this question.

Well, what capacitance did you use in your Tx line model? 
Medhurst's or something else?
> > 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.

It doesn't (if you take L and F as measured and assume the C you 
calculate is the real one). I have measured dozens of coils like this. 

> >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.

Conservation of energy - sorry.
> 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.

The top hat is far from being isolated though.