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

Hi Malcolm and all,

Some of the points raised here have been answered in a different post

Determination of the propagation parameters in a helical coil.

If the analysis is correct it shows how circuit analysis can produce an
relatively accurate answer.
It also shows that it produces a similar answer to Medhurst and why i.e. In
fact the coil I used for comparison was one of yours. But please note I do
not suggest this proves how a coil resonates any more than the Medhurst
calculation does.  It just shows that the circuit laws apply and Medhurst
shows that an empirical relationship applies.

I have read Medhurst paper and I am reasonable confident he is refereing to
isolated coils with one end connected to ground via a connection wire.
(perhaps my post on that got lost).

There are also some responses to the thread below not other wise covered.

>Original Poster: "Malcolm Watts" <malcolm.watts-at-wnp.ac.nz>
>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 realised 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
>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  agree.  But its not what you  measure with an LC bridge on an isolated
>> > 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.

Yes I agree it changes the apparent C or equivalent parallel C
which is also dependent on the mode.

But how does the resonance mode change the intrinsic C of the
coil i.e. the C you measure with an LC bridge or sheet C  ?

Or are we still talking about different Cs?

Perhaps this will help. Imagine you cut a very fine slot down one side of
the coil so each turn is isolated.  Then with the coil isolated you apply
same voltage to all the turns via a picoamp meter and measure the current.
You could then calculate the C of each turn.  For a close wound coil the
sum would be almost equal to the self capacitance of a hollow cylinder with
the same dimensions as the coil.  It would also be equal to the self C you
measure at low frequencies with an LC bridge on an intact ungrounded coil.
You can also refer each turn C to one end and get approximately med C.
ie 1/3 for very short coils. and more for long (now not certain about long
(only valid for one end grounded coils and low frequencies)

Did that help?

>       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

I dont want to go over old ground but what paradox?
Which circuit law is violated and how?

>> 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.

Not true expect for the first turn.
>> >Is the object of this exercise to model it from DC - light?
>> I offered a coupled transmission line model in response to a statement
>> no transmission model could resonate at the correct frequency without
>> unrealistic large values of L and C.  So the initial object was to show
>> 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.

Well I guess if you never thought that med C was true self C (C  you
measure with an LC bridge) or  you have not tried true self C with the
TM equations it is hard to believe.  It certainly surprised me.

>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 capacitance and the sum of the
>distributed inductance. 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

I would suggest its  difficult to build a component model and get the mutual
inductance right. You could try the real values (the L, Lm and C you measure
with an LLmC bridge) in a simulation and see what happens.  I can now supply
the true L and true mutual L for a coil.  Terry or I can supply the true C.
There is a potential problem as the coupling function is inversely
proportional to the cube of the separation. So to model it accurately you
a large number of sections. There are ways round that but then you are
relying on more analysis which may be disputed.

I guess it depends on what you want the model to show, slow wave behaviour
or ???

>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. ??  (Can someone with SPICE running please give it a whirl?)
>Reason - it lacks the turn-turn coupling of the real thing.
>>  > 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?

I used true self C in my analysis.
>> > 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.

I checked a coil  example you gave it was approx 13% error for C and 7% for
Ok not large but significant.  I had assumed this was a ground plain effect.

The question of the ground plain effect is very important.
I suggest we leave it to an other thread.

>> >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
>> equal to the L of the coil.  ie If you measure the model L or C it will
>> the same L and C as the real coil. The effect of the distribution is
>> 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
>> >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
>> >over inductance one is effectively trying to measure portions of it via
>> >portions of an inductance.............  This also throws into doubt the
>> >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
>> you use it in lumped model it will be pessimistic because in the real
>> 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
>> >filling
>> >in a toroid makes virtually no difference to its capacitance (or at
>> >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.

That is interesting.  All circuit laws comply, but empirical relationships
may not.

>> 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
>> the top load and coil.   However as the top load and the top of the coil
>> 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
>> to topload C can be determined for any model or analysis.
>The top hat is far from being isolated though.

I agree.   That is what I was trying to express.
>------- End of forwarded message -------