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# Re: Capacitance of a coil

``` Tony,

> Original Poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
>
> I wrote:
>
> > (While making the comment above I was imagining what would be the
> > effect of the distance to ground in the capacitance of a hollow
> > cylinder with constant voltage to ground. If the idea is correct,
> > it must reach a limit when the cylinder touches the ground, close
> > to the value given by Medhurst's formula, and not go to infinity,
> > as it may appear that is what would happen.
> > Would Terry's simulator be able to verify this?)
>
> Thinking better:
> More reasonable is to consider a hollow cylinder with the voltage
> rising along its length, linearly, or maybe better sinusoidally
> (the correct solution without top load), and compute the equivalent
> capacitance from the stored charge, as C=Q/Vtop. This is what
> Terry's simulator does, in the simplest case. (I didn't try yet, as
> it takes too long to complete. Will someone translate it to some
> -fast- language, as djgpp C?)
>
> Antonio Carlos M. de Queiroz

Your post stimulated some (meager) comprehension on my part; reaching
outside the box brought to light the following:

Given that any resonant state must satisfy SCF (self-consistent field)
theory; the current(I) distribution must follow the gaussian distribution
(like the particle in a box example of the electron in an atomic orbital)
. Only integer harmonics are stable at resonance. (Let's deal with the
coil by itself first) Since the frequency (at resonance) is dependent on
the the ratio of speed of transmission (some function of c, probably
proportional to copper permittivity [epsilon.sub.Cu] if not resistance
limited) and the length of the wire (no top or ground); and the

eq. (1)     Cself = pi*D/(3.6cosh^-1(s/d))    in pF

It makes sense that the capacitance should be proportional to the loop
length pi*D.
Standard capacitance between wires two wires with height (h) above a
ground plane is

eq. (2)     3.68/log2s/d * 1/(sqrt(1+(s/2h)^2)) in pF/ft.

The origin of the ratio between the pitch and wire diameter seems more
subtle, however . The capacitance is inversely proportional to the
distance between the surfaces, but  this is averaged for the entire wire
surface, to the distance between centers. This is the same value as the
pitch (s). The function of the wire diameter is actually the contribution
of wire surface area to the capacitance (actually pi*d).

The capacitance is also not just between adjacent wires but also between
each pair of wires in the loop with diminishing contribution with distance
and with integration of eq. (2) we derive eq. (1)

I apologise for the non-rigorous treatment here, Time is a factor. If
permitted I will pursue this furhter later if anyone desires.

> Mike,
>
> The winding length of the coil is not a parameter in this equation??
> When I use Medhurst's formula on my 10" coil, I come very close (15.88
> pF) to the measured value (based on reverse calculating from Ls and Fo).
> However, if I use the above formula, I only get 3.88 pF. Is there an
> error in the algebraic representation above?
>
> BTW, is the book Pender and Delmar's, "Electrical Engineers' Handbook :
> Electric Communication and Electronics"? I've got volume IV (Power) but
> not volume V. Is volume V worth getting, and how does it compare with
> Terman's Radio Engineers Handbook?
>
> -- Bert --
>
There also seems to be another factor not include in the original equation
of the L/D ratio. I would expect that given Bert's information his coil's
L/D is 4.1. Is that so Bert?

Bryan Kaufman

```