[Prev][Next][Index][Thread]
Musings on Medhurst
----------
From: Jim Lux [SMTP:jimlux-at-earthlink-dot-net]
Sent: Friday, June 05, 1998 1:44 PM
To: Tesla List
Subject: Re: Musings on Medhurst
Tesla List wrote:
>
> ----------
> From: Thomas McGahee [SMTP:tom_mcgahee-at-sigmais-dot-com]
> Sent: Thursday, June 04, 1998 2:45 PM
> To: tesla-at-pupman-dot-com
> Subject: Musings on Medhurst
>
> Malcolm, Terry, and other interested coilers,
>
> The recent discussions about the possibility of the
> Cself of a secondary being dominated by the capacitance
> between the coil and ground led me to the following
> thoughts.
>
> Assume that the same piece of wire of the same length
> is used to build four Tesla coil secondaries...
>
> A) A single wire stretched out straight would have
> zero "inter-turn" capacitance and maximum capacitance
> due to exposed surface area. Inductance would be minimal.
Streched straight out parallel or perpendicular to ground. It makes a
difference. In the parallel to ground case, the distance between the
"plates"of the cap (the wire and ground) is constant. In the
perpendicular case, it is proportional to the distance along the wire,
so the capacitance is proportional to the integral of 1/x. (or the log
of the length).
>
> B) A skinny coil would have a large inter-turn capacitance
> and its exposed surface area capacitance would be
> about half that of example (A), since the inside of the
> coil would be shielded. Inductance would be medium.
>
> C) A large diameter coil would have a larger inductance,
> about the same inter-turn capacitance, (but with a larger
> inductance per-turn than in (B)), and slightly larger exposed
> surface area capacitance, since shielding is not perfect.
>
> D) The final extreme. A single-turn secondary. Almost Zero
> inter-turn capacitance. ALMOST maximum capacitance due to
> exposed surface area capacitance. Fair sized inductance.
>
> (A) and (D) would be pre-dominantly 1/4 wave devices.
> According to the direction of the recent discussions on this
> List, it would seem that (B) and (C) would not.
>
> One method used to determine Cself is table-lookup, attributed to Medhurst:
>
> What is the correlation between H/D and K? Could it be related to
> the fact that as H/D grows smaller the ratio of exposed area
> capacitance and inter-turn area capacitance changes?
>
> Things to think about...
> Why does Medhurst's method only work if the base of the coil
> is effectively connected to ground?
I think it is because Medhurst is essentially a tabular/empirical form
of an equation which considers the cylinder above a ground plane as a
coaxial capacitor with the spacing between the inner and outer
capacitors getting greater as you go up the cylinder. C = 2 pi epsilon /
ln (router/rinner) where router = rinner + distance up the cylinder.
Note that, as in Medhurst, this equation does not care how many windings
there are, considering them all as simply a conducting cylinder. This
is probably a valid assumption, as long as the coil is a small fraction
of a wavelength, which at 100 kHz is 3 km.
The integration gets ugly, and results in a series which is essentially
something like:
Let u = (length + diameter)/diameter
the integral is = ln(abs(ln(u)) + ln(u) + u^2/(2 * 2!) + u^3/(3*3!) +
...
(this is from memory and is probably wrong)
> Coilers have often noted that certain H/D ratios work best for Tesla
> coil secondaries of a given diameter. WHAT is maximized at these
> particular ratios? Why is there not one single "best" H/D ratio
> that would work for ALL coil sizes?
A tradeoff of series R in the coil? The series R and L will have an
effect on the spark length.
> What is capacitively different about an operating Tesla secondary
> and one that is just hanging around waiting for the juice to be turned
> on? What is different about huge high power Tesla coils and smaller,
> more efficient but lower power Tesla coils?
>