# Wire Insulation Thickness

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From:  Malcolm Watts [SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent:  Monday, June 01, 1998 5:38 PM
To:  Tesla List
Subject:  Re: Wire Insulation Thickness

Hi Mike,

> From:  Hollmike-at-aol-dot-com [SMTP:Hollmike-at-aol-dot-com]
> Sent:  Thursday, May 28, 1998 4:23 PM
> To:  tesla-at-pupman-dot-com
> Subject:  Re: Wire Insulation Thickness
>
> Jim, all,
>    I am not too familiar with the Medhurst formula for a coil's self
> capacitance.  I have seen the equation and K values on Ed Sonderman's design
> spreadsheet, but do not know how those values were obtained.  I have never
> attempted to compare the results of that formula with measurements, so I
> cannot say anything in regards to it.
>    What I can do is quote from a book titled Electrical Engineer's Handbook,
> Communication Electronics,  published by Wiley & Sons in 1945 and edited by
> Pender and McIlwain.
>     First I will present a formula from this book for short (coil length
> approximately equal to the coil diameter) single layer coil:
>
>     Co = pi * D /  (3.6 cosh^-1(s/d))
>
> where s = pitch of winding,  d = bare wire diam., and D = coil diam.  All
> dimensions in centimeters.
>       This is an empirically derived equation that according to the book
> checks out "very well".  It does not state the max H/D ratio that it works
> well for, but should give a general idea of the effect of space winding on a
> coil's self capacitance.
>     It goes on to say: "From the results given, it is evident that the
> important parameters in the coil capacitance are the diameter of the winding
> and the ratio of the pitch of the winding to the diameter of the bare wire.
> The capacitance is practically independent of the number of turns."
>       I had much trouble trying to figure out how to calculate an inverse
> hyperbolic cosine on my calculator, so I dredged out my old calculus book and
> found that :
>
>    cosh^-1 (x) =  ln(x + SQRT(x^2  - 1))  where x > 1
>
> I would like to hear any thoughts on this as it seems to be an area of some
> discrepancy for coil design.
> Thanks,
> Mike Hollingsworth

All I can say is that I have thoroughly tested Medhurst and it works
*ONLY* for a coil used as a grounded resonator. It works equally well
for spacewound and closewound coils to within 5% for all the coils I
have tried it on. The formulae above obviously refer to ungrounded
coils.

Malcolm

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