# Re: Resonator Self Resonant Frequency

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--- Tesla List <tesla-at-pupman-dot-com> wrote:
> Original Poster: "Malcolm Watts"
> <malcolm.watts-at-wnp.ac.nz>
>
> Hi all (especially those interested in resonator
> resonant frequency),
>
>        In poking around the web a bit I came upon
> this url which gives
> some information from the list archives on this
> subject. I referred to
> this some time ago. I have tested the formula Ed
> Harris gives on a
> coil I often refer to when discussing coil
> characteristics and it works
> well:
>
>
http://www.pupman-dot-com/listarchives/1996/june/msg00227.html
>
> Regards,
> Malcolm
>
My calculations show a little more deviance from
quarter wavelength value, about 35% in the cited case
below. Ed Harris' info follows, where I rewrote the
formula to avoid ascii problems. HDN

If you are just interested in computing self-resonant
frequencies there is another method which I have found
useful and generally accurate to about 10% for all
coil sizes - space wound or not. Its limitation is
that it probably shouldn't be used for aspect ratios
(Height/Diameter)<1 due to the assumptions of the
original derivation.
Freq=29.85 *{the fifth root of H/D}/[N*D]

where
F= self resonant frequency in Mhz of an 'isolated'
coil
H= coil height in meters
D= coil diameter in meters
N= total number of turns

Applying the formula to 31 inches,[or .79 meters] of
20 inch diameter, or [.52 meter] Sonotube only yeilds
a H/D of 1.52, not a good ratio for a tesla secondary,
however two were built for a possible future bipolar
application. The other unusual parameter in applying
this formula to my first coil attempt some years ago
was that I used  #14 gauge wire for the secondary,
only yeilding 9 turns/inch or a low 280 for the N
figure. So I thought the list might be interested to
find how this formula stacks up to the quarterwave
length consideration that is ALWAYS used to my
knowledge to find the resonant frequency of a
secondary single layer wind air core without a top
load capacitance. The only further obfuscation in that
case then becomes the Medhursts approximations of
internal capacity made by geometry of the inductor
expressed as different H/D ratios. I have not
consulted this chart for this case as I fomerly
thought I had found that its influence was minimal on
this case, which I have a point of confusion here
also, if the spacing between wires is what consists of
internal capacitance, which is then why little exists
for this case of 9 turns per inch, then why does the
geometry expressed as the H/D exist as a predominat
factor in determining that internal capacitance?
Getting on with the comparison, I used 3 500 ft spools
for a total of 1500 ft which yeilds a quarter
wavelength of .28 mile. Thus one cycle occurs in 6.1
Us in which the reciprocal of this is around 163,600
cycles per second. Applying the  above given
information in meters to the above formula where the
fifth root of 1.52 is given as 1.086 yeilds around
222,600 hz in my calculations. This seems a little off
for a 10%  quoted figure of accuracy. Perhaps the
fomula only applies for thinner gauge wire
approximations? Following is  Ed Harris' comments on
this formula from the URL.

Make sure the top line reads " (H/D) to the 1/5 power"
Note that the frequency is a very weak function of the
aspect ratio (H/D), but a fairly strong function of
the number of turns and the diameter. This is an
adapation of the formula for Helical Antennas found in
Reference Data for Radio Engineers as well as in the
section on slow wave structures in "Fields and waves
in Communication Electronics" by S Ramo, J R Whinnery,
and T D Van Duzer. A form of this equation also
appears in both of the Corum brother's books: "Vacuum
Tube Tesla Coils" and "TC Tutor" Incidentally, the
Corums incorrectly attribute the analysis of the helix
to Kandoian and Sichak. These guys actually just made
a simplification of the formula reported earlier by JR
Pierce (1947) and Franz Ollendorf (1925) and even more
amazing : Pocklington (1897) (see below).
------------------------------------------------------------------
I have a list which has more complete references. -Ed
Harris

Thanks Malcolm for posting the URL, just wanted to
point out a possible discrepancy involved with
relative low N values.
Sincerely HDN

=====
Binary Resonant Systemhttp://www.insidetheweb-dot-com/mbs.cgi/mb124201

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