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Re: Resonator Self Resonant Frequency

Hello Harvey,

> Original Poster: "harvey norris" <harvich-at-yahoo-dot-com> 
> --- 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. 

What quarterwave length consideration? The wire? Bad choice. I've 
expalined why on a number of occasions.

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?

Because wire spacing doesn't govern the dominant capacitance. 
Actually this opens a can of worms. It has been argued (rightly in 
my opinion) that self capacitance is something of an artificial 
construct used to explain the distribution of charge on a structure 
(or something similar). I believe the Corums have something to say 
about this in a forthcoming work where the topic of Cself is 
discussed. Sort of like defining the speed of light in terms of 
permeability and permittivity. Speaking strictly of coil capacitance in 
the sense in which we understand it, it is most likely a function of 
surface area of the structure but that is probably not the whole story.

> 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.

If you actually build the coil you will find that Ed's formula is correct. 
I posted a couple of months ago pointing out the huge disparity 
between trying to use apply the free space wavelength to a piece of 
coiled-up wire. It doesn't work and never has.   

> 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

I can do no better than suggest that a measured result is better than 
a calculated one.