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*To*: tesla-at-pupman-dot-com*Subject*: Re: Resonator Self Resonant Frequency*From*: "harvey norris" <harvich-at-yahoo-dot-com> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)*Date*: Sat, 10 Jun 2000 07:33:23 -0600*Approved*: twftesla-at-uswest-dot-net*Delivered-To*: fixup-tesla-at-pupman-dot-com-at-fixme

--- 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 __________________________________________________ Do You Yahoo!? Yahoo! Photos -- now, 100 FREE prints! http://photos.yahoo-dot-com

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