Coil Self Resonant Freq/Signal generator Question

["harvey norris" <harvich-at-yahoo-dot-com> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

I am reposting Malcolm and Ed Harris info concerning
this in context with question of how to use signal
generator; as a different method gave me a high
number.

Subject: Resonator Self Resonant Frequency 
From: Tesla List 

Original Poster: "Malcolm Watts" 

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. 
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 ...
 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" 
Now it appears that because this other high freq
method(MWO) measured 416,000 hz, I now need to test
this via signal generator and scope method. I am a
little hazy on that method but was thinking of trying
the following; place the coil  to be meaured and scope
probe leads as parallel connections to the signal
generator. My initial thinking is that I also have to
have some kind of sensitive amperage input to measure
to rise in input amperage at resonance, but the
following occured to me, This is the coils self
resonant freq, not simply two resonant L and C
quantities in series{the lumped circuit?}) In that
lumped circuit there is a voltage rise within the
circuit. If the same thing happens at the self
resonant freq, than a voltage rise across the coil in
excess to the signal generators input might be
expected. If that were to occur than a single sweep of
various freq.s  could be made and the one with the
highest voltage deflection showing on the scope is the
resonant frequency. Can anyone say if this is a
possible method of using a rf signal generator and a
scope in combination to determine a coils self
resonant frequency, which we now understand is always
higher than the quarterwavelength value?
Sincerely HDN


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

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