coil self-resonant frequency estimation, theory, and history

Hi All, haven't been around much lately, but I noticed some interest
in coil frequency calculations. So I dug up these old posts:

-Ed HArris

These formulas are, of course, only valid for coils which are
base driven below the point of corona formation...
Hi Ed,

	Mark R. posted the self capacitance formula due to Medhurst
in a previous post. If you use this formula in conjuction with standard
inductance formulas for soleniods (like Wheeler's), you can compute 
the self resonant (no top terminal) frequency of most coils. I have found
that it works very well for predicting most of Malcolm's measured 

	If you want to read a little more of Medhurst try:
"HF Resistance and Self-Capacitance of Single-LAyer Solenoids" by
R.G. Medhurst, Wireless Engineer, Vol 2, p35, Feb 1947
*Note: the range of frequencies he used does not allow his Q formulas
to work at normal Tesla coil frequencies.

	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.

The formula is:
    29.85 x (H/D)
F = -------------------
     N x D

(hope the ascii came out)
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

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


From:	IN%"tesla-at-grendel.objinc.COM" 24-JAN-1996 11:15:15.05
To:	IN%"102527.764-at-compuserve.COM", IN%"71612.1234-at-compuserve.COM", IN%"BQPE24A-at-prodigy.COM", IN%"EDHARRIS-at-MPS.OHIO-STATE.EDU", IN%"GCerny-at-ix-dot-netcom.COM", IN%"alan.jones-at-bbs.os2bbs.COM", IN%"ccurran-at-earth.execpc.COM", IN%"chip-at-grendel.objinc.COM", IN%"jim
Subj:	New (fore me) Helical Resonator References


	I was seaching for some papers on superconducting tunnel junctions 
and my eye got caught by the following title:

	"Investigation of Superconducting Thick-Film Helical Resonator" by 
A. Centeno, et al. IEEE Transactions on Applied Superconductivity, Vol 5, 
No 1, March 1995, p19

	For fun you might be interested to know that they get unloaded Q of 
40,000 at 66MHz for a "bulk" helix which is somewhat disappointing compared 
to the copper helix which gives Q=15,000. 
Anyway,	one thing lead to another, and through this article I found two 
more interesting references:

	"Field Analysis of Helical Resonators with Constant-Bandwidth 
Filter Application" by D. Miley et al., IEEE Transactions on Materials and 
Packaging, Vol PMP-5, No 3, Sept 1969, p 127

	"Electromagnetic Wave Propegation on Helical Structures (A Review 
and Survey of Recent Progress)" by S. Sensiper, Proceeedings of the IRE, 
vol 43, p149-161, (1955)

****** special note here on helical resonator analysis ************

	The last paper is a bit of a suprise to me, because I missed it in 
previous seaches and not many people seem to have referenced it. It has 
an interesting historical review on analysis of the helix. --------- 
It appears that the first guy to puplish an analysis** was H.C. 
Pocklington in 1897 - this preceeds Ollendorf by 29years! and was even 
before Tesla went to Colorado Springs!! Pocklington's paper appears in
the 1897 "Proceeding of the Royal Society (London)" and is also referenced
in Kraus' book "Antennas".

	 Anyway, since Sensiper's paper is a review, it is probably one of
the best places to find most of the references preceeding 1955. In fact, 
there are 58 references listed of which 4 are references to more references!
A must have for anyone interested in the analysis for coils and magnifiers 

	-Ed Harris