Re: TC resonance estimation?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Malcolm Watts by way of Terry Fritz <twftesla-at-qwest-dot-net>" <m.j.watts-at-massey.ac.nz>

Hi Mike,

On 19 Jul 2002, at 8:14, Tesla list wrote:

> Original poster: "Mike Panetta by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <ahuitzot-at-mindspring-dot-com>
> 
> On Thu, 2002-07-18 at 13:46, Tesla list wrote:
> > Original poster: "Malcolm Watts by way of Terry Fritz
> <twftesla-at-qwest-dot-net>" <m.j.watts-at-massey.ac.nz>
> > 
> > Hi Mike,
> >         The good news is that you can *choose* the frequency you wish 
> > to operate at and design a secondary coil to do it for you. Several 
> > simple equations and an idea of what you want to achieve are all you 
> > need. The bad news is that if you design for a low frequency and a 
> > small coil to do it, the secondary losses will soar exponentially 
> > which is not good, especially for a CW coil where RMS currents are 
> > typically higher than a disruptive coil.
> 
> Would a coil of other then a 6:1 aspect ratio fix the problem with
> losses?  I was thinking about making a 12" x 2" coil until I saw that
> the resonance frequency (with a particular top load) would be somewhere
> around 1MHz...  This was someone elses project that I found on a web
> page out there on the web (it was a google search for ' small tesla
> coils '), so MMMV (My Milage May Vary ;) I guess...  Do you know of any
> web sites off hand that would describe how I would go about choosing my
> resonance frequency, and what the tradeoffs are of the various size
> coils?

There is a simple rule I use to make a design converge with 
acceptably low losses. If the coil is spacewound, aim for the wire 
diameter to be a minimum of 3 skin depths thick at the lowest 
frequency of operation you will run the coil (i.e. with the largest 
total - terminal+coil - capacitance). If the coil is to be 
closewound, I'd go for a minimum wire diameter of five skin depths at 
the lowest operating frequency. I don't have a ready made program to 
do it for you sorry. Perhaps I should write one. Using this rule and 
iteratively designing a resonator will give you a definite final 
result. 

Here is the basic algorithm:
    Start with knowing the desired frequency, and a projected maximum 
output voltage so you can choose the height of your coil. Then choose 
a desired aspect ratio. Next, choose your desired top terminal and 
find the capacitance of the structure (there is definite answer which 
doesn't require you having to know the inductance in advance). A 
simple calculation now yields the required inductance to do the job 
and from there, you can calculate the number of turns using Wheeler's 
equation rearranged (you know L, height and radius). Calculate the 
wire size required, then compare the diameter with a calculated skin 
depth figure (which needs only the frequency and the multiplier a la 
close/space wound). If the required wire diameter is significantly 
smaller than the skin depth calc tells you it should be, you know 
that an increase in coil size is required. The converse is true if 
you wish to make the coil smaller.

    The guide to wire diameter is based on experience and I am hoping 
that something more concrete might be refined by the TSSP project 
(Paul ;). It may be that the guides are too conservative or it may 
not. I do know that cramming heaps of inductance into a small coil is 
a total loser.

> > 
> >      Medhurst, Wheeler are the names to remember and there must be 
> > plenty of data on what adding a particular size of terminal to a 
> > particular size of secondary does to frequency in the archives. The 
> > final *minimum* radius of curvature of the terminal will determine 
> > what output voltage you can reach (assuming copper losses are kept 
> > low enough) before the coil can break out with a spark.
> 
> Do you think a google search on the names you gave above would return
> any useful results?  I think I may do the search anyways and find out
> myself ;).  As for the top load, I was thinking of using a steel float
> that I have as the top load, but I do not know how well it would do. 
> Its not spherical, but its kinda more like a short cylinder (maybe 3
> inches) thats has a hemisphere at each end to cap it.  As you can see, I
> am trying to keep this as cheap as possible to start with by using as
> much of things I already have on hand as possible ;)

Look out for Wheeler's formula for inductance and Medhurst's formula 
for self-capacitance in the list archives. No need to repeat what is 
already there. If the above sounds like work, it is. However, it 
increases the amount of "design" in the design procedure.

Regards,
Malcolm