Re: Tesla Coil Blunders

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

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

Hi John,

On 27 Mar 01, at 22:34, Tesla list wrote:

> Original poster: "John H. Couture by way of Terry Fritz
> <twftesla-at-uswest-dot-net>" <couturejh-at-worldnet.att-dot-net>
> 
> 
> Tesla Coilers may be making the worst of TC blunders when doing
> calculations for determining the operating resonant frequency of their
> coils. It is a well known fact that the calculated frequencies do not
> agree with the actual operating test frequencies. Many important
> design decisions are based on this unique frequency so it is important
> that it be correct. To circumvent this problem a fudge factor is used
> for all TC computer programs but this is only a bandaid for TC design.
> 
> The equation that coilers use for finding the TC resonant frequency is
> 
>       F = 1/(6.283 x sqrt(LC)
> 
> The TC secondary circuit is an RCL circuit but the "R" is omitted by
> coilers in the above equation which may be the worst of TC blunders.
> In the Tesla Coil Construction Guide page 5-1 the complete resonant
> frequency equation is shown including the "R" parameter. It is also
> mentioned that the "R" reduces the resonant frequency and if the "R"
> is large enough there will be no resonant frequency. In other words
> the "R" could be the reason the operating frequency does not agree
> with the calculated frequency when the "R" is omitted.
> 
> To my knowledge no one has ever determined how to find this very
> important "R" for an operating Tesla coil either by calculation or by
> tests. TC programs are hurting because of this lack of information.If
> anyone has any comments I would be interested in them.
> 
> John Couture

If you plug typical figures for ESR into the lumped free resonant 
equation you find that it doesn't actually make much difference. 
However, I don't see that as being a major problem in itself.
      It is worth noting at this point that the Medhurst-Wheeler 
thing should be regarded as no more than a recipe approach to coil 
design since lumped modelling is not truly applicable to distributed 
circuits. Having said that, I've found that I get quite close enough 
to real world answers using this approach not to worry about R except 
in a truly bad coil where the Q is very low. In fact, no coil is 
sufficiently isolated to produce a measurable result in exact 
agreement with the most exacting model. Environmental factors not to 
mention variable proximity to other objects are all going to affect 
both f and Q to a degree.
       If one views the coil as a lumped circuit (which it isn't), 
ESR is easy to arrive at by a number of methods, measurement 
included. I have no doubt an equivalent AC distributed 
resistance/conductance is equally derivable from a distributed 
circuit approach as well. I expect this will be one of the outcomes 
of Paul Nicholson et al's efforts.

Regards,
malcolm