Re: Transformerless Tesla coil

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

Original poster: "Jolyon Vater Cox by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>

Isn't the transformerless tesla coil described essentially a
Magnifier -where driver transformer has been reduced to a single inductor?

----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Tuesday, July 30, 2002 1:29 PM
Subject: Re: Transformerless Tesla coil


> Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>
>
> Tesla list wrote:
>
> > Original poster: "Ed Phillips by way of Terry Fritz
<twftesla-at-qwest-dot-net>"
> <evp-at-pacbell-dot-net>
> >
> >         Have you looked at a more elaborate design such as using the T
or PI
> > equivalent of a conventional double-tuned TC?
>
> Yes, but note the following:
>
> A transformer with inductances L1 and L2, and mutual inductance M is
> equivalent to a T of inductors:
>
> o---(L1-M)---+---(L2-M)---o
>              |
>              M
>              |
> o------------+------------o
>
> The original coupling coefficient was k=M/sqrt(L1*L2), and so:
> M=k*sqrt(L1*L2).
> The two series inductors must be positive:
> L1-M>0 => k<sqrt(L1/L2), an important restriction
> L2-M>0 => k<sqrt(L2/L1), but this is trivial, as L2>>L1 in a Tesla
> transformer.
> The maximum k is then k=sqrt(L1/L2).
> But this is also the inverse of the maximum voltage gain of the coil.
> Large gains then result in systems with very small maximum k, and
> so there is no reason to decrease k even further by using the
> three inductors. With just two (L1=M), the resulting circuit is as
> I implemented. It works with the maximum possible equivalent k
> for a given voltage gain, minimizing the number of cycles required
> for complete energy transfer, and the losses.
> Something similar happens with the PI equivalent. The faster circuit
> is obtained with just two branches.
>
> What would be the minimum practicable coupling coefficient in
> a conventional Tesla coil? The usual 0.1 results in a maximum
> gain in a directly coupled system of just 10.
>
> I added some comments in my page, showing that this kind of circuit
> was studied by Seibt, by Tesla's time too, I imagine.
> http://www.coe.ufrj.br/~acmq/tesla/mres4.html
>
> Antonio Carlos M. de Queiroz
>
>
>
>
>