Re: Transformerless Tesla coil

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

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