Re: Calculating secondary resonance of bipolar coils

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <twftesla-at-uswest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
> 
> Original poster: Gavin Dingley <gavin.dingley-at-ukf-dot-net>

> I sent a mail to the list a couple of days ago regarding secondary
bipolar coil
> resonance calculations. As there has not yet been a reply, I thought I should
> elaborate on the question I originally asked.
>...

I you consider that everything is symmetrical, the voltage at the center
of the coil is null, but what you have are not two identical Tesla coils
mounted back-to-back. There is the coupling between the two sides.

The correct, I think, would be to consider the primary as it is (L1,
C1),
the secondary inductance as it is (L2), considering the whole coil, and 
the self-capacitance of the secondary (C2') split in two, each
calculated 
by the Medhurst approximation, but considering only one half of the coil
(valid if the coil is far from the ground).
Add to this the terminal capacitance (Ct).
The system would operate at the primary frequency:

F = 1/(2*pi*sqrt(L1*C1)) Hz

The relation for correct tuning would consider both secondary
capacitances in series:

L1*C1 = L2*(C2'+Ct)/2

Really, the secondary resonates at a higher frequency, because C2'
is smaller that C2 (self-capacitance of the whole coil) and because
of the division by 2.

Considering the primary capacitor initially charged to V1max, The 
maximum output voltage (differential) V2max would be:

V2max=V1max*sqrt(2*C1/(C2'+Ct))

Note that this is higher that what can be obtained with a conventional
unipolar coil with the same coils, capacitors, and terminal size.

Antonio Carlos M. de Queiroz