Correction of Re: Tesla turns ratio ?

Subject:  Correction of Re: Tesla turns ratio ?
  Date:   Thu, 12 Jun 1997 10:53:23 +0500
  From:   "Alfred A. Skrocki" <alfred.skrocki-at-cybernetworking-dot-com>
    To:   tesla-at-poodle.pupman-dot-com

OK before anyone jumps down my throat! I goofed and messed up the 
derivation equations so here is what it should have been. Sorry!!!!

On Tue, 10 Jun 1997 23:37:37 -0400 Owen Lawrence
<owen-at-iosphere-dot-net> wrote;

> > Why people care about the number turns is beyond me since a Tesla
> > coil dosen't operate on a turns ratio!

> Alfred, can you please elucidate?  I thought the number of turns has
> a direct effect on the inductance of a coil, a very important Tesla
> parameter.  Or are you just talking about primary/secondary turns
> ratio? Thanks.

Owen, you are correct when you say the number of turns effect the
inductance of a coil and as such one should strive to get as any turns
on the secondary as is practical. BUT the actual turn count is
irrelevant because the ratio of transformation in a Tesla coil IS NOT
related to the ratio of primary to secondary turns! For the benefit of
anyone who is not familiar with the derevation of the ratio of
trasformation in a Tesla coil here it is:

              E = .5 x C x V^2  :energy stored in a capacitor
         Eprimary = Esecondary  :conservation of energy law

combining the two equations gives;

  .5 x Cprimary x Vprimary^2 = .5 x Csecondary x Vsecondary^2

dividing both sides by .5 gives;

       Cprimary x Vprimary^2 = Csecondary x Vsecondary^2

Solving in terms of Vsecondary gives;

        Vsecondary = Vprimary x(SQRT (Cprimary / Csecondary))

Since at resonance the capacitive reactance is equal to the inductive
reactance but they are oposite in nature, it can also be expressed as;

        Vsecondary = Vprimary x (SQRT (Isecondary / Iprimary))

where I is inducatance

Realize this is a theoretical maximum and many factors effect it such
as resistive losses, dialectric losses, coronal leakage, ect.
Examining the above equations should clearly show that ones goals are
to make the secondary capacitance as small as possible while at the
same time making the secondary inductance as large as possible or
looking at the primary circuit you want to make the primary
capacitance as large as is practical and the primary inductance as
small as is practical. I say practical because a one turn wide diaeter
primary may give minimum inductance but it may not transfer all the
primary energy to the secondary and using too large a primary
capacitance is no good because the power supply won't be able to fully
charge it during any given half cycle.

                              \\  ~ ~  //
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                           Alfred A. Skrocki
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