Re: Overcoupling?

To: tesla-at-pupman-dot-com
Subject: Re: Overcoupling?
From: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
Date: Fri, 07 May 1999 23:47:33 -0600
Approved: twftesla-at-uswest-dot-net
Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme

Hi Terry:

> Perhaps what you are saying could be looked at in the following way which
> may be more clear and easier to quantify.  In the loosely coupled case, a
> Tesla coil develops voltage across it's secondary length "basically" as a
> function of SQRT(Cp/Cs).  However, as the coupling is increased, the coil
> begins to act more like transformer where the voltage rise is governed by
> Ns/Np (N is the number of turns).  In the first case, for my coil, the
> SQRT(Cp/Cs) is equal to 25 and Ns/Np is equal to 67.  So, if the coil were
> just barely able to handle the voltage in the first case, increasing the
> coupling could substantially increase the voltage across the secondary
> length and cause the arcing to occur.  With a firing voltage of 20000
> volts, the first case would produce 500KV across the secondary while the
> second case would produce 1300KV!

But... If the system is correctly tuned, sqrt(Cp/Cs) = sqrt(Ls/Lp).
If all the magnetic field lines that go across the center of the
primary go also across the center of the secondary (maybe in a Tesla
transformer with a long coarse spiral primary wrapped around the
secondary, with highly insulated wire?) the coupling coefficient
would approach one, and really the voltage transfer ratio would
be very close to Ns/Np. But as in this case the inductances would
be proportional to N^2, Ns/Np = sqrt(Ls/Lp) = sqrt(Cp/Cs), and
the secondary maximum voltage is not changed, unless the
capacitances are changed too. If you change the primary to increase
the coupling significantly, you have also to change its shape,
adding more turns to keep the system tuned.

The "overcoupling" problem is not of creation of excessive voltage
in the entire secondary coil, but in the wrong areas of the
secondary coil.

Antonio Carlos M. de Queiroz