Malcolm Watts wrote:
> Very simply, calculate Cself of the secondary and Cself of the extra
> coil and add them together. That capacitance must also be added to
> effective terminal capacitance to give the total capacitance on the
> secondary side. Sum the two inductances, then use Ctot and the sum of
> the inductances to determine the frequency to tune the primary to.
This may be a reasonable approximation, but the presence of a
significant capacitance in parallel with the secondary coil
turns the system more complex, with three oscillatory modes
instead of two. The expressions that I posted in the past are
valid when the secondary capacitance is small.
It is true that a magnifier is subject to the same
restriction on maximum voltage tham a normal Tesla coil:
(*1 and *3 refer to the primary and tertiary system)
But in comparison with an equivalent two-coils system, in
a magnifier C3 can have a greater part of it coming
from the terminal capacitance, and only the charge
that ends at the terminal is immediately available for
starting and enlarging sparks.
The ideal design for a magnifier would create a
maximum -voltage- at the top of the third coil at
the same time that a minimum of -energy- at the
primary circuit -and- at the secondary circuit.
Some time ago, someone (bensonbd-at-erols-dot-com) posted a quick
note about a paper dealing with a three-coils system, that
apparently was overlooked.
I checked what that paper was, and what is there is precisely
a lumped version of a magnifier circuit, with expressions
that can be useful for dimensioning a magnifier, apparently
satisfying the ideal design conditions.
I am short of time now to check the expressions, and
could not find the original work mentioned in the paper
(second paper below).
The papers of interest are:
Bieniosek, Review of Scientific Instruments 61 (6) p. 1717, June 1990
Bieniosek, Proc. 6th IEEE Pulsed Power Conference, p. 700, 1987
Antonio Carlos M. de Queiroz