Re: Small TC experiments

["Tesla list" <tesla@pupman.com>]

Original poster: "by way of Terry Fritz <twftesla@uswest.net>" <paul@abelian.demon.co.uk>

"Ed Phillips <evp@pacbell.net> wrote:

> ...If you keep the winding dimensions the same the inductance goes
> up as the square of the number of turns, while the resistance only
> goes up as the wire diameter.  Net result is that the Q stays the
> same.

The proportionality of inductance to turns-squared applies to a
fully coupled winding, ie when all turns share the same flux, as in
an iron cored toroidal winding for example. The opposite extreme is a
coil in which air-cored turns are so separated that they contribute
only their self-inductance, in which case L is proportional to turns.
The tesla secondary is somewhere between these two extremes. 

Lets say for a TC secondary, L = gN^f
where N is turns, g is a constant of proportionality, and f is
an exponent somewhere between 1.0 and 2.0, larger values occuring
with smaller h/d ratios.

Also angular freq w is roughly (LC)^-0.5,

Then Q = wL/R = L^0.5 C^-0.5 / R

and if R = rN, where r is the ohms/turn.

Q =  L^0.5 C^-0.5 / R 
  =  g^0.5 N^(0.5f)/rN

so Q is proportional to N^(0.5f - 1).

The max possible value for f is 2.0, which gives Q proportional
to N^0, ie Q independent of N as Ed points out. Realistic values
of f will apply some negative exponent to N, ie Q will go down
as N increases, and more so if the wire diameter has to be reduced.

Having said all this, for a disruptive coil, the secondary Q is
of secondary importance. The potential advantage of increasing the
inductance comes from the fact that for a given primary coupling
factor, a larger primary inductance can be used, with possible
consequent improvement of primary gap efficiency - a theory 
expounded by John Freau.

See John's web page discussion of efficiency,

 http://hometown.aol.com/futuret/page5.html

As usual, numerous competing factors combine to complicate the real
world picture and there is plenty of room for careful experiments in
this area.

Regards,
--
Paul Nicholson,
Manchester, UK.
--