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Re: Small TC experiments
Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>" <paul-at-abelian.demon.co.uk>
"Ed Phillips <evp-at-pacbell-dot-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
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,
As usual, numerous competing factors combine to complicate the real
world picture and there is plenty of room for careful experiments in