Bill Sloman said:
You seem to have failed to take into acount the parallel capacitances
of the windings. No electronic component is pure - in the sense of
presenting only resistive, capacitative or inductive impedance - and
inductors/transformers are more imperfect than most.
Indeed, effective parallel parasitic capacitance is a valuable concept.
Sadly, it's just that, a concept -- the *actual* capacitance from end to
end of, say, a solenoidal coil (i.e., as more advanced modelers call it, a
helical resonator) is dramatically smaller than the turn-to-turn
capacitance.
Consider, if instead of a helix, you had a stack of rings. It's the same
basic structure, except skewed by a turn, so the turns aren't turns,
they're loops. Now ground ALL the rings, except for just the two ends.
What is the capacitance between those two rings?
The capacitance will not only be small due to distance, but almost
entirely shielded by the turns inbetween them. When you unground them,
all the intervening turns have their own capacitance, but it still doesn't
even act as an ideal capacitive divider, because there is finite
propagation delay along the structure (i.e., the speed of light) and
because the interspersed turns have a comparable loading all their own
(self capacitance to free space as well as "mutual capacitance" to
adjecent turns).
The same is true of the toroid, with the added boundary condition that the
magnetic field must be equal at both ends -- in the helical resonator,
they can be equal or opposite, allowing (N + 1) / 2 wave resonances;
toroids only allow integer N. Speaking of which, it stands to reason that
the bandwidth of this resonance should correspond to the evenness of the
winding; if the leads are not at exactly 0 and 360 degrees (give or take
the external reactance between them), the wave can be skewed by that many
degrees, across the unwound portion of the core.
Tim
