# E&M theory: resonator question

Discussion in 'Electronic Design' started by Tim Williams, Oct 10, 2013.

1. ### Tim WilliamsGuest

Has anyone ever seen analysis, formulas, data, etc. concerning (if it's
even a word) helicotoroidal resonators?

Banal example: any toroidal inductor, single layer winding. Example:
chokes with single layer windings, most CTs.

The simplest case ought to be the thin toroid (the physicist's old
standby): if the properties of a thin (or infinite) solenoid (helix) are
known, it should be easy enough to apply periodic boundary conditions,
making it into a loop (a thin toroid). So instead of infinite propagating
modes, standing waves occur.

The frequencies of those standing waves will depend on the dispersion of
the helix, which I understand is not the same as an ideal transmission
line, so they won't be a harmonic series. I would SWAG the resonances
occur at Bessel function zeroes, or something like that. But that doesn't
help much. More importantly, they will depend on geometry and stuff.

I would of course be most interested in what an actual toroidal winding
(of finite size and thickness, wire and turns, all around a permeable core
of known properties) does, but if I can hand-wave some ideas it would be
great.

Tim

2. ### George HeroldGuest

Hi Tim, I'm a bit confused. Do you want the cavity modes for a toroid? (Something like a donut covered with copper.)
Or the self resonant frequency of a 'real' torodial inductor.
Or something else?

George H.

3. ### Tim WilliamsGuest

Yes, but one wound with a helix of conductive material.

If it were simply the various modes inside a toroidal cavity, or a pipe
bent 'round, even accounting for permeability of the core, resonances
would be through the roof -- the fact that it's wound, potentially with
hundreds or thousands of turns, can push those modes down into the 100s of
kHz -- which you can imagine isn't good news for chokes or transformers
operating in that range.

The characteristics of a helicotoroidal resonator proper (probably one
inside a shielded box, with no permeable core), optimized for Q and size,
might be interesting for RF purposes, but I would guess because only full
standing waves are permitted, such a design will be larger than a regular
old helical resonator (which permits 1/4 wave modes).

Apparently there's such a thing as a two layer counter-wound toroidal
antenna (Corum and others).

Tim

Yes.

Tim

5. ### Tim WilliamsGuest

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