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E&M theory: resonator question

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

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  1. Tim Williams

    Tim Williams Guest

    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

  2. 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 Williams

    Tim Williams Guest

    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).

  4. Tim Williams

    Tim Williams Guest


  5. Tim Williams

    Tim Williams Guest

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