> "bitrex" <bitrex@de.lete.earthlink.net> wrote in message
> news:Qv2dnT8H2sPsr8XPnZ2dnUVZ_tCdnZ2d@earthlink.com...
>> I have a reference that may be helpful:
>>
>> http://www3.alcatel-lucent.com/bstj/vol37-1958/articles/bstj37-6-1599.pdf
>
> Oooh, good ol' BSTJ. Thanks!
>
> Yikes, pages and pages of equations... and it looks like they just dive
> right in. I'd have to read a lot of E&M and microwave stuff to get
> there.. hmm..
>
> Tim
>

Oooh, good ol' BSTJ. Thanks!
Yikes, pages and pages of equations... and it looks like they just dive
right in. I'd have to read a lot of E&M and microwave stuff to get
there.. hmm..
Tim
--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com

Reply by bitrex●October 11, 20132013-10-11

On 10/9/2013 9:47 PM, Tim Williams wrote:

> 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
>

> "bitrex" <bitrex@de.lete.earthlink.net> wrote in message
> news:eaydnUH2kPj9OcvPnZ2dnUVZ_qqdnZ2d@earthlink.com...
>> Are you essentially asking for the solutions of the 2D wave equation on
>> an annulus?
>
> 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
>

I think the case of a 2 dimensional annulus wound into a helix might be
able to be solved analytically. Take the 3 dimensional wave equation in
polar coordinates - the boundary conditions would be periodicity in
theta with boundaries at the top and bottom of the helix, boundaries in
R at the edges of the annulus, and periodicity in Z, with the Z axis
terminating after however many turns of the helix. In addition the
tangential components of E and the normal components of H must vanish at
all the boundaries of R (edges of the helix) and theta (top and bottom
of the helix).

Reply by Tim Williams●October 10, 20132013-10-10

"bitrex" <bitrex@de.lete.earthlink.net> wrote in message
news:eaydnUH2kPj9OcvPnZ2dnUVZ_qqdnZ2d@earthlink.com...

> Are you essentially asking for the solutions of the 2D wave equation on
> an annulus?

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
--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com

Reply by Tim Williams●October 10, 20132013-10-10

"George Herold" <gherold@teachspin.com> wrote in message
news:bc108024-d3dc-4f03-a4ea-1211ce43bde6@googlegroups.com...

> Or the self resonant frequency of a 'real' torodial inductor.

> On 10/9/2013 9:47 PM, Tim Williams wrote:
>> 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
>>
>
> Are you essentially asking for the solutions of the 2D wave equation on
> an annulus?

Subject to the boundary conditions implied by Maxwell's equations, of
course.

Reply by bitrex●October 10, 20132013-10-10

On 10/9/2013 9:47 PM, Tim Williams wrote:

> 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
>

Are you essentially asking for the solutions of the 2D wave equation on
an annulus?

Reply by George Herold●October 10, 20132013-10-10

On Wednesday, October 9, 2013 9:47:58 PM UTC-4, Tim Williams wrote:

> 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.
>

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.

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
--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com