Leakage inductance on toroids

[Tim Williams]

What defines LL on toroids? I mean, if I send a wire down the center
of one, is it zero? Nothing can be zero...

If it were an air core toroid, then it would be the ratio of a few
diameters, probably with a logarithm I'm guessing. And if it's a
ferrite core with such and such permeability, then it's roughly that
many times less leakage, right?

Additional question: can I calculate LL on, say, a dual C type core?
What defines that? Ugly geometry-dependent math I'm guessing, but how
about ballparks?

Reason I ask is, I tried this:
http://webpages.charter.net/dawill/Images/Induction1001.jpg
(That's 6 turns 1/4" Cu tubing secondary, in series with 20uF and 1uH,
and 24T 8AWG primary.) Resonant frequency was way low, like, lower
than I can go, which was 15kHz. It's supposed to be 35k, so LL is at
least 5 times bigger (>5uH). What was it actually at, and can I
estimate it for a toroid?

I contemplated wrapping a slab of copper sheet around the core (to
short out the leakage flux), but after a few minutes operation the
primary winding was too melted to try anything more. On a related
subject, I now despise proximity effect. ;-)

Tim

 

[MooseFET]

What defines LL on toroids?  I mean, if I send a wire down the center
of one, is it zero?  Nothing can be zero...

If it were an air core toroid, then it would be the ratio of a few
diameters, probably with a logarithm I'm guessing.  And if it's a
ferrite core with such and such permeability, then it's roughly that
many times less leakage, right?

Additional question: can I calculate LL on, say, a dual C type core?
What defines that?  Ugly geometry-dependent math I'm guessing, but how
about ballparks?

Reason I ask is, I tried this:http://webpages.charter.net/dawill/Images/Induction1001.jpg
(That's 6 turns 1/4" Cu tubing secondary, in series with 20uF and 1uH,
and 24T 8AWG primary.)  Resonant frequency was way low, like, lower
than I can go, which was 15kHz.  It's supposed to be 35k, so LL is at
least 5 times bigger (>5uH).  What was it actually at, and can I
estimate it for a toroid?

I contemplated wrapping a slab of copper sheet around the core (to
short out the leakage flux), but after a few minutes operation the
primary winding was too melted to try anything more.  On a related
subject, I now despise proximity effect. ;-)

I like Litz wire.

 

[Tim Williams]

I like Litz wire.

Got any 8AWG Litz to spare me?

 

[[email protected]]

Got any 8AWG Litz to spare me?

Hmm, I'm not sure the gauge, but I've seen some scrap pieces laying
around how long a piece do you need?

George H.

 

[Jon Kirwan]

Hmm, I'm not sure the gauge, but I've seen some scrap pieces laying
around how long a piece do you need?

Um. I think he was being 'funny.' 8AWG Litz would be... an oxymoron.

Jon

 

[James Arthur]

Got any 8AWG Litz to spare me?

You could braid your own. I did.

Cheers,
James Arthur

 

[legg]

Reason I ask is, I tried this:
http://webpages.charter.net/dawill/Images/Induction1001.jpg
(That's 6 turns 1/4" Cu tubing secondary, in series with 20uF and 1uH,
and 24T 8AWG primary.) Resonant frequency was way low, like, lower
than I can go, which was 15kHz. It's supposed to be 35k, so LL is at
least 5 times bigger (>5uH). What was it actually at, and can I
estimate it for a toroid?

I contemplated wrapping a slab of copper sheet around the core (to
short out the leakage flux), but after a few minutes operation the
primary winding was too melted to try anything more. On a related
subject, I now despise proximity effect. ;-)

Tim

Is the 1uH supposed to be the induction coil in your picture? I'd
expect to see secondary leakage leakage terms, for the secondary
structure shown, that were in the same vicinity as for the unloaded
coil. It might be better to put the series resonant capacitor in
series with the primary, so that induction coil loading has a reduced
effect. The intention is constant current - yes?

Assuming the circuit is primary current limited, shouldn't the primary
be constructed to carry this limit safely? ... or are you just
forgetting intended duty cycle limitations and the temperature limits
of the wire shown?

Don't forget to use insulation between the primary wire and the core.
Nomex is handy.

I can spare a couple of feet of 5.8mm OD litz, if you need it. This is
equivalent to somewhere in between 6 and 8 AWG. Larger gauge litz is
often constructed of multiple lighter gauges. I think this is 5x33 of
28AWG.

RL

 

[legg]

Hmmm. Is paper and Elmer's glue okay? ;o)

Hey, paper can handle heat at least as good as epoxy!

Kraft paper is a conventional insulation material for lower
temperature systems. That's approximately what brown paper bags are
made of - unbleached kraft stock. Layering is easy and effective.

It's hygroscopic, so for practical continuous use, it's better
accompanied by vacuum impregnation with varnish.

RL

 

[legg]

That was just the thickest, quickest wire I had on hand. I'd go for
copper strap on the real thing. Obviously I had no concern for the
wire's thermal limit, because I exceeded it quite flagrantly.

The circuit is NOT current-mode, if that's what you mean. I may
change that; I'm able to now. (With the Lmatch network, current mode
feedback just buzzed at the Lmatch + coupling C series resonant
frequency... ewww! Now the only thing it can buzz at is the resonant
frequency, which I want anyway. Maybe I can use current feedback
instead of a PLL!)

A series resonant circuit is current limited below resonance by C,
above resonance by L. Your's is shunted by the primary magnetic link,
making lower frequency excursions potentially hazardous to the primary
switches and conductors involved.

RL

 

[Jon Kirwan]

Not entirely. As a matter of fact, I have a fairly heavy air-core
choke, removed from a motor drive. This was an, Eaton Electric I
think, 10HP or so, thyristor powered VFD. This choke was either
snubbing something on the supply rail, or providing commutation.
Anyway, it's something like 6" diameter, maybe ten turns of 8AWG-sized
wire rope in a single loop (the turns are bunched together
toroidially, rather than as a flat solenoid). If it's varnished
together, it won't be much good to me as wire. I haven't checked.
That'd be the perfect kind of stuff to use though- either that or
copper strip.

I do have enough copper on hand to cut my own strip, no worries there:
http://webpages.charter.net/dawill/tmoranwms/Elec_Ind7_5.jpg

Well, I just recalled that Litz wire is designed for __skin__ effect.
And there is a depth equation I once saw that was 7.5/sqrt(f) in cm
for copper. 8 gauge is .326cm in diameter or .163cm in radius. So,
this solves to an f of about 2kHz. Okay. Maybe.

It still seems funny, too. And I thought that was what you were
reaching towards.

Jon

 

[legg]

So what defines LL on toroids?  I mean, if I send a wire down the
center of a toroidal transformer, is LL zero?  Nothing can be zero...
so what is it, why?

Tim

The minimum leakage inductance is roughly equal to the inductance of
the isolated coil structure in the absence of all other materials. It
follows the same inductance sizing rules as any air-cored structure.

RL

 

[legg]

So, you're saying it's identical to the stray inductance of the single
turn in free space?

The single turn in free space doesn't have stray inductance, save that
of the hook-up and test leads.

LL (or rather, k) of an infinite solenoidal transformer is only the
ratio of areas, right? Loop it around sideways into a toroid and you
get much the same thing, but now the diameters are constrained to be
less than the torus diameter. For the inner winding being much

A solenoid, infinite or otherwise, has a winding structure that has a
magnetic field path twice it's physical length. The magnetic field
path of a single turn in the solenoid does not, unless the
permeability of an introduced core is sufficiently convincing (has a
high enough permeability as compared to free space).

A single layer solenoid also has winding return leads that add to the
conductor shape. In a toroid, this effect can be minimized. With only
an air core, however, the effect is the same for both shapes.

smaller than the outer, it could still be around A1/A2, but when
they're both fairly similar to the torus diameter there's going to be
something else at work, like a log of a ratio. And that doesn't say
anything about a single turn, only a current sheet (infinite turns,
infinnitessimal current per turn; finite total current). Ah, but
counting only the stuff going through the toroid (thereby assuming
that everything outside sums magically to the same flux, which
fortunately, Kirchoff assures us it does), a single turn (particularly
at HF where skin effect dominates) will look like a current sheet
anyway, so that at least isn't too hard. So what it comes down to is,
the space between the primary winding (which is a winding as such) and
the secondary (a hunk of copper tubing) is where the leakage flux
goes? And so, to minimize LL, one must have that pipe as large as

Reduced leakage configuration will attempt to have all of the flux
embrace all of the turns through:

interleaving of turns
interleaving of layers
minimizing of turns
minimizing of un-interleaved turns and layers.
minimizing length of flux paths that are not within the loops.

possible, so it's as close to the primary as possible? Or
alternately, have the primary wires gathered as close to the pipe as
possible?

What are the limiting factors? An infinitely thin secondary seems
like it should have infinite LL, but I know that a current transformer
works by enclosed current alone. What's missing here?

Tim

Current transformers work like any other tansformer. The secondary is
effectively a short, so that inductance added to the low-turns count
primary tracking is close to the leakage term that would exist if the
core and secondary were not present.

RL

 

[legg]

An ordinary helically-wound toroid is basically a perfect transformer in
series with a 1-turn solenoid. There are winding tricks to reduce this
by an order of magnitude or thereabouts--the simplest one is to split
each winding into two sections on opposite sides of the core, wound with
the same current direction and opposite helicity. (I've never done this
or I'd be more specific, but I've seen references.)

Cheers,

Phil Hobbs

When the perfect transformer isn't perfect, and the core material is
free space, the part doesn't get simpler - the single solenoid turn is
still there, in series with the rest, reflecting worst-case effective
leakage inductance of similarly shaped parts with cores and
secondaries.

RL

 

[legg]

When the perfect transformer isn't perfect, and the core material is
free space, the part doesn't get simpler - the single solenoid turn is
still there, in series with the rest, reflecting worst-case effective

- not 'worst-case'; a minimum.

leakage inductance of similarly shaped parts with cores and
secondaries.

RL

 

[Fred_Bartoli]

Yup! Franz Litz composed great music....

I think not...

 

[Tim Williams]

The single turn in free space doesn't have stray inductance, save that
of the hook-up and test leads.

I should say, its inductance. Making the assumption that, in terms of
actual volts (which may not be measurable with real probes, in the same way
that a single thermocouple junction is unmeasurable with probes), most of
the voltage generated is where the wire passes through the toroid, so that
the rest of the loop doesn't matter as far as transformer action and you
would therefore wish to minimize all that loopiness, becoming undesirable
stray inductance instead.

A solenoid, infinite or otherwise, has a winding structure that has a
magnetic field path twice it's physical length.

Wait, what does this paragraph have to do with mine? And it doesn't help
that you cut the paragraph mid sentence, which doesn't even make sense. I
mean, yes magnetic field path is what induces voltage, but length is a non
sequitur, transformers work on Phi, not H.

A single layer solenoid also has winding return leads that add to the
conductor shape. In a toroid, this effect can be minimized. With only
an air core, however, the effect is the same for both shapes.

Well, lead inductance is negligible if the turns are much more numerous than
the wire's 20nH/inch inductance thing. This does happen to be a case where
turns are few, so lead length may have a noticable effect, but that doesn't
look like a good generalization.

As for some answers,

Reduced leakage configuration will attempt to have all of the flux
embrace all of the turns through:

interleaving of turns

Indeed. But hard to interleave one turn. Next,

interleaving of layers
Ditto,

minimizing of turns

Got it,

minimizing of un-interleaved turns and layers.
Yup,

minimizing length of flux paths that are not within the loops.

Okay, now slow down a moment. This one's harder. (Actually, it seems to me
this is all of the above rolled into one, but nevermind that...)

Now, by "loops", you mean the loops of primary and secondary wire, correct?
In the secondary case, it's just one loop, which goes around the core where
most of the flux is, so we know it will transform at least. What's left is
all that pesky flux around the outside, but like the solenoid, the external
field is fairly small so this flux is also small (ignoring the noticable
fringing from the small primary turn count).

Current transformers work like any other tansformer. The secondary is
effectively a short, so that inductance added to the low-turns count
primary tracking is close to the leakage term that would exist if the
core and secondary were not present.

Yeah, but what happens at the secondary doesn't do anything to the intrinsic
leakage, which is a geometry thing. If I put a CT around a piece of 40AWG
wire, straight down the middle, would I see shitty HF bandwidth, or what?

Tim

 

[Clifford Heath]

An ordinary helically-wound toroid is basically a perfect transformer in
series with a 1-turn solenoid. There are winding tricks to reduce this
by an order of magnitude or thereabouts--the simplest one is to split
each winding into two sections on opposite sides of the core, wound with
the same current direction and opposite helicity.

It's quite simple. Make half the winding, using up to half the core
(say from left to right across the bottom) then pass the wire through
to the opposite side (mirror image) from where you started, and make
the second half of the winding (again from left to right, but across
the top).