T
Tim Williams
Guest
"Phil Hobbs" <pcdhSpamMeSenseless@electrooptical.net> wrote in message
news:8fKdncAw8Lc99QTPnZ2dnUVZ_qadnZ2d@supernews.com...
Lossier, per resistive length, factored by current-carrying cross sectional
area? (Making some sort of estimation of current density and resistivity in
the areas where current does flow...) Of course, it ends up better in the
end, because you can use much finer wire, which gives much more perimeter,
and thus more cross sectional area for current to flow in, even though it's
choked up much worse from being forced into to a constant average current
density.
Compared to single strands in free space, even of much larger diameter than
the individual strands, the stuff is lossier. If you look at Rac/Rdc for
decreasing strand diameters, the single free strand might level off at, I
forget, 28AWG or something, at say 100kHz, whereas in a big Litz cable (say,
a thousand strands), it keeps going until 36 or 38AWG, and even then, the
total resistance for equivalent area is larger (in addition to the increased
length due to the weave). It's like making copper a better resistor (or
alternately, a worse inductor).
The nice part is, you get to carry more total current, in an only slightly
larger volume, which is significantly smaller than the volume required of a
single massive strand. That is to say, at high frequencies, a large solid
conductor is O(N), while fine conductors are O(N^2). Litz has a smaller
constant multiplier on that Big-Oh than a single fine strand, but
appropriately chosen, it scales independently of frequency (as diameter
squared), something a solid conductor doesn't (it's perimeter limited). One
of those things that "shouldn't work" by certain physical principles, but
when considered holistically by the engineer, works great. ;-)
But anyway, in a seven-conductor construction, the always-central bundle is
completely surrounded by fields from the other six, and so has much more
eddy current losses, or higher Rac, or stronger proximity effect, or thinner
skin depth, or however one likes to say it (they're all aspects of the same
phenomenon, after all).
Yes. Proximity effect is all over the stuff, which is why the strands have
to be so much finer than the free space skin depth would suggest. Even 10
strands of 28AWG will be noticeably higher in resistance than 1/10th of a
single strand. 100 or 1000 strands need strands finer and finer still. The
scaling between number of strands and required decrease in strand diameter
is of course "far from straightforward", for the same reason.
I haven't seen any analyses of tape, but I've seen it used here and there.
Trouble is, the field around a conductor 'wants' to be round, and forcing it
to wrap around a foil conductor is somewhat counterproductive. It
necessarily must penetrate the conductor, particularly along the edges. The
conductor must be thin enough to allow this; a thick conductor will shield
its self-induction, and you get standard skin effect along the edges (within
a constant factor).
The result is, eddy currents flow along the edges. This manifests as skin
effect. Except, because we're talking about a somewhat two-dimensional
conductor, it's really edge effect, and instead of bulk resistivity,
thickness can be factored into the area resistivity, which edge penetration
then takes as a factor. For a finite thickness, edge penetration is deeper
than the free space skin depth (which is the limit at infinite thickness,
i.e., an infinite slab), but I don't know by how much.
If depth is inverse with thickness (a crude but not unreasonable guess,
taking the area resistivity approximation as a suggestion), then one would
need a conductor of thickness t = d^2/w, for width w and skin depth d. (If
t = w, you have a square conductor of dimension d, which is in the right
order of magnitude.) Unfortunately, copper at 100kHz is already only a few
mils, so you need truely microscopic foils to actually achieve full
utilization across the width of an average bobbin. That stinks.
Proximity effect still applies, so while you're doing this, you can't just,
say, wrap ten turns of foil primary, a layer of tape, then ten turns of
secondary; the innermost facing turns will burn up from all the congestion.
Tape does at least suggest itself nicely for transmission line approaches:
if the turns are similar, just layer primary and secondary together, with
tape between, like the plates of a capacitor. Except with a core in the
middle. Isolation capacitance won't be great, but leakage inductance will
be teensy. The image currents from primary and secondary will tend to flow
along the faces as well as the edges, because it looks more like a parallel
plate transmission line than an isolated foil conductor; that helps
efficiency a lot.
You can of course apply the Litz trick to foil, but you don't have any free
lunch; the geometry reduction is still required whether putting together a
bunch of strips or strands. Ten strips woven together will have less
resistance than a single strip of the same width and thickness, but higher
than 1/10th of an isolated strip that size. I know of at least one company
that claims to have some sort of foil technology that reduces Rac like Litz,
presumably doing some kind of weave. Tempting to buy a bigass custom part
from them just to take it apart and look, see how they put the stuff
together. I can't imagine it's all that easy to make, considering there are
only two US companies making the round stuff as is.
Tim
--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com
news:8fKdncAw8Lc99QTPnZ2dnUVZ_qadnZ2d@supernews.com...
Lossier, per resistive length, factored by current-carrying cross sectional
area? (Making some sort of estimation of current density and resistivity in
the areas where current does flow...) Of course, it ends up better in the
end, because you can use much finer wire, which gives much more perimeter,
and thus more cross sectional area for current to flow in, even though it's
choked up much worse from being forced into to a constant average current
density.
Compared to single strands in free space, even of much larger diameter than
the individual strands, the stuff is lossier. If you look at Rac/Rdc for
decreasing strand diameters, the single free strand might level off at, I
forget, 28AWG or something, at say 100kHz, whereas in a big Litz cable (say,
a thousand strands), it keeps going until 36 or 38AWG, and even then, the
total resistance for equivalent area is larger (in addition to the increased
length due to the weave). It's like making copper a better resistor (or
alternately, a worse inductor).
The nice part is, you get to carry more total current, in an only slightly
larger volume, which is significantly smaller than the volume required of a
single massive strand. That is to say, at high frequencies, a large solid
conductor is O(N), while fine conductors are O(N^2). Litz has a smaller
constant multiplier on that Big-Oh than a single fine strand, but
appropriately chosen, it scales independently of frequency (as diameter
squared), something a solid conductor doesn't (it's perimeter limited). One
of those things that "shouldn't work" by certain physical principles, but
when considered holistically by the engineer, works great. ;-)
But anyway, in a seven-conductor construction, the always-central bundle is
completely surrounded by fields from the other six, and so has much more
eddy current losses, or higher Rac, or stronger proximity effect, or thinner
skin depth, or however one likes to say it (they're all aspects of the same
phenomenon, after all).
Yes. Proximity effect is all over the stuff, which is why the strands have
to be so much finer than the free space skin depth would suggest. Even 10
strands of 28AWG will be noticeably higher in resistance than 1/10th of a
single strand. 100 or 1000 strands need strands finer and finer still. The
scaling between number of strands and required decrease in strand diameter
is of course "far from straightforward", for the same reason.
I haven't seen any analyses of tape, but I've seen it used here and there.
Trouble is, the field around a conductor 'wants' to be round, and forcing it
to wrap around a foil conductor is somewhat counterproductive. It
necessarily must penetrate the conductor, particularly along the edges. The
conductor must be thin enough to allow this; a thick conductor will shield
its self-induction, and you get standard skin effect along the edges (within
a constant factor).
The result is, eddy currents flow along the edges. This manifests as skin
effect. Except, because we're talking about a somewhat two-dimensional
conductor, it's really edge effect, and instead of bulk resistivity,
thickness can be factored into the area resistivity, which edge penetration
then takes as a factor. For a finite thickness, edge penetration is deeper
than the free space skin depth (which is the limit at infinite thickness,
i.e., an infinite slab), but I don't know by how much.
If depth is inverse with thickness (a crude but not unreasonable guess,
taking the area resistivity approximation as a suggestion), then one would
need a conductor of thickness t = d^2/w, for width w and skin depth d. (If
t = w, you have a square conductor of dimension d, which is in the right
order of magnitude.) Unfortunately, copper at 100kHz is already only a few
mils, so you need truely microscopic foils to actually achieve full
utilization across the width of an average bobbin. That stinks.
Proximity effect still applies, so while you're doing this, you can't just,
say, wrap ten turns of foil primary, a layer of tape, then ten turns of
secondary; the innermost facing turns will burn up from all the congestion.
Tape does at least suggest itself nicely for transmission line approaches:
if the turns are similar, just layer primary and secondary together, with
tape between, like the plates of a capacitor. Except with a core in the
middle. Isolation capacitance won't be great, but leakage inductance will
be teensy. The image currents from primary and secondary will tend to flow
along the faces as well as the edges, because it looks more like a parallel
plate transmission line than an isolated foil conductor; that helps
efficiency a lot.
You can of course apply the Litz trick to foil, but you don't have any free
lunch; the geometry reduction is still required whether putting together a
bunch of strips or strands. Ten strips woven together will have less
resistance than a single strip of the same width and thickness, but higher
than 1/10th of an isolated strip that size. I know of at least one company
that claims to have some sort of foil technology that reduces Rac like Litz,
presumably doing some kind of weave. Tempting to buy a bigass custom part
from them just to take it apart and look, see how they put the stuff
together. I can't imagine it's all that easy to make, considering there are
only two US companies making the round stuff as is.
Tim
--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com
