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IamSmooth

Tue Jun 15 2010, 05:57PM

Registered Member #190 Joined: Fri Feb 17 2006, 12:00AM
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Posts: 1567

Here is a skin effect calculator

For a 100khz frequency I get a little under 10mils. So, if I have a flat conductor, does this mean it should be 20mils thick, which would allow 10mil penentration of current on each side?

Mattski

Tue Jun 15 2010, 06:30PM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

Current density falls off exponentially, something like exp(-z/delta) and skin depth is just the point where it falls to 1/e (z = delta). So you really want thickness to be 5+ skin depths in order to provide the lowest possible resistance.

I'm not sure about the two-sided thing though.

edit: I should also point out that you don't *need* 5 skin depths, it's just that at that point you've reduced the resistance to the minimum you can get at a particular frequency.

Marko

Tue Jun 15 2010, 07:35PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

Mattski wrote ...

Current density falls off exponentially, something like exp(-z/delta) and skin depth is just the point where it falls to 1/e (z = delta). So you really want thickness to be 5+ skin depths in order to provide the lowest possible resistance.

Hi,

Just to add on this - when we are designing a transformer, we want to save on copper and core material used. And actually thinnest possible strip with largest possible surface would be most efficient material usage - though we still want something we can practically wind onto a transformer, and is still used up by current by like 99 percent. Hence 3-5 skin depths or whatever as a choice.

I was curious about one other thing though - how do copper strips compare to litz conductors? I've learned that copper strips and bars in electromagnetic machines tend to experience current bunching towards their edges. In motors, current tends to bunch in parts of conductor farther from the core.
To what extent would this be prominent in a toroidal transformer, if at all?

Marko

radiotech

Tue Jun 15 2010, 10:37PM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
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"In motors, current tends to bunch in parts of conductor farther from the core.

In 60/50 Hz machines the current density in amps/cM^2 in the rotor core conductors (squirrel cage) imbedded close to the surface is a function of the torque but the depth of the slots in which the conductor (typically cast aluminum). The current density on the outer parts of the cage conductor might be more because the enshrowding iron has more effect on the self inductance of that portion without the open gap. The same thing happens at the stator winding coil ends where the wire emerges an essentially is in air.
On the rotor cage, the slot shape and stator teeth themselves are the root of high frequency currents due to shaping of magnetic fields, and those currents may be affected more by skin effect.

At the main magnetizing current, skin effect would be almost
impossible to demonstate unless the conductor area is above 500,000 circular mills. 60 Hz.

IamSmooth

Wed Jun 16 2010, 01:02PM

Registered Member #190 Joined: Fri Feb 17 2006, 12:00AM
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So is it safe to say, before I make a purchase of a flat conductor, that the current will be evenly distributed over the surface for a flat conductor at high frequency, and not at the edges?

If someone can make sure my calculations are reasonable for conducting 40A at 100khz as a primary toroid winding:

I figure that 270mil^2 are needed to conduct 1A. This gives me 10840mil^2 cross-section needed for 40A. The stip comes at a maximum thickness of 20mil, so the width would be 542 mils. This gives me 20mil x 500mil strips of insulated copper.

klugesmith

Thu Jun 17 2010, 05:39AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

[edit: interchanged paragraphs]

How big is your toroid core? (for well-behaved winding of 1/2-inch-wide strip) You could experimentally wind some of the plastic strapping used to secure loads in crates & on pallets.

What is the toroid made of? (for tolerable core loss at 100 kHz)

I think at 6A/mm^2 you are pushing the current density, for a large thick winding, but see myth 5 below.

There's a detailed analysis of skin effect, proximity effect, etc. here, tho' I can't attest to its accuracy.

Along those lines, these people

say
"Myth #7: If the wire diameter is less than the skin depth, there are no significant high-frequency losses
A very misleading and dangerous assumption. If you have a lot of layers in a winding, you can have very large proximity losses even with very small wire gauges, well below the skin depth in diameter."
and
"Myth #5: An optimum transformer winding has a current density of 500 - 750 circular mils per amp
... Current density is irrelevant. What matters is how much dissipation is in the wire, and whether there is sufficient cooling to keep its temperature in the acceptable range. Given the extreme types of cooling which may be used in power supplies, ranging from liquid immersion at one extreme, to operation in the vacuum of space at another, the appropriate current density in the wire will vary widely.
After designing practical transformers at Ridley Engineering for more than 20 years, frankly we have no idea what the current density of any them was. The only relevant question is: how hot is it?"

More practical SMPS info here.

DrZoidberg

Sat Jun 26 2010, 05:29AM

Registered Member #350 Joined: Mon Mar 27 2006, 05:14PM
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Doesn't the skin effect also depend on the resistivity of the material?

Patrick

Sat Jun 26 2010, 07:43AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

yeah Dr. Z it does but lead, copper, and, aluminum are prtty close in terms of permitivity. also Iam smooth you need to consider the TI / Unitrode PDF's which describe surface effects. ill post it here if i can find it.

and the skin effect allows a single depth of conduction between the positive and the ground / return wire, lets say you have a 1 inch square copper bar, with a similar bar returning next to it, well it you skin depth is 10 mils deep, then you would have 0.01 x 1.00, conductive area, you would not have 0.01 x 4.00 conductive area.( unless you distribute the return e-field around the circumference like co-ax)

i love futurama ! it returns!

DrZoidberg

Sat Jun 26 2010, 08:20AM

Registered Member #350 Joined: Mon Mar 27 2006, 05:14PM
Location:
Posts: 106

Yes, futurama is finally back.
I knew it was only a matter of time until comedy central came to their senses.

So what is the skin depth at 100 kHz if the conductor is the human body? How do I calculate that?

Bjørn

Sat Jun 26 2010, 12:20PM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

It would be very hard to calculate and the result would not be a number but something with many dimensions. The body is not a uniform conductor but several intermingled networks with different properties. The formula for a uniform conductor is here:

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