I designed and prototyped a custom inductor for a high-power boost converter.
The windings are getting super hot and I don't understand why.

The core is an E70 gapped to 400nH/n^2.
The winding is 3-filiar 18 AWG copper - 10 turns.
The zero-bias measured inductance matches the design calculations at 33uH. Working backwards from the scope trace it seems a bit less than that, maybe 25uH
The average current is about 15 amps and this matches the measured DC current into the converter.
So far, all of this is per the design.
Switching frequency 68 KHz.
Duty cycle 80%

THIS CALCULATOR gave me a resistance for each wire of 26milli-ohms so the 3-filiar winding should be 1/3 of that,. 8.7 milliohms. This gives me a copper loss figure of 15*15*8.7/1000 = 2 watts. I guess I don't know how to calculate the temperature rise from this but I didn't expect it to be a significant. I'm measuring a rise of 200C (with an IR camera) before I chicken out and turn it off. I'm starting to get that "hot transformer" smell. I even have a small fan blowing air over it.

Someone is going to say that it's core heating but I'm pretty sure it isn't. The core remains cool to the touch and I've calculated the peak flux density at 0.17 T yielding a core loss of 7W. Also, the current trace doesn't show signs of saturation. Even at 0.2T, 100 KHZ the data sheet gives 38W. And the surfaces of the core I can reach stay cool to the touch.

Why is my copper loss so far off? Even if it was one strand of AWG 18, I'd only expect 6 watts. This seems like hundreds of watts.

 

If You are satisfied that Copper-Loses are the problem,
just add more Copper,
looks like You have plenty of room for it.
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Well, that would be too easy Mostly, it bothers me that I don't understand it by a huge factor.
I can fix the inductor, as you say, with more copper. But that's not what I really want to fix. I want to fix
my understanding of the analysis.

 

It does not look like the three wires are well soldered together.
Are they?
You need to strip the varnish from the wires and apply flux to make a good solder connection.
The solder should smoothly flow across the wires without being globby.
You may also need a larger wattage iron.

 

Good question. So I reworked it but then I blew it up.

 

So I reworked it but then I blew it up.

So...it doesn't get hot anymore?

 

Magnetics will always contain some "Black-Magic",
and it gets worse with increasing Frequency.
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.

 

If You are satisfied that Copper-Loses are the problem,
just add more Copper,
looks like You have plenty of room for it.

Not exactly. I had this problem at 64 kHz -the transformer was too hot to touch with bare hands.

The magnetic flux near the core is rapidly changing across the diameter of the copper, causing eddy currents within the wire which result in large I2R losses.

The solution that worked for others besides me is to replace the large diameter wire with multiple strands of insulated wire. Enamel is fine for this. Consider it to be high powered Litz wire, which, if you have a budget, you can order.

I would run multiple strands of a finer wire, like #32 or #34 from my workbench to my son standing in the street in front of the house, then connect my end to the chuck of my electric drill and run the drill until the twists per inch looked about right, then give the wire a little stretch to orient the grain so it would retain the twists, and then use that to wind the transformer. It worked like a charm.

Initially the total area of the multiple strands of wire were approximately equal to the area of the single strand being replaced.

 

Litz wire is hard to find. Go to ebay.com. I use it often. The ebay wire is very old but good.

 

I don't know the answer but I know more. For future seekers with the same problem:

One possible answer was that my intuition about the temperature rise from a given amount of copper loss is just horribly off. i don't really have a good way to calculate it, but I feel like a couple of watts shouldn't do much.

So it occurred to me to test this assumption by running 15 amps DC through the winding. This also gave me a chance to actually measure the resistance. It barely gets warm to the touch. In fact, the power supply leads got hotter than the winding. So my intuition is OK but now I know the root problem is some kind of weird high-frequency effect. Maybe my skin-effect calculation is way off. At DC, the resistance of the winding is 10 milliohms.

 

Not exactly. I had this problem at 64 kHz -the transformer was too hot to touch with bare hands.

The magnetic flux near the core is rapidly changing across the diameter of the copper, causing eddy currents within the wire which result in large I2R losses.

The solution that worked for others besides me is to replace the large diameter wire with multiple strands of insulated wire. Enamel is fine for this. Consider it to be high powered Litz wire, which, if you have a budget, you can order.

I would run multiple strands of a finer wire, like #32 or #34 from my workbench to my son standing in the street in front of the house, then connect my end to the chuck of my electric drill and run the drill until the twists per inch looked about right, then give the wire a little stretch to orient the grain so it would retain the twists, and then use that to wind the transformer. It worked like a charm.

Initially the total area of the multiple strands of wire were approximately equal to the area of the single strand being replaced.

Thanks, Ron! I hadn't thought of circulating currents within an individual wire. I did wonder what happens if the length of the strands and/or the intercepted flux isn't balanced. I am certainly going to try your suggestion of smaller wire, especially now that I know it really is some kind of high-frequency-related effect.

 

In case you missed it: When using smaller wire use multiple strands to get about the same copper cross section as with the original wire otherwise you will be increasing another type of copper loss (resistive).

Please let us see what happens!

 

As Dick suggested, multiple strands solved the problem. I used 20 strands of AWG 30 wire. The current waveform is a ramp from 0 to 47 amps and the inductor doesn't even get warm. Note that I did NOT have to match the total cross-section of the original wire because the skin depth is more than the thickness of AWG 30 so I'm effectively using all of the copper.