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calculating power handling capability of a toroid core

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IamSmooth

Sun Oct 17 2010, 08:49PM

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

Can anyone run through some numbers to determine the power capability of a toroid?
Here are some numbers of a core that I saw:

Dimensions are OD 5.3/8 inches, ID 2.3/8 inches and height 1.3/8 inches

THe formula for power is

P = f * B * Wa/(17.26*S)

B = Vx 10^8 / 28.638*f*N*a

The other formulas are listed here

f = 120vac @ 60hz

I don't know the difference between the window area and the core cross-sectional area; they seem the same.
I don't know where I get the value for "S"

Thanks.

Dr. Slack

Mon Oct 18 2010, 07:25AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

I hate potted equations like that. Not only do they bury a lot of physics (which is OK if you need a quick answer), but they bury a lot of assumptions (which is not OK if you need an appropriate answer for your circumstances).

There is no such thing as "power handling" for a toroidal core, because the winding has been totally neglected. Just as the core has a maximum flux density to limit it, the core has a maximum current density. The power is the product of these two. The core's maximum current density is then given by temperature rise, which depends on things like duty cycle and wave shape. I'll admit that the buried assumption of using copper wire is almost certainly valid. The most conservative assumption for duty cycle is 100%. If that has been assumed in the potted equations then you'll get a safe design, but if you do want max power, and you can restrict running to 1 minute in 10, you can get much more power during the 1 minute if it can cool down during the other 9. For a ferrite core, Bmax is limited by core heating, so you can use a higher Bmax at low duty cycles.

It is really worth deriving this sort of thing from first principles if you can - Bmax and frequency gives volts per turn via the core area, then times current density gives you power. Do remember that the the amount of copper you can get in the winding window is much less than you'd think. Once hexagonal packing, insulation thickness, untidyness, space to wind the last turn have all had their chew at the available winding window, you'll be lucky to get 25% of the window area as solid current-carrying copper. That copper fraction is another vital assumption that doesn't get reflected in potted forumlae.

Steve Conner

Mon Oct 18 2010, 08:26AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

I assume that "S" is the core cross-sectional area. That's the cross-section of the magnetic part, as opposed to the winding window area, which is the area of the hole available for stuffing wires through.

To me, the power capability of a core would be whatever gets it to the maximum safe temperature on the basis of core losses plus copper losses. The maximum temperature is determined by the winding insulation, except in the case of iron powder cores which have a degradation mechanism at high temperatures (see Micrometals app notes for more details)

In a good transformer design, the core losses and copper losses are roughly equal, so to get a ballpark answer you can just calculate either one and double it. That of course assumes you're capable of designing a good transformer in the first place, so it somewhat begs the question

You can improve the winding packing fraction by using square wire or foil, though obviously neither of these works on a toroid.

For hobbyist transformer designs, I always recommend picking the biggest core you can find. Guess the number of turns, fire the transformer up, and feel it to see how hot it gets.

If it doesn't get too hot, you're done.

If the wire stays cool but the core gets too hot, put some more turns on to decrease the core losses. Use thinner wire if necessary to make it fit.

If the core stays cool but the wire gets too hot, try fewer turns of thicker wire.

If both the core and the wire overheat, you needed a bigger core.

Because you're only making one, the time saved by not having to optimize the design more than pays for the extra cost of the larger core.

Arcstarter

Mon Oct 18 2010, 10:06PM

Registered Member #1225 Joined: Sat Jan 12 2008, 01:24AM
Location: Beaumont, Texas, USA
Posts: 2253

Thanks Conner! This is a good thread...

Sulaiman

Tue Oct 19 2010, 05:17AM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

ditto to Steve's reply except
S is the current density in circular mils per ampere (Generally 750 to 1500 cir mils),
as stated in the article.
It is the inverse of the more commonly used amps per square millimeter
(with a constant multiplier)
It refers to current in the wire and wire csa.

We Europeans use a simpler system of units.
System International (Except USA and Liberia)

Weston

Tue Oct 19 2010, 05:42AM

Registered Member #1316 Joined: Thu Feb 14 2008, 03:35AM
Location: Cambridge, MA
Posts: 365

If it is a careful balance between winding loss and core loss, why do torodial transformers have so much unused winding space? I have some 300 watt toroids that have a few square inches of winding space that is unused. In the case of winding a toroid is it just the number of turns that can be efficiently wound? As after a number of turns the wire starts to bunch up on the inside of the toroid.

Steve Conner

Tue Oct 19 2010, 07:57AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Yes. There has to be a big enough hole left in the middle for the hoop of the winding machine to pass through.

Also, for toroidal inductors meant for high frequencies, you run into self-capacitance problems if you use more than one layer of wire.

Dr. Slack

Tue Oct 19 2010, 12:47PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

I've just sketched out your quoted dimensions, and it seems to have quite a small hole for copper compared to the large core cross section. Can you confirm the dimensions, perhaps in mm this time?

IamSmooth

Tue Oct 19 2010, 10:36PM

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

I got the numbers from an Ebay sale item

It is possible this person wrote them down wrong. I just was curious what power it could handle.

klugesmith

Wed Oct 20 2010, 05:48AM

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

Steve McConner wrote ...
For hobbyist transformer designs, I always recommend picking the biggest core you can find. Guess the number of turns, fire the transformer up, and feel it to see how hot it gets. ...
Because you're only making one, the time saved by not having to optimize the design more than pays for the extra cost of the larger core.

Someone on this forum once said, about transformer design for commercial products:
"If it gets too hot, you need a bigger core. If it doesn't get sort of hot, it's too expensive".

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