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Toroidial Core Power Calculation

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KLH

Wed Jan 28 2009, 10:58PM

Registered Member #1819 Joined: Thu Nov 20 2008, 04:05PM
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Posts: 137

I've looked at Amidon's databook for their magnetic cores, and I saw their graph showing Toroid Size and Frequency vs. Power. However, the graph only extends to 100 kHz, and in another page of the databook, there was a list of the types of ferrite saying that the 77 material had low core loss up to 1 MHz.

Is there an equation that can tell me what the absolute maximum power is of a core at its maximum frequency? Does it involve core cross section, volume, surface area, or some combination of these?

Any help would be greatly appreciated.

Shaun

Thu Jan 29 2009, 12:42AM

Registered Member #690 Joined: Tue May 08 2007, 03:47AM
Location: New Jersey, USA
Posts: 616

I'm not entirely sure but I believe maximum power throughput at a given frequency is directly related to cross-sectional area. So, 10X the frequency should allow for approximately 10X the power.

...

Thu Jan 29 2009, 04:56AM

Registered Member #56 Joined: Thu Feb 09 2006, 05:02AM
Location: Southern Califorina, USA
Posts: 2445

The power is ultimatley limited by the copper losses of the transformer, but one of the main limiting factors is the volts/turn you run, which is inversely proportional to frequency. Likewise, going from 100hz to 1Mhz will let you run 10,000x as many volts per turn (which would imply 10,000x as much power through the core). BUT, the core material is also very important, and you can't compare a 100hz iron core to a ferrite core, you also need to know the permeability of the cure and you can then calculate the maximum v/tun based on the core cross section. But at that point its just as easy to wrap a few turns of wire around your core and see how much voltage it takes to saturate the core at your operating frequency.

Although what you should take away from this is that calculating the 'absolute maximum power' going through a core isn't easy, and depends on a whole mess of factors.

Dr. Dark Current

Thu Jan 29 2009, 06:26AM

Registered Member #152 Joined: Sun Feb 12 2006, 03:36PM
Location: Czech Rep.
Posts: 3384

... wrote ...

The power is ultimatley limited by the copper losses of the transformer(...)

umm what?

If this was the case then we could run iron core transformers at kilovolts per turn at 1MHz... The upper frequency limiting factor is the heating of the core, including hysteresis losses and eddy current losses.

...

Thu Jan 29 2009, 06:48AM

Registered Member #56 Joined: Thu Feb 09 2006, 05:02AM
Location: Southern Califorina, USA
Posts: 2445

As I said, what you should take away from this is that there isn't a magic formula that will tell you that a core of size X can transfer Y amount of power through it.

You can, however, get a ballpark figure by finding how many v/turn you can run before saturating the core (which will be limited by your frequiency, which is limited by core losses), and then find out how much current you can run based on how thick a piece of wire you can use to wind your primary/secondary and still fit enough turns to satisfy your maximum v/turn limit. Of course depending on the frequency and voltages you are running you will run into all sorts of other problems (insulation, self capacitance, leakage inductance, etc) that will further limit you.

Dr. Slack

Thu Jan 29 2009, 10:06AM

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

Core maximum power throughput is absolutely thermally limited. You need to take into account whether you have a continuous or an intermittent application.

If it's intermittent, you can increase the current until the copper goes 20C to 90C in X seconds, and the core frequency and peak flux until the core gets as hot as fast as the copper. Obviously the smaller X is, the higher power you can run. As heat is stored, you can do the calculation seperately for both core and windings.

If it's continuous, you'll need to dissipate the excess power, rather than just storing it in the thermal mass. Forced cooling, and planning the windings for cooling, may make a significant difference. As heat flows from both core and windings to ambient, the optimum partition of losses to maximise the throughput will not be obvious, though splitting them 50% to each may make a reasonable first stab, as would 33% to the harder-to-cool core with the balance in the windings.

Another softer limit is efficiency. The harder you run the windings, the lower the efficiency at maximum current. The harder you run the core, the higher no-load losses. You may have a figure anywhere in the range 50% to 90% in mind for limiting efficiency.

So, no magic formula.

KLH

Thu Jan 29 2009, 02:44PM

Registered Member #1819 Joined: Thu Nov 20 2008, 04:05PM
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Posts: 137

I have the whole Amidon databook, and there is this formula:

_____VPk * 100_____
4.44 * Ac * Nt * F

Steve Conner

Thu Jan 29 2009, 02:47PM

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

Another important point is that the maximum volts/turn on ferrite cores doesn't increase linearly with frequency (ie, constant Bmax)

Rather, because core losses increase with frequency, you have to run lower Bmax at higher frequencies to keep from overheating the core. Even at regular SMPS frequencies, your Bmax is limited by heating, rather than actual saturation.

So the highest frequencies maybe aren't as attractive as they might seem. The highest frequency SMPS I've worked with is one of those 1kW Xantrex things, that runs at 125kHz.

KLH

Thu Jan 29 2009, 02:53PM

Registered Member #1819 Joined: Thu Nov 20 2008, 04:05PM
Location:
Posts: 137

Thanks for all your replies, but I still have a question.

The two push-pull transformers I'm working on are a 12V primary 4+4 turn transformer operating at 50kHz, and 169.705V (120 VAC * sqrt(2)) primary 75+75 turn transformer operating at 100kHz. I want to know if I can push the second transformer's core (FT-140-77) to 1MHz with 33+33 turns without excessive losses.

I have the whole Amidon databook, and there is this formula:

_____VPk * 100_____
4.44 * Ac * Nt * F

where Vpk is the applied peak voltage, Ac is the core cross-sectional area, Nt is the number of turns on the core, and F is the operating frequency.

There is also a table showing maximum flux density, and it says:

100kHz: 500-700 gauss
1MHz: 150 gauss

Is this the right formula to help me determine the amount of turns I can use without the core saturating (and indirectly, the volts per turn)? If this is the correct formula, then I think that my transformer should be okay running at 1MHz.

Dr. Slack

Thu Jan 29 2009, 07:43PM

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

killah573 wrote:

100kHz: 500-700 gauss
1MHz: 150 gauss
Is this the right formula to help me determine the amount of turns I can use without the core saturating

No, it's the right formula to determine the amount of turns you can use without the core overheating

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