# How to design/ calculate inductor with a toroidal core?

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#### polashd

##### Member
I’ve some toroidal inductor cores of different types (iron powder, ferrite, MPP).
I want to make inductor/ transformer for SMPS.

To do this I need to know/calculate the max power capacity of the core, max current before saturation.
Searched internet, ended with many different methods/ formulas which are confusing for me (as a hobbyist).

For example I’m providing data of two toroidal cores:
1) MPP core# C055120A2-2 (datasheet attached)
2) Iron powder core# T-106, material#52 (permeability=75, AL=95nH/N2, OD=26.9mm, ID=14.5mm, h=11.1mm)

Can anyone please provide me simple method/ formula (based on above core data) to:-
-Calculate maximum power capacity.
-Calculate maximum current without saturation.
-How to use the DC bias curve (in the datasheet)

#### Attachments

• C055120A2.pdf
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There is no exact maximum current without saturation. There is a gradual saturation, which is why there is a DC bias curve.

You quoted AL=95nH/N2 and the datasheet for the other core quotes AL = 72nH/T2. Either N or T are used for number of turns.

Those factors allow you to calculate the inductance, so the one in the data sheet would have an inductance of 7.2 μH with 10 turns or 28.8 μH with 20 turns.

The DC bias curve shows how the inductance would reduce as the DC bias increases. With 10 turns, and a DC current of 20 A, there would be 200 A.T (Amp turns) so the AL would have dropped to about 32nH/T2, so the 10 turns would only be giving 3.2 μH

The maximum power capability depends on so many factors that the core manufacturers can't possibly quote it. Making an SMPS transformer isn't easy. I suspect a lot of trial and error goes into it even with established manufacturers.

What sort of SMPS is it? There are flyback converters, and forward converters.

If you are using mains voltages, be careful to make sure that you have the correct isolation between windings, and testing can be dangerous.

(Edit for unit corrections)

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Those factors allow you to calculate the inductance, so the one in the data sheet would have an inductance of 7.2 mH with 10 turns or 28.8 mH with 20 turns.

The DC bias curve shows how the inductance would reduce as the DC bias increases. With 10 turns, and a DC current of 20 A, there would be 200 A.T (Amp turns) so the AL would have dropped to about 32nH/T2, so the 10 turns would only be giving 3.2 mH
this confuses me! as A.T & nH/T2 both are dependent on each-other how to calculate T? without AL value I wont find T, after getting T I find A.T which affects AL and again the calculation loop continues (what am i missing!).
For example: a 3A smps buck circuit need 100uH inductor. what should be the value of T & how to calculate? what if the current is variable?
The maximum power capability depends on so many factors that the core manufacturers can't possibly quote it. Making an SMPS transformer isn't easy. I suspect a lot of trial and error goes into it even with established manufacturers.
How do a circuit designer know which core to use?
What sort of SMPS is it? There are flyback converters, and forward converters.
Mostly variable (40v max) bench power supply (50w max) or fixed voltage adopter, (buck, boost, flyback) for hobby experiments.

I just saw that I got my units wrong in my first answer, which I've now corrected.

In your example, you may need to calculate a few times. If you start with the need for 100 μH. With the figure of 72 nH/T2, you need 100000/72 = 1389 turns squared, so around 37 turns.

If you have 3 A and 37 turns, that gives 111 Amp turns. That reduces the AL to about 55, which would put the number of turns up a bit, to 42. That gives 126 Amp turns, which reduces the AL a tiny bit more. You can keep going a few times, and it will get closer and closer to a value that will work.

Or you can see where it is going and guess a number of turns. Say you go for 50 turns, that is 150 AT, so AL is about 45, then the inductance is 112 μH. So you try 46 turns, 138 AT, AL is 48 and you get 102 μH. As the tolerance is 7% so that's as close as you're going to get.

You then need to see how easy it is to get 46 turns of whatever wire you need, and any other windings, onto the core.

As the inductance will change with current, if you need the inductance to be accurate at all currents, you will need a much larger core. However most designs don't rely on accurate inductances.

I don't know how designers know which core to use. I guess that others do calculations like I've just done, and go up in size if the winding won't fit and down in size if the core would take a lot more windings than are needed.

There are lots of other considerations, so like with all design, there are lots of things to consider. Some parameters will be critical, others will be unimportant.

The inductance needed depends on the circuit. That is where you start.

I did the calculation that way (with different values of AT from the curve. Ms excel helped to find T (using goal seek tool).

But still I don't know the power capacity, can it handle power conversation from 24v to 12v 3A (for example) at a given frequency.

That is what the inductance tells you. The voltage across the coil is equal to the inductance times the rate of change of current.

If you have 12 V across the coil, and it's 100 μH, then the current will change at 12/0.0001 = 120,000 Amps per second. It will take about 25 μs to get from 0 to 3 A. If the current is increasing for the same time as it is decreasing, and it goes from zero to 3 A and then back to zero, the average current will be 1.5 A and the frequency will be 1 / (25 μs + 25 μs) or 20 kHz.

You haven't said what the circuit topology is, so there are lots of guesses as to how the inductor is used.

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I’ve some toroidal inductor cores of different types (iron powder, ferrite, MPP).
I want to make inductor/ transformer for SMPS.

To do this I need to know/calculate the max power capacity of the core, max current before saturation.
Searched internet, ended with many different methods/ formulas which are confusing for me (as a hobbyist).

For example I’m providing data of two toroidal cores:
1) MPP core# C055120A2-2 (datasheet attached)
2) Iron powder core# T-106, material#52 (permeability=75, AL=95nH/N2, OD=26.9mm, ID=14.5mm, h=11.1mm)

Can anyone please provide me simple method/ formula (based on above core data) to:-
-Calculate maximum power capacity.
-Calculate maximum current without saturation.
-How to use the DC bias curve (in the datasheet)

For the Rio powered cores, Micrometals established the material number formulations and corresponding color codes of the core. Micrometals used to have an online calculator (I haven't been on their site in years). I think they bought Arnold Magnetics as well. In any case, the calculator should show max frequencies and saturation at frequencies.

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