Non linear inductor for 32Arms sine source.

[cupoftea]

Hi,

We are making a 32Arms sine source (50Hz). .using a 40khz switching bridge. Its simply to shovel 32Arms through the conductors of a mains distribution box so as to high current test it.

We wish to use a kool mu torroid inductor in the switching bridge.

It is Mag inc part number 77907A7, and will be approx 31uH at peak current (45A).

Mag inc part number 77907A7 datasheet:

https://www.mag-inc.com/Media/Magnetics/Datasheets/0077907A7.pdf

We want to work out the peak B (so we can check it wont saturate) and the delta B, (so we can calculate core losses).

The 77907A7 datasheet only gives a graph of AL vs NI.

To get the “B vs Current curve”, we have done as in the attached excel.

Basically, we have taken the graph as being piecewise linear and considered three linear sections, with the three gradients. Thus we get the "equation" for the graph, as in the excel attached.

We end up calculating the ur from the AL value. We then get the uo.ur value for each current value. uo.ur is the gradient of dB/dH....so we actually calculate the dB/dH at each value of H, and thus gradually build up the B curve, as it accumulates upwards as the current increases.....in the end , we dont even end up plotting the graph, but just get the table of values, which suffices well enough for the purpose.

At the peak current of 47.5A , we calculate a peak B of 0.357T.

Would you say this sounds right?

We also calculate a delta B of just 26mT at the peak of the sine, which seems very low?

Is it correct? Is this the right way to go about the calculation?

 

[FvM]

ΔB is a function of inductor parameters, bridge input voltage, operation point and modulation scheme. It can't be derived from the given information. If the shown simulation waveform with ΔI of about 2.1 A is realistic, ΔB will be actually very low.

--- Updated Aug 22, 2021 ---

The Magnetics powder core catalog is presenting different calculation methods for ΔB. For small AC currents with DC bias, you can appy simple methods.

 

[cupoftea]

If the shown simulation waveform with ΔI of about 2.1 A is realistic, ΔB will be actually very low.

Yes i agree, ..and it does come out very low, as the top post shows.
Do you believe the vale of peak B of 0.357T is correct?

The datasheet gives a graph of NI vs AL.....that, i am sure you would agree, is enough info to calculate peak B for any givien inductor with N turns?

AL , as you know, is the allowance.......the reluctance is (1e9/AL)....from reluctance we can easily calculate ur........and then uo.ur. "uo.ur" is the gradient of the B vs H curve.

So what we are saying, is that we can calculate the gradient of the B vs H curve at every single point. We know that when B=0, H=0, so we can therefore start building up the B vs H curve from there.......because we know the gradient of the B vs H curve at any H value that we like.
I just cant understand why the Mag Inc website dont propose this method?.......its the intuitive way.

I dont see in the Mag Inc website where they show there calculation for peak B, given a current of "A" amperes in a kool mu torroid of N turns?

--- Updated Aug 22, 2021 ---

It can't be derived from the given information.

Thanks, but i must confess, that the reason for the shown method, is from directions kindly given by yourself a year or two ago......Surely you agree this is correct?......i mean it simply employs the fact that dB = uo.ur.dH.

The stupid mistake i made a year ago was when i forgot that uo.ur was the gradient of B vs H at any point of H....but you kindly dug me out of this hole.

 

[FvM]

Bpeak looks right according to Kool Mµ material characteristics.

But I don't see where you get ΔH for the calculation.

 

[cupoftea]

But I don't see where you get ΔH for the calculation.

Thanks, good quesion....i get it by simply stepping the current up by 100mA in the table, and then calculate H at every current value...then delta H is just the difference between adjacent readings of H.....i confess my explanation has been poor here, and apologiose for this. (in the excel, the current being stepped up by 100mA each time, can be seen...and the calc of H for each current value is done)

--- Updated Aug 22, 2021 ---

Bpeak looks right according to Kool Mµ material characteristics.

Thanks, and that also means that my delta B must also be correct. I must thank yourself for this FvM, it was your own close guidance some time back that lead me to this technique.

 

[FvM]

directions kindly given by yourself a year or two ago

I guess you are referring to this previous thread: https://www.edaboard.com/threads/fi...-iron-torroid-inductor-in-an-2tfc-smps.396176

It's about an application with relative large (> 40%) current variation. But even in this case, using AL or µr versus DC bias relation (Method 3 in the Magnetics catalog loss calculation) and putting in average DC current gives fair estimations for ΔB and losses.

ΔI is set by the application, and I simply don't find information about it in this thread, except for the said waveform.