Finding inductance of single turn ferrite core pair inductor

Hello,
We are looking to find the inductance of the following ferrite core set-up. (attached)

Is the following ok..

Ampere’e Law N.I = H.dl
..substitute H = B/(u0.ur)
N.I. = [B/(u0.ur)] * dl
..substitute B = (L.i )/ (N.A)

Eventually gives
( [N^2] .A u0.ur) / dl = L

Where:
A = minimum core pair area
dl = magnetic path length
etc

Draw its equivalent magnetic circuit (which is like at page 23) and find all reluctances.
L=N^2/total reluctance
total reluctance=R1+Rg(if any)+R2/2 (assumed R3=R2, otherwise, R3//R2)

https://ocw.mit.edu/courses/electri...ring-2011/lecture-notes/MIT6_007S11_lec11.pdf

L = N^2 Uo.Ur Ae / lg

with an air gap, it dominates, and lg = the air gap length, and Ae = the effective area of the air gap.

For ferrite with finely ground (mirror finish) faces, the lg is the effective length of the core structure, and Ae is the effective area.

Note that for high Ur, and no air gap, the inductor will saturate at quite low currents, and its effective L will vary as soon as the bendy over part of the B-H loop is reached.

B = uH = UoUrAmpTurns/Lmag. Given that Lmag (length) is usually small (<< 1metre) then a Bsat of 0.3T is easily reached with no gap ...

For EE core structures with small but finite gaps the L is a combination of the two...

L = N^2 Uo.Ur Ae / lg

Click to expand...

Thanks, and this demonstrates how inductance is proportional to permeability. As we know, ferrites have permeability which varies enormously with temperature. Also, with some ferrites, permeability also varies with the Ampere.turns. This is a nightmare for people making resonant power supplies and who need to pretty exactly set a certain LC resonant frequency when the L is all over the place.
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Its also worrying because the Effective Area (Ae), is that area which gives a certain inductance according to L = B.Ae.N/i
..However, once the Flux density , B, has saturated in the region of minimum core area (Amin), then the inductance doesn’t correspond to L = B.Ae.N/i any more.
Getting an exact inductance value with the type of inductors shown in the top post is going to be very problematic.

You simply set the inductance with the air gap, and ensure the B = 0.25T at peak I. Same for any gapped choke.

Draw its equivalent magnetic circuit (which is like at page 23) and find all reluctances.
L=N^2/total reluctance
total reluctance=R1+Rg(if any)+R2/2 (assumed R3=R2, otherwise, R3//R2)

**broken link removed**

Click to expand...

Thanks, I am not sure its like in page 23, because our case doesn’t have the turns on the centre leg. With our case, its more like two overlapping , square-ish torroids. I don’t think the Rel1 + Rel2/2 equation applies in our case?

energy in a choke = 1/2 L I^2, also energy = 1/2 B.H Vol. thus, L.I^2 = B.H.Vgap, we know B = UoUrH, so L.I^2 = B^2 Vgap / Uo - for air (Ur = 1)

Thus, if you know the max B you can have, at the max I, then you can work out the volume of the gap, then, knowing the area, you get the Lgap.

Given the core is there you will always get a bit more L that calc, and a wee bit more energy storage - all to the good, either increase the gap to get the desired L, or take turns off (in the prototype) or a combo, and voila, you have a choke that will meet your needs (wire dissipation another matter)...

easy peasy ...

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You have a centre leg, with one complete turn, the Reluctances add (in series) - but you can ignore the core to a 1st order approximation ....

You simply set the inductance with the air gap, and ensure the B = 0.25T at peak I. Same for any gapped choke.

Click to expand...

Thanks, in our case, we don’t have an air gap. We cant have an air gap and our ferrite surfaces are lapped and tightly clamped together. We can’t have an air gap because we only have one primary turn, and any air gap would make the inductance too low. We would then get too much magnetising current in our transformer…..(because there will also actually be a secondary, but that can have more turns than one)

This is our overall setup…
https://www.edaboard.com/showthread.php?377465-Waterproof-LED-lighting-system-with-no-contacts

If an air-gap is needed in order for us to set an exact inductance value, then i think maybe we should use some of that intrinsically-gapped ferrite? -It kind of has the gap kind of integrated into the ferrite material, and there isnt an actual air-gap , so to speak.

It would be best to size everything so that the gap is at least = 0.2mm or greater. There are very few other ways to get a close tolerance L.

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Oh, p.s. you likely know - but a 0.1mm sheet of, for example Nomex, on all 3 legs = 0.2mm gap...

Thanks, and this demonstrates how inductance is proportional to permeability. As we know, ferrites have permeability which varies enormously with temperature. Also, with some ferrites, permeability also varies with the Ampere.turns. This is a nightmare for people making resonant power supplies and who need to pretty exactly set a certain LC resonant frequency when the L is all over the place.

Click to expand...

It seems to me like the hidden question behind this thread is "can we make a ferrite inductor or resonant transformer without an air gap"? Because all considerations in the above quote make only sense for a gap-less inductor.

The simple answer is, no you can't. Inductance variation is one point, but first of all you don't get reasonable I²L amount without a gap. Energy is stored in the air gap, not the ferrite.

Thanks, the other point is that we need to know the inductance at 50kHz. -Since our inductors will have a 50kHz sine current in them.

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The simple answer is, no you can't. Inductance variation is one point, but first of all you don't get reasonable I²L amount without a gap. Energy is stored in the air gap, not the ferrite.

Click to expand...

Thanks, then we’ve had it, because we only have a single turn primary and we simply can’t have any air gap no matter how small, because we need to get our primary magnetising inductance up high because we only have one turn on the primary……the primary current in one of our systems for example is fixed at 1.9A RMS………..(it’s a 50khz sine). If most of this 1.9A current is magnetising current, then we aren’t going to have any “primary referred secondary current”……and then we won’t be able to get anywhere near enough secondary current for our LED luminaires…
This is our setup..using clip-on ferrites as in the top post….
https://www.edaboard.com/showthread.php?377465-Waterproof-LED-lighting-system-with-no-contacts

But anyway, in our ferrite inductive couplers, we don’t need energy storage…because they are used as transformers…however, the resonant power stage in the driver will see the inductances of the primaries, and therefore we need to know what they are , because they will effect the resonant frequency of the driver stage which produces the fixed 50khz rms sinewave current.

Thanks, the other point is that we need to know the inductance at 50kHz. -Since our inductors will have a 50kHz sine current in them.

Click to expand...

If you are using a gapped of-the-shelf core, you'll take the datasheet Al value, it's o.k. for 50 Khz

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O.K., the thread is somehow sailing under false colours, you are designing a transformer not an inductor.

Can you give ballpark numbers for core cross section and input voltage respectively transformed power? Or did you already calculate the magnetizing flux?

Thanks , we will calculate the magnetising flux, or rather in our case, the saturation current by i(sat) = B.A.N/L

We also want to check our inductance calculation with the LCR45 inductance meter...
https://www.tester.co.uk/peak-lcr45...MI_86M7rK32wIVBLftCh2qsgABEAQYBCABEgLyEPD_BwE

....it offers test frequencies of 1khz, 15khz and 200khz.
Which one do you think will be best for our ferrite core with single turn (as in the top post)?

..as you know, this should not matter, the frequency should pertain just to parasitics...i mean, say if there is a lot of interwinding capacitance the 200khz one may be inaccurate.

Quality LCR meter should give consistent measurements for all frequencies, I would use nearest 15 kHz.

treez said:

Thanks, I am not sure its like in page 23, because our case doesn’t have the turns on the centre leg. With our case, its more like two overlapping , square-ish torroids. I don’t think the Rel1 + Rel2/2 equation applies in our case?

Click to expand...

Well, that it was what it looked like from your picture. Otherwise, put it on the other leg and recalculate total reluctance for that leg.

LCR meter seems a faster (and more accurate) way though.

Your basic problem here is that you appear not to have given yourself enough room to design a choke - or part of a transformer - with sufficient size to allow a small air gap to fix the inductance. With no gap the L will be high (Ur ~ 2300) until you put some current thru it ( ~ 5 amp say ) then the L will fall over as the ferrite saturates. If you use a low Ur high freq ferrite the effect will be less pronounced, but still there - some may suggest a low Ur iron powder core - but you will still have the issue of falling L and higher losses than for ferrite.

you appear to need a Tx with a single turn high current input? or output? if you are trying to make an LLC xfmr then you can have a Tx with no gap and good coupling and put the L on the HV side - a fixed L, ferrite, gap, litz (or whatever). i.e. a separate part.

It is important in a design not to paint your self into a corner too early - make a full schematic of ALL the bits and then address each one to see how feasible it is.

We had a lot less trouble building our current loop for our distributed cats eye system, constant o/p current up to a fixed Vmax, sine wave, with plenty of circulating current at the driver to account for no load to full load variation, and of course dimming ( lower loop current ).

We were lucky as in practice the load was fixed ( except for the odd failures due to damage etc) and only dimming was required, bright at dusk, dawn, lower at mid night)

which was easy to do for a parallel loaded SRC...

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also if really part of a Tx, the load determines what the impedance of the Tx looks like. Do you really need to have a fixed inductance as part of the Tx, just go for max magnetising L, but if the load fails and goes open ckt - then you have an issue as a lot of volts will be developed on the sec side - you need to detect this and have a crowbar ckt (or zeners rated for the power but above the lamp volts) to "short" out the Tx so the power can still flow to the other lamps.

Better still to have a "weak" connection to the lamps so open or short ckt failure of the lamps has little effect - this is what we did with our long const I "loop" although it was only a "loop" near the lamps.

Thanks,
May i ask, would you describe the schematic in the top post of this...
https://www.edaboard.com/showthread.php?377465-Waterproof-LED-lighting-system-with-no-contacts
..as a parallel loaded SRC?

No it is a modified LCC

Thanks,
Please don't answer , but in your system , did you find that the long twisted pair cable formed a significant part of the resonant tank and that the lamps off each inductive coupler should draw current in a power factor corrected way, otherwise problems occur?

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Thanks,
Please don't answer if you dont wish to , but in your system , did you find that the long twisted pair cable to which the inductive couplers get connected formed a significant part of the resonant tank and that the lamps off each inductive coupler should draw current in a power factor corrected way, otherwise problems occur?