Hi again.
Spent a bit of time trying to find a catalogue source for cores in the USA. Not much luck. Perhaps you do have something useful in your parts bin or you might be able to get some 'samples', cough cough.
I've 'massaged' the basic circuit to 'optimise' things. One of the limitations of the previous equation is that it does not account for core loss on the assumption that ripple current in the inductor will be low compared to the average current. It's another trade off.
Anyway it looks like a close answer will be 50uH/3.2mH. Using the Spice model these are the current waveforms in the 50uH 'primary',
That is 1.73A RMS and 2.75A Peak. Using,
Aw.Ae = L.Irms.Ipk/Bpk.J.Ku.Kw
with
L = 50uH
Irms = 1.73A
Ipk = 2.75A
Bpk = 300mT
J = 4E6
Ku = 0.7
Kw = 0.5
Gives Aw.Ae = 5.66E-10. Assuming Aw = Ae then take the square root of that for a guess of 23.8mm^2. Now you have to go and find a core/bobbin set that satisfies those parameters.....
You might notice that 'something' perhaps slightly 'underhand' is going on here. Effectively what I am doing is looking at the problem and making decisions and adjustments, iteration, to arrive at a solution. I'm sure others don't do it this way...
Surprisingly it turns out that an EFD20 Core/Bobbin set might fit the bill,
https://www.ferroxcube.com/prod/assets/efd20.pdf
Ae = 31mm^2
Aw = 26.4mm^2
Aw.Ae = 8.12E-10 > 5.66E-10
Now you have to work out the minimum number of turns required for LBA. The sum is,
Nmin = L.Ipk^2/Bpk.Ae
L = 50uH
Ipk = 2.75A
Bpk = 300mT
Ae = 31E-6
Nmin = 14.78 so use 15
Then you need an Al value which is,
Al = L/N^2
Al = 222nH/root turn
This is slightly disappointing because it is not a 'standard' gapped value. The chances are you would not be able to buy one anyway although you can see what is supposedly available from the data sheet. Otherwise you have to calculate the gap yourself.. :sad:
That's too much like hard work for me to work out the relevant sums about how that is done at the moment and Seimens, now Epcos, provide some funky K factors that give more precise results. Unfortunately the documentation for that has been split up making it harder to find...
Anyway,
This is what the bobbin looks like,
Taking the appropriate dimensions the winding width is 13.5mm and the winding depth is 2.25mm. With the required 15 turns and assuming a single layer then your wire diameter is 13.5/15 or 0.9mm. That might cause 'concerns elsewhere' but for the moment you can see that it will occupy less than, but close to, half the winding window as required by setting Ku to 0.7 and Kw to 0.5. Again it is not an exact 'science' but this 'looks' near enough.
In terms of current density then assuming it was all copper then the copper area is pi.(0.9E-3/2)^2 or 6.36E-7 which with J at 4E6 suggests the wire can carry 2.5 amps versus the hoped for 1.73ARMS value.
The 'concerns elsewhere' are that the wire is carrying a high frequency AC current. It's made worse because of the nature of the waveform that results from the way the converter operates. In a 'normal' inductor you would see a triangular ripple current which might be considered as being 'benign'. In this case it is effectively a square wave which is not so nice.
I'll mention that the flux excursion in the core is still, overall, going to be triangular with relatively low amplitude and might be ignored with regard to core losses. Regarding the AC resistance and losses then... Unitrode to the rescue,
https://focus.ti.com/lit/ml/slup197/slup197.pdf
and yes things do get very complex. The 'quick' rule of thumb is that you choose a wire diameter twice that of the penetration depth at your operating frequency. Dixon gives,
Dpen = 7.5/f^0.5 cm
I'll change that to
Dpen = 75/f^0.5 mm
so for the chosen 100KHz operating frequency we get Dpen = 0.23mm. Double that gives 0.46mm. Of course you might just stick with the original 0.9mm OD and see if it works. Otherwise you move to a 'twisted rope'.
Without wishing to think too hard three strands of 0.46mm diameter will result in something close to the original 0.9mm in overall diameter. Wire tables would be good...
**broken link removed**
AWG is, naturally, American Wire Guage. IEC317-0-1 are 'metric' versions. Light, Single, Heavy and Triple relate to the insulation thicknesses. For Offline work Heavy is normally used.... I believe it is rated to 500V
Scanning through then something in the range AWG26-AWG27 looks about right. Using AWG26 heavy then that has an overall diameter of 0.452mm with a copper diameter of 0.404mm. Three strands as a rope will have a copper area of 3.85E-7m^2 and carry 1.54ARMS. In terms of 'power' that is 20% down on the target.
Did I mention this is not a 'science'. Naturally moving to light or single would improve things but for the moment I'll run with that.
Now for LBB. As suggested it has 8 times as many turns as LBA so that will be 120. It's very tempting to say 4 layers which would be 40 turns per giving a wire diameter of 0.33mm and a total winding depth of 1.32mm. No need to use a rope here.
So LBA takes up a depth of 0.9mm with LBB taking 1.32mm for a total of 2.22mm versus the available 2.25mm. That might be pushing things especially when you take kinks and other things into account. Still I suppose I am not the person who is going to have to wind this thing so should I care?
Yes I do but there is, such as it is, the method.
Enough for now. Next up, sometime.... working out the required gap.
Genome.