Yes the AL value for a gapped core is for one gapped core half , fitted to an ungapped core half.
By the way...make life easy for yourself and use an offtheshelf gap size.....otherwise it costs much to get the ungapped cores grinded down......(if you do get them grinded, then you simply have to specify your desired AL value and they will put the necessary gap in there for you....they won't even let you specify a gap size...[unless you really scream and scream])
But yes you do have to know roughly how big the gap will be because too big a gap is a problem with leakage flux (fringing flux).
The magnetic design tool software that FvM tells about is the one i uses for the TDK cores (search under EPCOS for it). Its good for getting gap sizes……in fact, if you scale by the same ratios, you can also use it for the ferroxcube cores as they are the same size and shape.
In theory you can use reluctance equation to calculate your AL value for a core with a given gap…..but in practice, its not accurate and so you need the Magnetic design software tool.
But as said, don’t use a custom gap, use an offtheshelf gapped core…and use two inductors if need be, as Easy Peasy said.
*********************************************
If it helps, rather than remembering too may equations.........think of Amperes Law [N.I=H.dl], Faradays Law V = N.d(phi)/dt, Lenz’s Law V = L.di/dt
And common equations like
B = uo.ur.H; B=(phi)/A where phi = flux in webers
L = (N^2)/Reluctance
N.I = Flux.Reluctance
Reluctance = (Path Length in magnetic material) / [uo.ur.A]
Eg reluctance of gap = [gap length]/[uo.ur.A]
Where u0 = 8.854e-12 and ur for air is 1 and A = core cross sectional area
From the above common equations, you can figure out your Flux density etc.
If you want a feast of equations for SMPS…then here you are…
https://massey276.wixsite.com/maths
*********************************************************************************
By the way. You need to get the Watts/Volume vs Flux density graph for your core so that you can calculate the core loss. This graph will have lines drawn on it for various frequencies.
And by the way, we got some great ferrite cores from a place in China. I think (not too sure) it was called “Pairui” or “Fuantronics”, but I’m not too sure.
BTW, here is a nice course on SMPS with stuff on LLC
https://drive.google.com/file/d/0B7aRNbu3Fes4TU92Mkw3YlA3ams/view?usp=sharing
**********************
Regarding heating of a resonant inductor in an LLC….i once took apart a 3Kw EV charger (from a reputable company) with a 3Kw LLC inside it. They were using a well coupled transformer and external resonant inductor and even an extra external magnetising inductor aswell. The core for the resonant inductor was the same core as the LLC transformer core (probably because it was same height and could be gap padded to the metal case top). It was a PQ40/40 or PQ5050. What surprised me was that it was also gap-padded to a aluminium heat sink (gap pad thickness approx. 5mm). The aluminium heatsink was a kind of a “tombstone” (50mm*40mm*5mm thick) on the PCB alongside the resonant inductor. The PQ4040 is quite an open core, and so I was surprised to see they’d put a metal heatsink so close to it..and alongside the “Open” bit of the core…as you’d have thought it could have interfered with the flux around the PQ4040 resonant inductor.
***********************
By the way, I thinks its already been said above…with an LLC, you wont need to worry about 400kHz….as you will be in very light load if the frequency goes that high.
With most LLC controllers, you can set a maximum frequency above which you will not go....and if the load goes that light, it just goes into burst mode