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In the EVM datasheet schematic, two input beads and 2 output beads are used.
In my application, I drive 56V 5A COB LED. Input voltage is 22-50V, so input current can be ~6-13A. I read on Internet, that beads saturate and lose their filtering efficiency, so, it is better to use beads with current ratings 3-4 times higher. How can I implement such filter, as in the example in the datasheet? There are no ferrite beads with current ratings higher than 11A.
Identify what filtering is needed, then design a filter for it.
That filter can use ferrite beads, if the required impedance is suitable, and DC bias falls within the saturation current (for whatever saturation threshold you find acceptable).
Ferrite beads are poorly described, for the most part; some manufacturers do provide bias curves, usually located on their website database. Laird is the standout exception, providing bias curves for almost their entire catalog (right there in the catalog).
Ferrite beads are a poor choice for power filtering, as they saturate quite easily, even those with high ratings. A typical 100Ω (at 100MHz) 1206 chip will saturate at 200mA or so; the situation does not improve much with size. (It does improve with low impedances: a 10Ω 1210 might be usable here; but that's also not adding very much impedance!)
What is a ferrite bead, anyway -- why do we use it? It's an inductor with significant resistance. This gives good damping at RF, modest filtering at HF, and a reasonable LF (or so) bandwidth when used as a lowpass filter. This is great for signal filtering, and addressing resonances on cables for example, but not so great for power filtering purposes where we might want a lower cutoff, and need higher current capacity (without affecting the impedance).
So just use a regular old inductor, and dampen it adequately with some parallel resistance!
The main downside is the need for two components, and the single-pole response doesn't have as wide bandwidth -- ferrite beads generally have a \$Z \sim \sqrt{F}\$ response, meaning equal parts R and X, or Q ≈ 1, over a fairly wide range of frequencies. You don't really have to think about it, it doesn't matter too much what you're trying to filter or damp, it's almost always going to have at least a modestly well damped response. Whereas the L || R network simply has inductance below cutoff, and resistance above, and that resistance is flat (constant with frequency), so it needs to be sized as a compromise between RF filtering and filter damping.
In the given circuit, I might not worry about the ferrite beads at all, but use a few small (0.1-1uH?) inductors on the various connections for differential filtering (L3-L7; L4 and L6 can be removed because it would be differential mode filtering), then common mode chokes for what's left (which compensates the DC bias, so that a ferrite-bead-like characteristic can still be had).
In return, some damping is likely welcome, such as a lossy bulk capacitance. An electrolytic in parallel with C10 and C3, or something equivalent, would be fine. The capacitance needs to be much larger than the parallel equivalent ceramics (whatever is directly in parallel with it, or opposite the inductor -- so, in parallel with C9 and C10, ≫10uF; in parallel with C3, ≫20uF), and ESR = \$\sqrt{\frac{L}{C}}\$ where L is the inductor and C is the same parallel equivalent capacitance.
By "something equivalent", all that's important is the impedance; ceramics could be used, with an external ESR added, it just might be annoying having to use so many (i.e. two in parallel without ESR, plus four or more with ESR).
To be clear, we don't have to use LR damping, but can substitute RC damping instead, when the circuit is a pi filter for example. The damping also addresses power-on (inrush) surge and dynamic stability, so is highly recommended in general. (A TVS might also be desirable, in case the battery here is likely to be hot-plugged often, or subject to noise like an automotive supply, or may be reversed accidentally.)
If the total capacitance starts to get difficult for the regulator to handle, probably a compromise should be met between low-ESR ceramics and modest-ESR bulk.
L3 and L4 carry opposite current.. Same goes for L5+L6. (Or perhaps even the trio of L5+L6+L7...I don't fully understand the schematic.)
These should be Common-mode chokes, which are basically two or more beads on the same core, arranged to prevent the DC bias issue. That way, you can use much more permeable and much smaller cores.
Several 100 Ohms of impedance at amps of current is otherwise really hard, and you would need a really big bead to achieve that.. I guess these come only in the form of slide-on or clamp-on large ring core beads that you put on cables. And they are probably several cm in size.
You can use several beads in parallel. The current capability is multiplied, and inductance is fraction of one bead.
