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When it comes to power transmission elements, e.g. in DC-DC converters, using shielded inductors makes perfect sense to me. I am not sure the same is true for LC filters at the input of these converters, used to suppress conducted EMI on the power lines. Would unshielded inductor work just fine there?
To avoid confusion, I am talking about LDM2 component on page 3 of this datasheet.
I am not sure the same is true for LC filters at the input of these converters, used to suppress conducted EMI on the power lines.
These will work just fine. Being unshielded means that there is some "escape" of magnetic field but, it does not mean it acts like a poor inductor in supressing conducted emissions when used correctly. That escape of magnetic field is not far-reaching; it attenuates with distance cubed. Compare this to an electromagnetic wave; its electric and magnetic components attenuate with distance linearly (not distance cubed).
If you keep other unshielded inductors a few mm away and, there are no conducting objects close by that can be influenced by a leakage magnetic field, you should be fine.
But, in all uses of inductors in EMI filtering, the self-resonant frequency (SRF) is very important. I noticed that the inductor you linked has an SRF of about 30 MHz. So, if your circuit produces high frequency EMI above 30 MHz, the inductor won't work very well as a suppressor and, you may find you get radiated emissions on your power feed all the way up to and beyond 1 GHz. That could be a big problem of course i.e. non-measured conducted emissions producing radiated emissions.
Conducted emissions are measured up to 30 MHz and, an inductor having an SRF of 30 MHz and above, will work adequately whether it is shielded or not.
The DC-DC converter datasheet lists switching frequency at 2MHz.
A 2 MHz switching frequency can produce significant harmonics easily into the hundreds of MHz and, because conducted emissions are usually tested no higher than 30 MHz, an SRF of greater than 30 MHz will attenuate them. But, radiated emissions can be tested up to 2 GHz and, if your inductor is relied upon to help with these emissions then, an SRF of 30 MHz is going to be a problem. This is usually why two inductors are used and why ferrite beads are also/often used (supplementing the main inductor).
For what it's worth, I suspect they're being overly cautious in the datasheet there; it's not clear exactly how they tested it, but I suspect they hooked it up to a (mains style?) LISN, and measured the full (conducted) emissions spectrum that way. Normally, a DC-DC converter comes nowhere near a LISN: for example running from internal battery power, or via external (AC-DC) adapter.
If you're not connecting to DC mains or PoE, most likely ~1uH and 10uF is enough here.
Maybe with a larger electrolytic (100uF+ in parallel with the 10uF) would be desirable as well, or a TVS, and perhaps fusing, to account for possible situations like hot-plugging (inrush surge) and reverse polarity -- in case these are relevant during manufacture (first time plugging in the battery?) or use (user may attempt incorrect or backwards power adapters?).
Or if this is automotive for example, reverse polarity as well as overvoltage protection would be wise. You'll be subject to different emissions standards in that case, anyway.
Note that SRF (self-resonant frequency) isn't the whole story: an inductor's impedance peaks at SRF. This is good for a filter: it's the point of maximum attenuation. The rated SRF is the lowest (first), parallel resonance (highest impedance).
Resonances always alternate, and since the inductor's impedance is rising (over the inductive range), it reaches a peak at the SRF. Its impedance is then capacitive (falling with rising frequency), until the next mode, which will be series resonant; and so on. When and where the resonances lie, however, depends. At the most basic, it's transmission line effects, but unlike an ideal transmission line (a wire over ground), the wire is wound up on itself, and loaded by ferrite or powdered iron besides, so the frequencies are not harmonic, but spaced closer together, and the impedances are generally higher, but the losses of the core material dampen higher resonances especially. Manufacturers rarely give impedance measurements past the first SRF, so aside from measuring it, you're basically left to guess. Fortunately, these resonances generally aren't very strong, so you can probably assume worst-case the inductor looks like a lumpy resistor at frequencies much higher than SRF.
In the event you have to -- the easiest way to deal with poor attenuation at high frequencies, is to add another ("roofing") stage to the filter, using smaller value components (higher Fc), which will also have higher SRFs.
By the time you're using 2 or 3 stages of LCs on the power inlet, you've probably dealt with the differential mode noise well enough that everything else in the circuit is a higher priority: common mode due to poor grounding or layout, and other signals (MCU clocks, comm pairs, etc.) and connectors.
