Why does the DMM make this circuit "work" ? (Power issues : servo & bluetooth)

BabyGeezer:
meanwhile, on your webpage that you linked, it says using inductance values of tens of milli-henries.

i've been calculating what length and radius of coil that would involve and it's huge !

My 10 mH inductors are still the standard 10mm radius, 12mm tall. Not too bad. Ohmic resistance is increasing of course (I'm sure the larger the induction the thinner the wire used to be able to have more coils, so more resistance per length and more overall length) so I'm normally using 330µH for my filters. Just 2-3Ω so not too much losses.