I tinkered together this (see pictures) active antenna preamp, mostly inspired by the PA0NHC mini-whip circuit:
http://www.pa0nhc.nl/Miniwhip/indexE.htmThe output coupling-capacitor, tuning-capacitor, and BNC-connector are through-hole which somewhat detracts from the "SMD-deadbug" style

It seems to work quite well!
I made a ferrite sleeve loop coil with 10pcs 10mm diameter 200 mm long ferrite rods and 0.3 mm PU-coated copper wire. My first try showed about 25 mH on an LCR meter which was too much. Even at minimum capacitance of my 65pF tuning-cap the resonance frequency was too low. This indicated about 140 pF of input/parasitic capacitance in the resonance circuit even with the tune-cap set to minimum!? That could probably improve a lot with a proper PCB and layout?
Anyway by removing almost half of the turns I got the inductance down and resonance frequency up to spec.
Does it make sense to include a second stage (op-amp?) with amplification also? Most circuits I've seen (mini-whip etc) just use a unity-gain emitter-follower to drive a (long) 50-ohm coax to the receiver.
Hopefully this could be used with a coax-loop antenna also, similar to this one:
http://www.qsl.net/df3lp/projects/lfloop/index.html