The theory behind the "height gain"
observed using small LF active antennas at different heights has to do
with compression of the near-earth LF potential gradient caused by the
grounded "mast" holding the antenna.
The essential bit is that there is
a grounded connection between the antenna and receiver, which may be
just the outer of the co-ax cable. It would be an interesting
experiment to repeat the "height gain" experiment without any
connection to ground. This could be done by building an active antenna
with a little transmitter to re-radiate the received LF signal (on 2.4
GHz?) and poking it up using a fibreglass mast. If the theory is right
then there wouldn't be any height gain. Might do it myself sometime but
anyone else interested?
Walter G3JKV.