Hello Luis,

The antenna is fed over the coax.

DC is injected via the primary winding of the isolating transformer.
The ground connection of this winding is isolated for DC but for RF 
the path to ground is via a 1 uF and 220 uF capacitor.
This works excellent and a rf choke can be omitted.

Regarding battery feed versus mains power, so far I have not been 
able to find any difference between the two. 

The major point with active whip antennas is to connect the shield 
of the coax to a ground stake (or building frame, when you live in a 
high rise building). At my location I have a ground stake at the 
bottom of the mast and at the cable entry to the house. Either work 
the same.

73,
Roelof Bakker, pa0rdt