Go back to the ARRL antenna handbooks from the 1970's or 1980's... Look
in the chapter for HF antennas for 160 and 80 meters... Somewhere in
there will be the diagram for an end fed long wire using a parallel
tank circuit - an inductor and a variable capacitor in parallel...
This will work just the same for your end fed half wave vertical on 6
meters...
The bottom end of the tank circuit goes to your ground/radials... And
the top end goes to the bottom end of your half wave vertical wire...
Your transmitter coax has the braid going to the bottom end of the tank
circuit and the center feed of the coax is tapped up a few turns from
the bottom of the coil to match 50 ohms.. Use a few turns of the coax
as a choke for common mode currents on the outside of the braid...
Obviously you will not be using components with as much inductance and
capacitance as you would for 160 meters... As a guess I would say that
for 50 mhz you will be tapping up roughly between 3/4 turn to one and
a half turns from the bottom to get a match... This of course depends
on the form factor of your coil, i.e. short/fat versus long/skinney..
Trying this on your work bench is the best way.. Make up a coil from
#14 AWG solid house wiring and a variable capacitor, use a length of
the house wiring for the radials and vertical and experiment...
Another method is the J Pole matching system.. Look in chapter 18 of
the current ARRL Antenna Handbook...


cheers denny / k8do