berkeman said:
But won't you get reflections from just joining the shield to one of the dipole elements? Going from the unbalanced coax to the balanced dipole would seem to require a balun to get a reasonable SWR...
The main effect of not having a balun is that the outside of the coax becomes part of the antenna.
Signals and noise can get picked up by the outside of the coax and they become part of the received signal.
The SWR would be largely unaffected because the 50 ohm coax is a reasonable match for the dipole.
A dipole with a huge reflector like this could have a feedpoint impedance of about 10 ohms, though, so the unbalanced feed would be the least of your problems.However I balked at mentioning baluns considering other aspects of the thread.
From this OP's point of view he could use something like this:
These are like this internally:
This would give a 4:1 step-down effect but the large reflector would already give a low feedpoint impedance.
So, a folded dipole would be better, and even that would give a feedpoint impedance of about 100 ohms with this reflector. Stepped down 4:1 this gives about 25 ohms.
So, I suspect that the balun would add more complexity than benefits.
The main point is, though, that this is not a viable project without reasonable test equipment.
Wide band TV antennas are designed with great care and then experimented with, to actually get them to work.
Edit...
One possibility would be to add a number of ferrite toroid rings on the outside of the coax near the antenna feedpoint. With suitable ferrite, this may be a simple enough solution.