The only wideband antenna for your application is a log periodic. The ARRL
handbook has the designs. Unless you are good with welding, this isn't
trivial. The ones I've built were done with threaded Al rods, which means
you need to use a tap and die. [There are tricks to do the Al to Cu
interface.] You do this kind of work for antennas you can't buy, i.e. for
SIGINT. For TV, you buy the damn antenna. It is cheaper.
Now if you want to build an antenna for ONE channel, it will have to be a
folded dipole due to the TV bandwidth. The folded dipole is the driven
element. You need at least one reflector and one director. These are not too
difficult to make if you use brass rods and a wooden boom.
The deal is unless you know what you are doing, these outdoor antennas will
degrade faster than commercially made antennas. It is a waste of time.
If you really insist on this project, look at this website:
http://www.george-smart.co.uk/wiki/432MHz_Yagi
The site is kind of slow. I found it by doing an image search because 90% of
the designs on the internet are wrong. This is the right approach, though I
haven't checked his math. The driven element is a folded dipole for
bandwidth. The loop balun works well. The boom has to be wood. Metal boom
design changes the math a bit, and the modeling programs like NEC do not
work well with metal booms, so most yagi designs on the internet with metal
booms are fiction.
I have one of these scaled for the federal 400MHz band and it is awesome.
[Like I said, you go through this nonsense for things you can't buy.]