To help with your search you might add 'log periodic' - as this might help narrow your search. It seems like the typical commercial TV antenna is a combination of VHF and UHF log periodic designs.
Since you didn't say directional then it would seem that simple rabbit ears would qualify but that's not really something you design. A 'discone' antenna is kind of like an omni-directional version of the log periodic - very wide bandwidth with some gain as compared to a simple dipole. Discones are often used for scanners and might work well for television service, especially if you aren't too far from the transmitting stations.
I agree with Nigel in that you probably can't purchase the materials for less money than a complete antenna.