I need a directional antenna for 10 m that is less than half the size of a yagi or quad with more than about 7 dBi of gain, does anyone know if such a thing exists ?
I use a 10m moxon, which when vertically polarized is about 6ft wide. It's probably 80% the height of a similar yagi.
If you use Cebik's model, it should have gain similar to a 3 element yagi, and at least 7dbd gain.
You can control the bandwidth by picking the correct diameter elements. For instance, you could use the outer shield of coax or copper pipe and get some pretty good bandwidth.
Anything smaller will probably need loading coils, and might not have the gain you want.