Of course the quad will only be directional on one

band - or it might point different ways on 20 and 17m,

depending on the tuning of the parasitic elements.

For multi-band use (at least over a 2 : 1 range or so)

a single wire loop should work, and it can be fed with

either 300 or 450 ohm line. For multi-band gain I'd

try something like a lazy-H or some sort of curtain.

But, to answer your question, there are "standard"

formulas for quad dimensions, and they may work to

some extent, but design is really a lot more complicated.

I recommend the quad design series at

www.cebik.com(for example, "new quad studies".) This includes a

set of basic programs to calculate optimized dimensions

based on the desired frequency and wire size.