"art" wrote
A quad radiator is a wave length radiator with a gain more
than a half wave as one sample.

In your first post you wrote, "The most efficient radiator is one wave
length long where it is considered to be in equilibrium with a parallel
electrical cuircuit," and that is what I responded to.

Now you are writing about gain. Efficiency and gain are not synonymous.

Both of the dipole antennas in my previous post will radiate nearly 100% of
the r-f energy available from a matched, balanced source connected to their
input terminals. Therefore the radiation efficiency of those two
configurations does not favor the 1-wave over the 1/2-wave, which was your
opening premise.

They won't have the same gains in every direction, because their radiation
patterns are different. Same for your quad and "half wave" example.

RF