Richard Clark wrote:

Hi Owen,

And you have already allowed that superposition does not fail. Thus
there must be some other failure to be found in the choice of antenna.
From other correspondence, it is asserted that a gain antenna, by
virtue of its size, cannot be placed in null space (that point wherein
all contributions of energy sum to zero) which is planar and
equidistant between sources (there being two of them for the purpose
of discussion).

Have I described this accurately?

I think it might be more fundamental and perhaps subtle than just a
limitation of size. If the null space is a whole plane, as with the two
radiating elements of my example, you have an infinite area on which to
construct your antenna, although it would have to have zero thickness.
But even allowing infinitely thin elements, I don't see any way you can
construct it entirely on the plane so it will be more sensitive to
signals coming from one side of the plane than the other. That is, use
any number of elements you want, oriented and phased any way you want,
and as long as all elements lie entirely on the plane, I don't think you
can make it favor the signal from one of the radiators over the other. I
believe you'll find this same problem with any region of total wave
cancellation. I don't have any rigorous proof of this, just intuition
from observing the symmetry, and would be glad to see an example which
would prove me wrong. (It might reveal a whole new class of directional
antennas! Maybe one of Art's Gaussian marvels would do it?) But if I'm
right, then there's no way to do as Owen originally proposed, namely to
determine entirely from a null space that the null is the sum of
multiple fields, let alone the nature of those fields -- at least with a
directional antenna. It has to extend out where it can a sniff of the
uncanceled fields to do that.

Roy Lewallen, W7EL