Question (repeated here for convenience):
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Assume a receiving antenna is in the center of a sphere and the
received signal is coming in equal amounts from all points on the
surface of the sphere. Which receiving antenna would capture more
power, an omni or a high gain beam? There are no noise and no losses.
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First, thanks for all the comments. They have helped me better
understand the answer. I am leaning toward the belief that the omni
(isotropic) antenna would capture more power and, as odd as it may
seem, would have more gain than a high gain beam (or any other
directional antenna for that matter). Here is my thinking:

This is a very unusual RF field. Usually the field is assumed to be
planar with coherent rays - then antennas behave as expected. But this
field originates uniformly from all points on the surface of a sphere.
It does not spread but converges at the focal point of the sphere.

An isotropic antenna placed at the focal point would collect all of
the rays whereas a directional antenna at would not.

Therefore, in this particular situation, the isotropic would have
higher gain and capture more power than any directional antenna.

Please correct me if I am wrong.

Well, for one thing, your model assumes something which does not and
cannot exist. It assumes the existence of an actual isotropic
antenna. Such cannot actually be constructed - there's no way to get
a truly omnidirectional radiation pattern without violating Maxwell's
equations.

I suspect that you'll find the same problem existing, in the reverse
direction, if you try to construct the sort of RF field you're talking
about. If you try to specify the E-plane and H-plane field components
for a uniform, arriving-from-all-points-of-a-sphere field, I believe
that you'll find that you can't achieve your goal: there will always
be "seams" (abrupt discontinuities or cancellations) in the field
components in some directions.

--
Dave Platt AE6EO
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