Ron wrote:
. . .
By "focal point" I meant the center of the sphere where the rays
converge and where the antenna would be located.

I have to admit, I was looking at this a more of a problem of equal
signals arriving from all directions, rather than at the middle of some
sort of convergence. Of course, any rays reaching the center would
continue on through, Cecil's unique theories notwithstanding. I don't
have the spare time to contemplate what the end field distribution would
be like at the center of the antenna or its periphery.

When an antenna intercepts one watt from a field having a power density
of one watt per square meter, it's said to have an "effective aperture"
or "capture area" of one square meter. The higher the gain of an antenna
in some particular direction, the larger its effective aperture in that
direction. Consequently, a high gain antenna would "capture" more power
from a wave arriving in its favored direction than an isotropic antenna
would. It would, of course, capture less from other directions, but
assuming equal efficiency, both antennas would capture equal amounts
overall.


In the unusual field defined in my example, the algebraic sum of all the
rays collected by the antenna would be higher in the isotropic antenna
than a high gain antenna.

It's not obvious to me why that would be.

Think of the front to back ratio of the high
gain antenna which would result in very little output from the rays
behind and on the sides of the antenna.

That's true. But the output would be higher in reponse to the rays
arriving from the front. We call that "gain". Another way to express it
is that it intercepts a field from a larger area of the wave front.

Therefore, the isotropic would
have a higher output which is indicative of higher gain.

You're right that higher output means higher gain. I maintain that both
antennas have the same total gain, i.e., the same total interception of
power from all directions. This follows directly from the reciprocity
principle.

I do not understand what you mean by "capture equal amounts overall".
Energy which may strike the antenna but does not result in any output
power isn't "captured".

The field you're creating comes from something and goes somewhere. If
you subtract the total amount going from the total amount generated,
you'll get the amount dissipated in the load connected to the antenna.
That is the amount of energy "captured" or "intercepted" by the antenna.
And that's what I thought you were talking about all along.

The "capture area" isn't some physical region with boundaries -- it's
simply a way of expressing how much power is extracted from a field
having a given power density. In other words, it's just another way of
expressing antenna gain.


How about a dish antenna? Isn't the capture area proportional to the
physical area of the dish?

Indeed it is, in the front direction. But how about a dipole? The
capture area (or gain) broadside to an infinitesimal dipole is just
slightly less than that of a half wavelength dipole. And wire diameter
makes almost no difference.

Sorry, the theoretical construct is just a little too much like
Calvinball to hold my interest. I'll bow out now. Best luck in sorting
it out.

Roy Lewallen, W7EL