ok, so for an isotropic antennae the radiation pattern is uniform in all directions (i.e. a sphere). So for this pattern, is there a formula for determining the diameter of the sphere, or is such a measurement meaningless?

also, suppose a ground-plane an arbitrary height below the antennae, the ground plane would reflect the signal and look something like this??

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berkeman
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The diameter of the sphere is meaningless, as you say. The pattern distribution in that kind of drawing is meant to indicate power relative to angle. If the pattern is not isotropic, that means that more power goes in the direction of the bulges than in the other directions.

A ground plane does make the pattern push up something like that. I'm not that familiar with ideal isotropic antennas, since they aren't very real in most E&M situations. For a more realistic antenna like a dipole, when you see its pattern from the side, the lobes stretch out horizontally. There is no vertical pattern from a dipole. When you put a ground plane a wavelength or so below the dipole, it pushes up the side lobes so that they aim more up at an angle. I'll see if I can google some plots....

Edit -- I googled antenna pattern dipole ground plane, and got some good hits. Check this one out:

http://www.microhams.com/binfile/talks/Antennas%20Demystified.ppt#8 [Broken]

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russ_watters
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The only way for the sphere to be meaningful is if you make a bunch of concentric spheres corresponding to signal strength, much like a topographic map.