Losses (ground and otherwise)

One of the reasons for considering a phased array, whether it be all driven or partially parasitic elements, is that it can reduce the ground losses. In a simplistic analysis, which would work for patterns, you can just independently sum up the far field responses for each element, scaled as appropriate by the element current. After all, there's no nonlinearities, so it's linear and superposition works.

However, when you start to consider loss effects, it's not quite so simple. A single dipole might have substantial ground loss, yet an array, with the same total power spread among them, have less. Why is this? Why isn't the loss the same as the individual element losses?

Consider a small chunk of the (lossy) ground under the antenna. The amount of energy dissipated (lost) in this chunk is proportional to (the square of) the current through (I^2*R) or voltage across the chunk. If the fields from multiple elements combine to reduce that total current or voltage, then the dissipation is less. It gets to be a lot less real fast, because dissipation goes as the square of the induced current: cutting the field in half cuts the dissipation by a factor of 4.

In practical terms, if I started with an isotropic radiator, and now I have an antenna with 10 dB of gain in the horizontal plane, I've reduced the amount of power I'm beaming at the ground. It's not quite that simple, because most likely you're in the near field, and highly directive antennas tend to have very high fields within the near field. Recall that in the near field, by definition, energy is being stored in the fields around the antenna, flowing between antenna and field on every cycle. One can even think of it in terms of a resonant cavity with a "Q", in that in each cycle, energy at the feedpoint is dumped into the cavity, and some amount is radiated away, and some larger amount is just "circulating" back and forth.

 

radio/antenna/phased/losses.htm - 2 Feb 2003 - Jim Lux
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