Math CentralQuandaries & Queries


Question from Evan, a student:

I am making a parabola for my home wireless LAN. I feel pretty confident that I can make a parabolic trough that will work. But I am curious about size. Is there really any advantage to using a deep (more depth) parabolic shape over a shallow one as long as you use the correct focal point. And is bigger better? I know that my parabola has to be bigger than the waves it is getting which wont be a problem but if I make the diameter bigger does it get more effective or is there such a thing as "too much of a good thing"? I have looked everywhere for an answer and have come up short. Thanks!

Hi Evan.

I'm no expert in such things, but I expect that larger is generally better because it makes imperfections in the parabolic surface to have a smaller effect on the overall focusing.

A receiver that is larger has a larger cross-sectional area from which to gather parallel signals as well. So larger means more comprehensive collection and a bit of translational flexibility (if your aim is slightly off, it doesn't matter).

A larger transmitter spreads the signal over a larger cross-sectional area, which I think would mean less dense signal dispersion (not good if your receiver dish is smaller than your transmitter or they aren't well-aimed).

In your application, the receiver and transmitter are a single unit, so I'd suggest going with a larger dish if all else is equal (including aesthetics and cost).

The other major question to consider is the amount of three-dimensional angle that the actual detector/transmitter is interacting with. This will depend on the devices themselves. However, you should realize that a large dish that is distant from the focal point won't cover the same angle of collection as a smaller dish whose focal point is pretty tight to the dish surface. But again, you will need to beware of the limitations of the transmitter/receiver effective angles as the point of diminishing returns will probably be
quickly reached.

Those are my thoughts, but I'm not a communications technician and have never owned a dish, so consider the ideas, but take them with the appropriate NaCl.

Stephen La Rocque.>

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