How can I mathematically determine curvature for a satellite dish for a specific radio wavelength?
It has nothing to do with the wavelength. And the fact that they are actually called parabolic antennas should give you a clue as to their curvature ;)
As DrClaude said it isn't frequency related
The curvature amount determines the focal point location
The physical size --- diameter of the dish will affect the gain at a given wavelength ( frequency)
eg say a dish of 2 metres diameter is going to have much more gain at 10 GHz (3cm wavelength) than it is at 5GHz ( 6cm wavelength)
that 2 metre dish is going to have very low gain at 144MHz ( 2 metre wavelength) and even worse as the wavelength becomes significantly larger than the size of the dish
OK, thank you.
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