What are the definitions and equations for circular aperture antenna parameters?

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QuestionWhat are the definitions and equations for circular aperture antenna parameters?
Answer
These are definitions and equations for gain, size, and beamwidth for antennas.

Antennas are described by their gain pattern, g, which indicates how the gain is spatially distributed with respect to the antenna coordinate system. The most important parameters are:
gain - the maximum value of a gain pattern
beamwidth - the measure of the angle over which the most of the gain occurs
sidelobes - the amount of gain in off-axis directions

Ideally, you want highly directional antenna patterns with maximum gain over narrow beamwidth with negligible sidelobes. 

Gain = Efficiency x (4 x pi x lambda^2) x Area of Antenna Aperture 

Where:
lambda = (speed of light) / frequency 
Area  =  a function of antenna type (which is a function of the diameter, d) 
Beamwidth = lambda[d x square root(efficiency)]  

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TitleWhat are the definitions and equations for circular aperture antenna parameters?
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