beamwidth an power reveived of antenna

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hogmeade

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For a short linear antenna (l<< lama) the received power increases in direct proportion to the length of the antenna?
The higher the directivity of an antenna the wilder the beamwidth? Anyone has equation o prove these?
Thank you so much.
 

exactly the opposite : high gain small beamwidth and viceversa. The bigger is the antenna the bigger is the gain
 

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