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aperture and gain: proof of the relation

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wave1

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Does anyone knows where I can find proof/derivation of the relation between aperture and gain -
G = (4*pi)*Aeff/(lambda^2)
 

If you use the definitions of the IEEE Std. 145-1993 for gain and effective area (I assume that you mean this with aperture - although that not the IEEE definition) you probably can derivative the equation.
Furthermore, in a note on the definition of the effective area this equation is stated in the standard.
 

in the note you just find that it says ... equals Gain*(lambda)^2/(4*pi)
my question is - where does it come from ?
 

Read a basic textbook on antennas, like JD Kraus: Antennas of 1947. Antenna aperture directs more energy into a solid angle defined by its size vers. wavelength; this is how a directivity and gain is created. A point radiator will spread the energy into a full sphere, 4 pi is its solid angle.
 

wave1 said:
Does anyone knows where I can find proof/derivation of the relation between aperture and gain -
G = (4*pi)*Aeff/(lambda^2)
Click to expand...

You will find the proof in any professional antenna book. Krauss, Jasik, Balanis to name but a few.

There is a web site well worth looking at. At first I thought it had a proof, but I see it does not, but the proof is not very hard. Think about the area of a sphere being 4 Pi R, and having 4 Pi steradians of solid angle. That's where the 4 Pi factor comes from.

https://www.antenna-theory.com/basics/aperture.php

The guy that runs this site does know his antennas, so it can be trusted far more than many web sites about antennas.


Deborah.
 
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