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Tractable mathematical formula for Antenna Gain

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syedshan

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Hi all,

In the attached figure, one can find the antenna gain formula. But the authors have simplified it for the main lobe only. Can someone please let me know the exact form of the following simplified formula.

G(θ)=1+dcos(nθ), 0≤d≤1, n∈N+

Also, In my opinion this formula gives a general idea and can be extended to 3D form (i.e. Azimuth or elevation). The issue is that this is the only Tractible formula for the gain that I have come across
after all my search.

PS. I checked the reference that the author mentioned and it is more than 1000 pages book and I cannot find the formula there :(

111.PNG
 

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