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finite element array grating lobe condition

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yefj

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Hello, i heard that the general collage formula is just an aprroximation for N>>1 as shown bellow.
Does anybody know how we develop this "non approximated formula from the basic Grating Lobe theory?
Thanks.

1671751385574.png

1671751025006.png


1671751197020.png


1671751523545.png
 

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Those look like excerpts from Balanis' text; I think he walks through the derivation. You just have to re-perform it without making the approximations he does, I think in the earlier equations.
 

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