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Calculating waveguide size

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i am studying av-comm polarizer and "polopipe" (from brazil) (device for convert circular to linear)
i have found some calculation about wavelenght in pipe but i have two variant of the same equation :

LG = L / (racine (1 - ( L / (2.d))^ 2))
LG = L / (racine (1 - ( L / (1.6406.d))^ 2))

lg = wavelenght in pipe
L=wavelenght in air
d=pipe diameter

in the second way 1.64.06 matches with polopipe described on south american forums
first way is classical value found in mathmatical...

Calculating waveguide size

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