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How to design non-longitudinal slot antenna (slotted waveguide/siw)?

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Terminator3

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I can't find any good reference on non-longitudinal slot arrays. Most information is given for longitudinal slot arrays (admittance is analyzed)) and inclined slots. Slot is perpendicular to waveguide longitudinal axis. How to characterize such slot? Only a little information in few papers on leaky-wave antennas. I am interesting in this topics:
1) power division between non-longitudinal slots
2) matching (equivalent circuit for non-longitudinal slot, similar to admittance of longitudinal slots)
 

Hi Terminator3,

I guess you are telling slots like "f" and "g" in this figure (waveguide in TE10 mode). Right?

slots1.png

There is a bit of information in "Modern Antenna Design, 2nd Edition" by Thomas Milligan (Wiley-IEEE Press, 2005), section 5-24 .
(I saw more information in some other book, but now I don't remember which one.)
 
Antenna Engineering Handbook, 4th Edition - Volakis (Editor), Mc-Graw Hill, 2007. Chapter 9: Waveguide Slot Antenna Arrays.

Alternatively: (same title), 3rd Edition - Johnson and Jasik (Ed), McGraw-Hill, 1993.Chapter 9.
 
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