Element pattern for circular arrays of waveguide-fed axial slits on large conducting cylinders

Abstract

Analytical and numerical results are presented for the array element pattern of axial slits in conducting cylinders. The slits are fed by parallel-plate guides in the TEM mode and are matched to free space. Both harmonic series and integral representation for the far-field patterns are obtained and numerically evaluated as a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kr_{0}</tex> and spacing. The integral representation is treated asymptotically for large values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kr_{0}</tex> . The element patterns exhibit two characteristic features: a dip off broadside and a ripple in the main beam near broadside, the level of both being <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kr_{0}</tex> dependent. While the harmonic series offers no basis for an explanation of these effects, the asymptotics clearly demonstrates that the pattern can be decomposed into two parts: 1) a space wave contribution which can be directly obtained by substituting the circular array "admittance crater" into the appropriate planar array formulas and exhibits a dip analogous to a grating lobe effect; 2) a set of creeping waves which, unlike the more common type, contribute significantly in the forward region and, by interfering with the space wave, cause the ripple near broadside. These creeping waves are the fast (usually <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = -1</tex> ) space harmonics (grating lobes) of the fundamental, slightly slow set, and their presence does not seem to have been recognized in the literature.