Analysis of Radiation from Waveguide Arrays on Metallic Cylinders, Including Mutual Coupling Effects

Abstract

Arrays of open ended rectangul-ar waveguides in metallic cylindrical surfaces are considered. An analysis which uses mode matching at the cylinder surface to derive inter-element coupling coefficients is described, and some results are presented.The analysis is then extended to obtain expressions for the radiated far field in terms of the aperture distribution in the elements. Element patterns are presented, and compared with a measured result from an experimental cylindrical array; good agreement is seen.The computed far field pattern for a more practical array is presented, and various features of the pattern are discussed. ANALYSIS OF APERTURE FIELI)SIn order to find the fields on the surface of a circular cylinder, our first requirement is to find expressions for the fields in free space external to the cylinder. To do this it is necessary to solve the scalar Helmholtz equation:-where v2 is the Laplacian operator, k0,is the free space wave number and § is the required scalaE potential.For our purposes, it is most convenient to express V in cylindrical polar coordinates (r, 0, z), when (1) may be solved in a similar manner to that of Harrington [1] The result appropriate to our case, which has only outward travelling waves, is:-g(r, 0, z) = H2 r(krr) exp (j(vo + kzz))(2) where kr2 + k = k2 and v is arbitrary. is the Hankel function of the second kind, of order r.