On the scattering cross section of passive linear arrays

A general formula is derived for the scattering cross section of a passive n-element linear array consisting of isotropic radiators. When all the reactances are tuned out and scattering in the mirror direction is investigated, it is found that A,,, the relative scattering cross section is equal to the square of the maximum gain the array can produce. As a consequence, for forward scattering in the limiting case of zero spacing between the elements, A , , = n4. The cross section of a scattering object having cylindrical symmetry is defined as follows A, (e&) = &-r2 power density a t distant point r in direction e2 poaer density of plane wave incident, from direct,ion el . (1) For an array one is more interested in t,he relative scattering cross section where A,i is the scat.tering cross section of the individual radiator. In this Communication we shall express A s r ( O l , & ) in terms of the geometry of the array and of t.he parameters of the matching matrix. A general formulation for an arbitrary three-dimensional array is certainly possible, but we shall, for simplicity, restrict the investigation to linear arrays consisting of isotropic radiators. In t.hat part.icular case there are several theorems available making order mod& are below cutoff A 20 percent bandwidth capability thus leaves a margin of about 14 percent, part of which (-12 Manuscript receiped December 4, 1972; revised January 11, 19i3. percent) is used as guard between the 1oWer edge of t,he operat,ing ~ ~ b i ~ l u ~ ~ ~ ~ ~ , ~ of Denmark, LJmgby, ~ ~ ~ ~ ~ ~ k . The author, is Ft.h the Laboratory of Electromagnetic Theory, the Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on October 2, 2009 at 10:35 from IEEE Xplore. Restrictions apply. 392 IEEE TMNSACTIONS O X -44NTENNAS AZXD PROPAGATION, MAY 1973 Substituting for i from (7) and using (5) we get