Qualified 'separability' in the measurement and computation of antenna radiation patterns

A rectangular waveguide horn of N/2 by M/2 wavelengths will in general have a complex aperture distribution which is 'separable'-that is, it can be expressed as the product of a vertical and a horizontal distribution: F(x,y)=F/sub x/(x).F/sub y/(y). Its far-field radiation pattern is then similarly separable, being the product of a horizontal pattern due to the x distribution and a vertical pattern due to the y distribution. The complete 2D aperture distribution and far-field pattern can then be fully determined by N (near or far-field) samples giving the x distribution (at constant y) plus M samples giving the y distribution (at constant x), in place of the full set of M.N samples (further reduced by any known symmetry). This independence of the distributions over the two orthogonal axes-i.e. 'separability'-is maintained when the rectangular horn feeds a rectangular parabolic reflector, but not in the more common configuration where that reflector is circular or elliptical. Because of the associated economy in far or near-field measurement, separability is however commonly assumed, even when not really justified. The authors briefly review the types of antenna that are or are not separable and then consider how one can regain the economy in measurement and the accuracy of far-field computation normally associated with separability when measuring practical, non-separable antennas.<
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