Estimation of intercardinal antenna pattern based on cardinal data

Measuring antenna patterns costs time and money. Therefore effort is placed where necessary: only in the cardinal i.e. the azimuth and elevation planes. EMC engineers are interested in the intercardinal values, since an interfering system may be placed off boresight, both in azimuth and elevation. This paper suggests a method to estimate the intercardinal gain, G(φ,θ), based solely on the cardinal patterns, G(φ) and G(θ). The common approach is to assume that the gain at an intercardinal angle, (φ,θ), is equal to the sum (in dB): G(φ,θ)=G(φ)+G(θ). This is a rather simple way of estimation. It has, however, no mathematical proof or physical basis. The approach suggested in this article adopts an opposite line of logic. Rather than trying to estimate G(φ,θ) based on G(φ) and G(θ), we will estimate one equivalent angle, φ´ or θ´ to be used with one of the cardinal patterns, G(φ) or G(θ). The basic idea is to look for the geometric locus in space, of pairs of angles φ and θ, having an iso-gain. The assumption is that these loci are circles drawn on a sphere if BW_AZ=BW_EL and ellipses drawn on a sphere, in the general case, when BW_AZ≠BW_EL. Also, a way to reduce estimation errors is suggested. Finally, a quantitative comparison between the suggested equations and a simulated spherical antenna pattern, illustrates the small error of the new technique