On the size requirement for finite phased-array models

The question considered is how large an array model must be in order to capture approximately the characteristics of both the interior and the edge elements of a large multi-octave phased array. Arrays with tapered slot elements and with top-loaded dipoles are analyzed at element spacings as small as 0.1λ and it is concluded that at any frequency, a finite array model with this type of element should be at least 5λ×5λ in size. This suggests the generalization of the 10×10 element model often used as an engineering "rule of thumb" in the normal narrow-band case with 0.5λ element spacing. An array model with a 5:1 bandwidth thus needs about 25 times more elements than a narrow-band model. The array feed impedance is considered and it is found that the array active reflection coefficient in finite arrays but not in infinite arrays is dependent on the matching condition at the feed. The finite-difference time-domain (FDTD) technique is used to analyze arrays up to 49×49 elements, demonstrating that computer power now makes feasible the full wave solution for large phased arrays with complex geometry