Measurement of scan element pattern of wideband arrays

Scan Element Pattern, SEP, (formerly active element pattern¹) was developed circa 1960 by Allen [1], Oliner [2], Hannan [3], Stark [4], and others, to provide phased array gain behavior versus scan angles. It's utility for decades has been to give insight and results on the scan performance of various elements and lattices. A common measurement procedure terminates all elements in the array, with the excited center element connected to a gain measurement setup. As early as the Lincoln Lab reports [1] it was recognized that the impedance seen in the measurement procedure was not the Scan Impedance (SI), (impedance seen when all elements are excited with the proper amplitude and phase), due to the passive mutual couplings. In Allen's derivation the textbook definition of gain was used; Scan Impedance mismatch was not included. Hannan did include mismatch, but his formulas were based on “intuitive reasoning”. Clearly his SEP proportional to cos θ is only approximate; it fails for large scan angles. Allen derives SEP for the center element excited case under the assumption that the isolated element pattern is equal to the element pattern in the array with all elements terminated. With this assumption it can be shown that transmit SEP (single element excited) equals receive SEP, with impedance determined in both cases with all elements excited. For single mode elements such as dipoles this assumption is very good; almost nothing will affect the shape of current on a thin dipole. However for more complex elements the element pattern with other elements terminated is not equal to the isolated element pattern.