Design of corrugated plates for phased array matching

The reflection coefficient for an array of identical nonuniformly corrugated plates phased to launch a plane wave in any direction is calculated exactly. The plate spacing is limited only by the grating lobe condition, and the corrugations in each plate may be of arbitrary depth, or the bottom of each corrugation may be terminated in an arbitrary admittance. The conditions for the occurrence of a surface wave effect, corresponding to a total array mismatch or a null in the element pattern, are derived in general for arrays having an adjustable short-circuited parasitic element (such as a corrugation) with each driven element. It is shown that the existence of such a surface wave effect often can be predicted solely from the symmetry of the array in question. The optimum position of the short circuit for the best match also is discussed. Although corrugated plate arrays can be deliberately adjusted to exhibit a surface wave phenomenon in the
H
plane, the effect is easily avoided for the most practical ranges of scan. Design data are given for an array with one corrugation per plate for varying amounts of
E
-plane and
H
-plane scan, and for scanning within an octant of a sphere.