Applicability of the Hansen-Woodyard condition

The Hansen-Woodyard condition is reviewed, and some of its various forms are discussed. For continuous arrays, the directivities for ordinary endfire and Hansen-Woodyard excitation are compared with the maximum obtainable directivity. Similarly, the directivities of discrete arrays, which are optimised with respect to the spacing under the above excitation constraints, are compared with the maximum obtainable directivity. It is concluded that, from a practical point of view, the Hansen-Woodyard condition yields results which are very close to the optimum, except for very short arrays.