In a linear endfire array of n elements, a choice of current phasing that improves the directivity is given by the Hansen€“Woodyard condition:

where the plus or minus sign choices give maximum radiation along Ï• = 180—¦ and 0—¦, respectively. Applying this phasing may not necessarily lead to unidirectional endfire operation (zero backward radiation), but it will do so with the proper choice of element spacing, d.

(a) Determine this required spacing as a function of n and λ.

(b) Show that the spacing as found in part (a) approaches λ/4 for a large number of elements.

(c) Show that an even number of elements is required.

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