Aperture Distributions for Maximum Endfire Directivity From a Continuous Line Source With a Uniform Phase Progression

An optimized aperture distribution is investigated to achieve the maximum endfire directivity for a continuous line source with a uniform phase progression. The optimization method has the advantages of simplicity and efficiency, in which the aperture distribution is expanded into a set of cosine functions and the optimization reduces to solving a constrained linear-least-squares problem. Based on the copious computed results from the optimization, an approximate closed-form expression is derived for the maximum directivity. The expression can serve as a bound for the endfire directivity for a line source with a uniform phase progression. It is found that the optimum directivity increases almost linearly with an increase of the normalized phase constant, but with a decrease in the radiated power. Nevertheless, the enhancement in the directivity is much higher than that in previously studied superdirectivity, under the same constraint in the ratio of reactive to radiated power. The current distribution does not oscillate widely as is does for superdirectivity, and is therefore more practical than for superdirectivity.