Optimum element lengths for Yagi-Uda arrays

An analytical method is developed for the maximization of the directivity of a Yagi-Uda array by adjusting the lengths of the dipole elements. The effects of a finite dipole radius and the mutual coupling between the elements are taken into consideration. Currents in the array elements are approximated by three-term expansions with complex coefficients that convert the governing integral equations into matrix equations. Array directivity is maximized by a perturbation procedure that adjusts the lengths of all array elements simultaneously and that converges very rapidly. This method can be combined with the previously developed spacing-perturbation method to form a double-perturbation procedure and obtain a Yagi-Uda array of nonuniformly spaced elements of unequal lengths. which yields a maximum directivity.