In the radiation pattern of a 3-element array of isotropic radiators equally spaced at distances of $${\lambda /4}$$ it is required to place a null at an angle of 33.56 degrees off the end-fire direction. Calculate the progressive phase shifts to be applied to the elements. Also calculate the angle at which the main beam is placed for this phase distribution.

Two vertically oriented half wave dipoles are spaced 1.5 wavelengths apart to from an array. Calculate the half power beam widths of the major lobes of the array, in the horizontal plane for the following two cases when the dipoles are fed with

(a) equal and in - phase currents (Broadside array)
(b) equal currents but with a phase difference of 540⁰ between the two currents (End fire array)