On the End-Fire (Super) Directivity of an Array of Two Elementary Dipoles

The concept of source currents of a radiating source can be employed to express directivity in some particular cases analytically. For an antenna array, this concept can be combined with concepts of mutual radiation intensity and the mutual power of array elements. Using these approaches, we treat the evaluation of the directivity for an elementary dipole, and its end-fire array, which is of special attention due to superdirective properties. A closed form expression for the directivity of this array with out-of-phase excitation is derived. It is observed that end-fire directivity can be further enhanced by optimizing the excitation currents of the array. Their optimal relative phase and corresponding increased directivity are also found analytically. The results are validated by a full-wave simulator.