Methods of expressing the radiation patterns of phased arrays in closed form that include the effects of radiated mutual coupling are investigated. The two basic methods considered are the classical array analysis method and the active element pattern methods. The theoretical derivations of the active element pattern methods are presented and the various types of active element patterns are defined. Also, a new method based on active element patterns, the hybrid active element pattern method, is introduced which accurately predicts the patterns of small and moderately-sized arrays of equally-spaced elements. Arrays of center-fed dipoles are considered in this study since dipole arrays can be fully characterized, including mutual coupling, using modem numerical electromagnetic analysis codes, thus allowing verification of the array analysis methods presented here. The results are general, however, and may be applied to arrays of any type of element. The array patterns computed using the classical analysis method and the active element pattern methods are compared to those computed using ideal array analysis and the highly-accurate numerical codes. / Master of Science