Before revision: For antenna arrays, the closed form expression for Directivity for progressively phased array of isotropic sources will be given by, where, is the total number of elements on the aperture; represents the location of elements in Cartesian co-ordinate system; is the complex excitation coefficient of the -element; Phase component (progressive phasing); is the wavenumber; is the angular location of the far-field target; is the Euclidean distance between the and element on the aperture, and Further studies on Directivity expressions for various cases, like if the sources are omnidirectional (even in the array environment) like if the prototype element-pattern takes the form , and not restricting to progressive phasing can be done from.
After revision: For antenna arrays, the closed form expression for Directivity for progressively phased array of isotropic sources will be given by, where, is the total number of elements on the aperture; represents the location of elements in Cartesian co-ordinate system; is the complex excitation coefficient of the -element; is the phase component (progressive phasing); is the wavenumber; is the angular location of the far-field target; is the Euclidean distance between the and element on the aperture, and Further studies on directivity expressions for various cases, like if the sources are omnidirectional (even in the array environment) like if the prototype element-pattern takes the form , and not restricting to progressive phasing can be done from.