Relation between the active input impedance and the active element pattern of a phased array

It is well known that the active element pattern of a phased array, obtained by driving a single radiating element of the array while all other elements are match terminated, can be expressed in terms of the scattering matrix parameters of the array. In this paper, it is shown how this relationship can be inverted so that the scattering parameters for all elements of a phased array can be obtained from the active element patterns of the array. In addition, it is also possible to obtain the active input impedance of any element in the fully excited array, at any scan angle, from active element pattern data. The theory is developed for linear and planar arrays and an example is presented for a linear array of slot antenna elements.