Mutual coupling, gain and directivity of an array of two identical antennas

It is shown that there is an optimum nonzero value of mutual coupling and passive reflection coefficient that is a function of only the embedded element pattern and element spacing. Optimum is defined as yielding maximum array gain. For closely spaced arrays, the optimum mutual coupling and passive reflection coefficient are quite large, but tend to cancel in the active mode to produce a low active reflection coefficient. A smaller value of mutual coupling would give lower gain than the optimum case. This again demonstrates that mutual coupling is a natural and desirable effect in array behavior. It is well known that it is possible to achieve array superdirectivity, in the sense that the directivity of an array of "
N
" elements is greater than "
N
" times the embedded element directivity; however, in this case the mutual coupling and passive reflection produce an active reflection coefficient that results in an array gain lower than "
N
" times the embedded element gain. In fact, higher superdirectivity always implies lower gain, relative to embedded element gain.