The total phase difference,
, between the fields due to adjacent elements is algebraic sum of the current and the propagation phase difference.
Without losing generality, let us assume that the electric field due to individual antennas has unit amplitude at the observation point P. Also let the first element be the reference element. Then by definition the phase of the field due to antenna 1 is zero.
The total field at the observation point is
The RHS of the equation is a geometric series with summation given by
After some algebraic manipulation, we get the electric field at the observation point as
The maximum electric field is obtained when all the terms in the series add in phase ( i.e. for
). The maximum filed therefore is N.
The expression gives the variation of field as a function of the direction, , and hence is the radiation pattern of the antenna array.
The radiation pattern is generally normalized with respect to the maximum value N to get the ‘ Array Factor ' as
This is the general expression for the radiation pattern of a uniform array.
A typical radiation pattern is shown in Fig.
The range of the angle is from 0 to , and the 3-D radiation pattern is the figure of revolution of the Array Factor around the axis of the array.
From the general array factor we can study the Direction of Maximum Radiation.
, between the fields due to adjacent elements is algebraic sum of the current and the propagation phase difference. 
). The maximum filed therefore is N. 
, and hence is the radiation pattern of the antenna array. 
is from 0 to 
, and the 3-D radiation pattern is the figure of revolution of the Array Factor around the axis of the array. 
