2. Two-element Array
• Consider two infinitesimal z-directed current elements placed
symmetrically about the origin along the z-axis
3. For positive values of α, the current in dipole 2 leads the current in dipole 1. The
electric field of the two-element array can be computed using Eqn (5.6) with
N =2, which is
4.
5. • The array factors of a two-element array for different element
spacing's from 0.25λ to 2λ .
• As the element spacing increases from 0.25λ to 0.5λ, the main
beam gets narrower. At d = 0.5λ, two nulls (along θ = 0◦ and
180◦) appear in the pattern.
• Further increase in the spacing results in the appearance of
multiple lobes in the pattern.
• At d = λ, the pattern has three lobes, all of them having the same
maximum level.
• Further increase in the element spacing results in a similar
behavior of narrowing of the main beam and appearance of more
lobes. The pattern is independent of φ.
6. • We will now derive the expressions for the directions of the
maxima and nulls of the array factor.
• The maxima of the array factor occur when the argument of the
cosine function is equal to an integer multiple of π.
• where, θm are the directions of the maxima and can be written as
• For maxima to occur along the real angles, the argument of the
cosine inverse function must be between −1 and +1
• This implies that there is always a maximum corresponding to m =
0 which is directed along θ = cos−1(0) = 90◦. The number of
maxima in the array factor depends on the spacing between the
two elements.
7. • The array factor always has a maximum along the θ = 90◦ direction
or the broadside direction, hence the array is known as a broadside
array.
• The nulls, θn, of the array factor satisfy the condition
• Therefore, the directions of the nulls are given by
• For the nulls to occur along the real angles, we must have
• which gives the condition
• For a null to appear in the pattern, the spacing between the
elements must be at least equal to λ/2, and corresponding nulls
appear along θ = 0 and π.
