# 4 Array Factors and Element Patterns

So far, only isotropic point sources have been considered as elements in the arrays. This chapter takes a first step toward a more realistic antenna array through the introduction of an element pattern with its associated gain and polarization. Formulas for the normalized far-field element patterns and directivity of many common elements are given in this chapter for use with the array factor formulas already presented. More complicated antennas require the use of a numerical model to calculate the element pattern. Calculating the impedance of an element is important in order to determine the bandwidth.

## 4.1. PATTERN MULTIPLICATION

The elements in an actual array are not isotropic point sources. Instead, they have directionality that is proportional to their size. They also have frequency, impedance, and polarization properties not associated with point sources. Normally, the elements in an array are spaced relatively close together, so an element is typically no larger than λ/2 × λ/2 in area in a square lattice. As such, the element pattern is too small to have sidelobes. A typical element pattern for an array in the xy plane can be reasonably approximated by cos θ or sin or the change in the projected area of the element [1].

Element spacing in an array is determined by the distance between phase centers of adjacent elements. A point source ...

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