HFSS15: Theory of the Array Factor Calculation

The composite far-field pattern, E_array (f, q) from an array of N identical radiating sources, each with far-field pattern E_element (f, q), may be factored into the form

(1)

where the "array factor" AF (f, q) is defined as

(2)

and where

• (f, q) are the field-point spherical angles.

• W_n is the complex weight assigned to element n.

• j is .

• k is 2p/l., wherel is the wave length in the global material environment.

• r_n is the position vector of element n, <xn, yn, zn>.

• is the pattern angle unit vector, qcosf, sinqsinf, cosq>.

The complex weights W_n in (eq. 2) may be written in terms of a (real) voltage amplitude A_n and (real) phase as:

(3)

To scan a regular array in the direction (f₀, q₀), the element phases are set to

(4)

where

(5)

is the scan-angle unit vector.