Theory of the Array Factor Calculation
The composite far-field pattern, Earray (f, q) from an array of N identical radiating sources, each with far-field pattern Eelement (f, q), may be factored into the form
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(1) |
where the "array factor" AF (f, q) is defined as
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(2) |
and where
- (f, q) are the field-point spherical angles.
- Wn is the complex weight assigned to element n.
- j is
.
- k is 2p/l., wherel is the wave length in the global material environment.
- rn is the position vector of element n, <xn, yn, zn>.
- is the pattern angle unit vector, <sinqcosf, sinqsinf, cosq>.
The complex weights Wn in (eq. 2) may
be written in terms of a (real) voltage amplitude An
and
(real) phase 
as:
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(3) |
To scan a regular array in the direction (f0, q0),
the element phases 
are
set to
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(4) |
where
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(5) |
is the scan-angle unit vector.