Using the product theorem given in Section 13.16, the directivity pattern is equal to the product of the directivity patterns for two line arrays at right angles to each other [see Eq. (4.89)]. The directivity pattern for this type of radiating source with dimensions l
_{
x
} and l
_{
y
} is given by the formula

$D\left({\theta}_{x},{\theta}_{y}\right)=\frac{\mathrm{sin}\left(\frac{1}{2}k{l}_{x}\mathrm{sin}{\theta}_{x}\right)}{\frac{1}{2}k{l}_{x}\mathrm{sin}{\theta}_{x}}\xb7\frac{\mathrm{sin}\left(\frac{1}{2}k{l}_{y}\mathrm{sin}{\theta}_{y}\right)}{\frac{1}{2}k{l}_{y}\mathrm{sin}{\theta}_{y}},$

(13.318)

where θ
_{
x
} is the angle between the normal to ...

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