Array factor

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The array factor ${\displaystyle AF}$ is the complex-valued far-field radiation pattern obtained for an array of ${\displaystyle N}$ isotropic radiators located at coordinates ${\displaystyle {\vec {r}}_{n}}$, as determined by:^[1]

${\displaystyle AF({\hat {r}})=\sum _{n=1}^{N}a_{n}e^{jk{\hat {r}}\cdot {\vec {r}}_{n}},}$

where ${\displaystyle a_{n}}$ are the complex-valued excitation coefficients, and ${\displaystyle {\hat {r}}}$ is the direction unit vector. The array factor is defined in the transmitting mode,^[2] with the time convention ${\displaystyle e^{j\omega t}}$. A corresponding expression can be derived for the receiving mode, where a negative sign appears in the exponential factors, as derived in reference.^[3]

References[]

See also[]

• Array antenna