Array factor

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

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

where $a_{n}$ are the complex-valued excitation coefficients, and ${\hat {r}}$ is the direction unit vector. The array factor is defined in the transmitting mode^[2], with the time convention $e^{j\omega t}$ . 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

^ Balanis, C. A. Antenna Theory, Analysis and Design (3 ed.). p. 291.
^ "IEEE Standard for definitions of terms for antennas". IEEE Std. 2014.
^ Frid, Henrik (2020). Analysis and Optimization of Installed Antenna Performance. Stockholm, Sweden: KTH (PhD thesis). pp. 36–39. ISBN 978-91-7873-447-4.

References

See also