# Isotropic Radiator as a Reference

The isotropic radiator is used as a reference for the computation of the resulting antenna pattern. It radiates the same power density in all directions.

As already mentioned, the isotropic radiator is a single point of radiation. The coordinates of this point are determined based on the coordinates of the single antennas used in the configuration. In a first step, the geometrical mean ${M}_{geo}$ of the single antennas (each of them concentrated in a single point) is determined. Each antenna is weighted with its individual part of the Tx power (if power splitters are used). So, in power splitter mode, ${M}_{geo}$ will be closer to the high power antennas.

The total Tx power ${P}_{t0}$ fed to the isotropic radiator is the sum of the powers fed to the individual antennas. With this power, the received power ${P}_{r}$ in a distance $r$ can be computed with

(1) ${P}_{r}\text{\hspace{0.17em}}=\frac{{P}_{{t}_{0}}{G}_{t}{G}_{r}{\lambda }_{0}^{2}}{{\left(4\pi r\right)}^{2}}\text{\hspace{0.17em}}$

For the computation of the resulting antenna pattern, the field strength and not the power is relevant. Therefore, the power density ${S}_{r}$ is computed with

(2) ${S}_{r}\text{\hspace{0.17em}}=\frac{{P}_{{t}_{0}}{G}_{t}}{4\pi {r}^{2}}\text{\hspace{0.17em}}$ .

With

(3) ${S}_{r}\text{\hspace{0.17em}}=\frac{{|{\underset{_}{E}}_{eff}|}^{2}}{{Z}_{F0}}\text{\hspace{0.17em}}$

the power density ${S}_{r}$ can be transformed to the effective electric field strength ${E}_{eff}$ ( ${Z}_{F0}$ is the free space impedance, and its value is ).