# 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

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

With

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 $120\text{}\pi \text{}\Omega $ ).