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 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, will be closer to the high power antennas.
The total Tx power fed to the isotropic radiator is the sum of the powers fed to the individual antennas. With this power, the received power in a distance 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 is computed with
With
the power density can be transformed to the effective electric field strength ( is the free space impedance, and its value is ).