The Friis transmission equation gives the power received by an antenna from another antenna that is transmitting a known amount of power at a distance under ideal conditions. The formula was derived by Herald T. Friis at Bell Labs in 1945.

The Derivation of the Formula can be seen below:

Assumption: Assume that the Transmitting antenna sends out a power (P_t). We assume that the transmit antenna is omni-directional, lossless and that the receive antenna is in the far field.

Step 1: The Power Density of the plane wave incident on the receive antenna which is at a distance ® from the transmitting antenna, can be calculated by:

Step 2: We assume that the transmit antenna has a gain (G_t), then the power density becomes:

Step 3: We assume that the receive antenna has an effective aperture of A_e. Then the power received by the receive antenna is (P_r):

Step 4: The Effective Antenna Aperture A_e, can also be defined as:

Step 5: The Final formula for the power received at the antenna can be denoted by the Friis Transmission Equation:

OR – If you prefer to use frequency over wavelength