Friis transmission equation

The Friis transmission equation is used in telecommunications engineering, and gives the power received by one antenna under idealized conditions given another antenna some distance away transmitting a known amount of power. The formula was derived in 1945 by Danish-American radio engineer Harald T. Friis at Bell Labs which was later published in 1946.

In its simplest form, the Friis transmission equation is as follows. Given two antennas, the ratio of power available at the input of the receiving antenna, ${\displaystyle P_{r}}$, to output power to the transmitting antenna, ${\displaystyle P_{t}}$, is given by

where ${\displaystyle G_{t}}$ and ${\displaystyle G_{r}}$ are the antenna gains (with respect to an isotropic radiator) of the transmitting and receiving antennas respectively, ${\displaystyle \lambda }$ is the wavelength, and ${\displaystyle R}$ is the distance between the antennas. The inverse of the third factor is the so-called free-space path loss. To use the equation as written, the antenna gain may not be in units of decibels, and the wavelength and distance units must be the same. If the gain has units of dB, the equation is slightly modified to:

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