Friis Transmission equation

Description

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.

n 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, P_r, to output power to the transmitting antenna, P_t, is given by the formula show here.

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.

Related formulas

Variables

Prpower available at the input of the receiving antenna (watt)
Ptoutput power to the transmitting antenna (watt)
Gtantenna gain (with respect to an isotropic radiator) of the transmitting antennas (dimensionless)
Grantenna gain (with respect to an isotropic radiator) of the receiving antennas (dimensionless)
λwavelength (m)
πpi
Rdistance between the antennas (m)