From Microstrip and Printed Antenna Design
D.1 Friis Transmission Formula
An equation which describes the path loss between two antennas was introduced by Friis.  The formula was introduced in terms of the effective area of the transmitting and receiving antenna.
P r is the power available at the output port of the receiving antenna.
P t is the power fed into the input port of the transmitting antenna.
A r is the effective area of the receiving antenna.
A r is the effective area of the transmitting antenna.
R is the distance between the antennas
? is the wavelength
The power delivered to the terminals of an antenna is defined as:
S is the power density of a plane wave incident on the antenna in W/m 2
A e is the effective area of the antenna m 2
The gain of an antenna in terms of effective area is:
The Friis equation may now be written in terms of antenna gain.
G t is the transmit antenna gain
G r is the receive antenna gain
The relationship between gain over an isotropic source ( G) and that gain in decibels with respect to an isotropic source is:
It is often useful to write the Friis equation using logarithms to determine path loss:
F is frequency in MHz
R is the distance between antennas in meters
The Friis Transmission Formula assumes the value of R is sufficiently large so...
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