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. [1] 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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