##### 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.

Where:

*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:

Where:

*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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