Free-space Path Loss

Friss Equation

Friss Transmission Equation gives an estimate of power received by an antenna from another antenna radiating power at some distance away.

If the antenna radiates power uniformly in all directions, it is called isotropic antenna. Power() flows out from the transmit antenna in spherical wavefronts. Thus the power density at a distance R from the transmit antenna is .

If an antenna radiates power in a specific direction, it is called directional antenna. It is characterized by gain(G).

The units of antenna gain are expressed in dBi.

If the gain of transmit antenna is , then power density at the receive antenna is . If the receive antenna has an aperture area of , then the total receive power is (watts)

The effective antenna aperture area is related to wavelength and receive antenna gain as

Therefore received power of antenna is

Path loss is the power loss in the channel and is given by

(1)

(2)

where, → path loss in free space
→ distance from the transmit antenna().
→ wavelength of propagating wave in free space().
→ frequency in Hz.
→ speed of light in free space, ().

It can alternatively be expressed as

(3)

where, → frequency in , and
→ distance in

The pathloss increases with frequency of transmission and distance. For example signals transmitting at 2.4GHz incur much higher path loss than the signals transmitting at 900MHz.