In general, the path loss, as a deterministic parameter, is defined in the following way. A transmitter transfers P _T (W) into the port of an antenna with gain G _T, and the perfectly co polarised receiving antenna with gain G _R delivers power P _R (W) into a perfectly matched load at its port. The path loss L is defined from the Friis transmission equation, which reduces to

It is clear that the 'path gain' is simply the reciprocal of the path loss. A few simple equations show the important relations between path loss and field strength.

At a distance d(m) of free space from the phase centre of the transmitting antenna, the power density S is

Sometimes the field strength at the receiving antenna, E _R (V m ¹), is wanted instead of the path loss. The relation between E _R and S is

and so

At the receiving antenna, the incident power density S is multiplied by the antenna effective cross section A _R, defined by

to give the received power as

The power ratio can now be written

and thus the free space path loss is given by the expression

The free space path loss is also well known in its logarithmic form, where the frequency is expressed in MHz and the distance is in km:

Note that for frequency independent antenna gains, the path loss...