rss_friis.m

received signal strength

In its simplest form, the Friis transmission equation is as follows. Given two antennas, the ratio of power available at the input of the receiving antenna, P_r, to output power to the transmitting antenna, P_t, is given by
\frac{P_r}{P_t} = G_t G_r \left( \frac{\lambda}{4 \pi R} \right)^2
where G_t and G_r are the antenna gains (with respect to an isotropic radiator) of the transmitting and receiving antennas respectively, \lambda is the wavelength, and R is the distance between the antennas. The inverse of the factor in parentheses is the so-called free-space path loss. To use the equation as written, the antenna gain may not be in units of decibels, and the wavelength and distance units must be the same. If the gain has units of dB, the equation is slightly modified to:

P_r = P_t + G_t + G_r + 20\log_{10}\left( \frac{\lambda}{4 \pi R} \right) (Gain has units of dB, and power has units of dBm or dBW)
This simple form applies only under the following ideal conditions:

R\gg\lambda (reads as R much greater than \lambda). If R<\lambda, then the equation would give the physically impossible result that the receive power is greater than the transmit power, a violation of the law of conservation of energy.
The antennas are in unobstructed free space, with no multipath.
P_r is understood to be the available power at the receive antenna terminals. There is loss introduced by both the cable running to the antenna and the connectors. Furthermore, the power at the output of the antenna will only be fully delivered into the transmission line if the antenna and transmission line are conjugate matched (see impedance match).
P_t is understood to be the power delivered to the transmit antenna. There is loss introduced by both the cable running to the antenna and the connectors. Furthermore, the power at the input of the antenna will only be fully delivered into freespace if the antenna and transmission line are conjugate matched.
The antennas are correctly aligned and polarized.
The bandwidth is narrow enough that a single value for the wavelength can be assumed.
The ideal conditions are almost never achieved in ordinary terrestrial communications, due to obstructions, reflections from buildings, and most importantly reflections from the ground. One situation where the equation is reasonably accurate is in satellite communications when there is negligible atmospheric absorption; another situation is in anechoic chambers specifically designed to minimize reflections.

Modifications to the basic equation