
Free Space Path Loss  Friis Equation


Can You Say, "Friis Equation?" 
Most RF engineers are familiar with the Friis
equation, which predicts the received power level.
Harald T.
Friis, born in Naestved, Denmark, is its namesake.
Just as with "Fresnel" (Fresnel
zone), many people do not know the proper pronunciation of "Friis"  I did not. So, I asked a native Dane,
Jørgen Jakob Friis, how he pronounces the name. He responded with actual audio files of him speaking H.T.
Friis' name and hometown.
Friis
Harald
T. Friis
Naestved
Many thanks to Jørgen for his assistance!


As the transmitted signal traverses the atmosphere its power level decreases at a rate inversely proportional to
the distance traveled and proportional to the wavelength of the signal. The formula used by
RF Workbench accounts for only the diminishing voltage without accounting for
absorption or dispersion by the atmosphere. Both a 1Way and a 2Way Path Loss Calculator are included in
RF Cafe Calculator Workbook for FREE.
Note that when the distance (d) is equal to 1/4π, path loss is
calculated as 0 dB, and a shorted distances the path loss is calculated as a negative number. This clearly goes
against intuition, and rightly so. Therefore, this equation has practical limits. A typical rule of thumb is to
not use this path loss equation for distances less than about a wavelength. At less than a wavelength, physical
factors like antenna dimensions dominate and force the use of electromagnetic field equations.
The Friis Equation (H.T. Friis, 1946) gives a more complete accounting for all the factors from the transmitter
to the receiver:

where: 
G_{Tx} = transmitter antenna gain G_{Rx} = receiver antenna gain
λ = wavelength (same units as d) d = distance separating Tx and Rx antennas L = system
loss factor (≥ 1) 
Information in the transmitted signal is seldom concentrated at a single frequency, so the path loss will
actually be different for every frequency component in the signal. Fortunately, the ratio of the bandwidth to
center frequency is usually small enough to not matter. Still, a signal that is transmitted with a constant power
across some bandwidth will appear at the receiver with a power slope that decreases at the upper end of the band.



