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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.

Listen to Jørgen Jakob Friis pronounce "Friis"Friis


Listen to Jørgen Jakob Friis pronounce "Harald Friis"Harald T. Friis


Listen to Jørgen Jakob Friis pronounce "Naestved"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 1-Way and a 2-Way 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.

Path loss equation formula - RF Cafe

The Friis Equation (H.T. Friis, 1946) gives a more complete accounting
for all the factors from the transmitter to the receiver:


Path loss equation formula - RF Cafe where: GTx = transmitter antenna gain
GRx = 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.

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