As a 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
or dispersion by the atmosphere. Both a 1-Way and a 2-Way Path Loss Calculator are
Calculator Workbook for FREE.
These equations are valid when the distance is greater than about a wavelength.
At distances less than that the electric field is transitioning between near field
and far field where, physical factors like antenna dimensions dominate and force
the use of electromagnetic field equations.
Note: When using these formulas, be sure to keep dimensional
units consistent; i.e., do not mix kHz with MHz, mm with inches, etc. It is safer
to use base units (e.g., Hz, m) for calculation, then
convert result to desired units.
1-Way Path Loss Equations
(double for 2-way radar signal loss)
The Friis Equation (H.T. Friis, 1946) gives a more complete accounting for all
the factors from the transmitter to the receiver:
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.
Free Space 1-Way Path Loss (km)
Free Space 1-Way Path Loss (miles)
Here is information on propagation time,
radar equation and
Most RF engineers are familiar with the
Friis equation, which predicts the received power level.
Harald T. Friis, born in Naestved, Denmark, is
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.
Harald T. Friis