Free-space path loss

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In telecommunication, free-space path loss (FSPL) is the loss in signal strength of an electromagnetic wave that would result from a line-of-sight path through free space, with no obstacles nearby to cause reflection or diffraction. It does not include factors such as the gain of the antennas used at the transmitter and receiver, nor any loss associated with hardware imperfections. A discussion of these losses may be found in the article on link budget.

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Free-space path loss formula

Free-space path loss is proportional to the square of the distance between the transmitter and receiver, and also proportional to the square of the frequency of the radio signal.

The equation for FSPL is

where:

• $\ \lambda$ is the signal wavelength (in metres),
• $\ f$ is the signal frequency (in hertz),
• $\ d$ is the distance from the transmitter (in metres),
• $\ c$ is the speed of light in a vacuum, 2.99792458 × 108 metres per second.

This equation is only accurate in the far field where spherical spreading can be assumed; it does not hold close to the transmitter.

Free-space path loss in decibels

A convenient way to express FSPL is in terms of dB:

where the units are as before.

For typical radio applications, it is common to find $\ f$ measured in units of MHz and $\ d$ in km, in which case the FSPL equation becomes

For $\ d$ in statute miles, the constant becomes $\ 36.58$ .