Free-space Path Loss - Free-space Path Loss in Decibels

Free-space Path Loss in Decibels

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

\begin{align} \mbox{FSPL(dB)} &= 10\log_{10}\left(\left(\frac{4\pi}{c}df\right)^2\right) \\ &= 20\log_{10}\left(\frac{4\pi}{c}df\right) \\ &= 20\log_{10}(d) + 20\log_{10}(f) + 20\log_{10}\left(\frac{4\pi}{c}\right) \\ &= 20\log_{10}(d) + 20\log_{10}(f) - 147.55 \end{align}

where the units are as before.

For typical radio applications, it is common to find measured in units of GHz and in km, in which case the FSPL equation becomes

For in meters and megahertz, respectively, the constant becomes .

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