Editing Free-space path loss (section)

== Free-space path loss in decibels ==

A convenient way to express FSPL is in terms of [[decibel]]s (dB):<ref name="Pasternack">{{cite web |title=Free Space Path Loss Calculator |url=https://www.pasternack.com/t-calculator-fspl.aspx |website=Pasternack |access-date=October 16, 2021}}</ref>
:<math>
\begin{align}
\operatorname{FSPL}(\text{dB})
  &= 10\log_{10}\left(\left(\frac{4\pi d f}{c}\right)^2\right) \\
  &= 20\log_{10}\left(\frac{4\pi d f}{c}\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}
</math>
using [[SI unit]]s of meters for <math>d</math>, [[hertz]] (s<sup>−1</sup>) for <math>f</math>, and meters per second (m⋅s<sup>−1</sup>) for <math>c</math>, (where c=299 792 458 m/s in vacuum, ≈ 300 000 km/s)

For typical radio applications, it is common to find <math>d</math> measured in [[kilometers]] and <math>f</math> in [[gigahertz]], in which case the FSPL equation becomes
:<math>\operatorname{FSPL}(\text{dB}) = 20\log_{10}(d_{km}) + 20\log_{10}(f_{GHz}) + 92.45,</math>
an increase of 240&nbsp;dB, because the units increase by factors of {{10^|3}} and {{10^|9}} respectively, so:
:<math>20\log_{10}(10^{3}) + 20\log_{10}(10^{9}) = 240.</math>

(The constants differ in the second decimal digit when the speed of light is approximated by 300 000 km/s.  Whether one uses 92.4, 92.44 or 92.45 dB, the result will be OK as the average measurement instruments cannot provide more accurate results anyway. A logarithmic scale is introduced to see the important differences (i.e. order of magnitudes), so in engineering practice dB results are rounded)