What is free space path loss (FSPL), and how is it calculated?
FSPL is the signal attenuation that occurs due to distance alone with no obstacles, and it is calculated with FSPL(dB) = 32.44 + 20*log10(d_km) + 20*log10(f_MHz). At 100 m the loss is 65.2 dB at 433.92 MHz, 71.2 dB at 868 MHz and 80.2 dB at 2.45 GHz. At 150 m these values become 68.7, 74.7 and 83.7 dB respectively.
The constant 32.44 in the formula is not arbitrary; it is the value the expression 20*log10(4pi/c) takes for kilometre and megahertz units. The formula itself derives from the Friis transmission equation and assumes isotropic antennas.
It is enough to memorise two behaviours:
- Every time the distance doubles, the loss increases by 6 dB.
- Every time the frequency doubles, the loss again increases by 6 dB. Going from 433.92 MHz to 2.45 GHz means
20*log10(2450/433.92) = 15.0 dBof extra loss.
FSPL is a lower bound: on a real site, obstacle loss, multipath fading, Fresnel zone violation, polarisation mismatch and cable loss are added on top. This is why the range calculated with FSPL is never obtained in the field; the calculation is only the starting point of the link budget.
The correct use is this: calculate FSPL, put it into the link budget, compare the resulting received power with the receiver sensitivity, and make sure the difference leaves at least 10-20 dB of safety margin. A link with no margin left is cut by the first rain or the first crane movement.
Full topic: Wireless remote control installation: pairing, relay, safety