Engineering
Free-Space Path Loss (FSPL), Friis RF link power & Inverse-Square dB drop
Calculate wireless RF attenuation FSPL(dB) = 20*LOG10(d_km) + 20*LOG10(f_MHz) + 32.44, Friis received dBm, and acoustic -20*LOG10(d2/d1) distance attenuation.
Model wireless Wi-Fi / LoRa / satellite path loss & 6.02 dB distance doubling!
Harald Friis's Free-Space Path Loss equation quantifies spherical wave spreading + effective antenna aperture in decibels for line-of-sight RF links using distance d (km) and carrier frequency f (MHz): FSPL(dB) = 20 * LOG10(d_km) + 20 * LOG10(f_MHz) + 32.44.
Adding transmitter power Pt (dBm) and antenna gains Gt + Gr (dBi) gives Friis Received Power Pr(dBm) = Pt + Gt + Gr - FSPL. And because intensity falls as 1 / d^2 for both radio and outdoor sound waves, every doubling of distance adds 20 * LOG10(2) = 6.02 dB of attenuation!
The Friis estimate assumes far-field free-space propagation, matched polarization and antenna gains applicable in the link direction. It omits cable losses, obstruction, multipath, atmosphere and interference. The sound analogy applies to an ideal point source in a free field, not arbitrary outdoor conditions. A positive modeled link margin does not establish a reliable deployment.
| RF Link Parameter | Cell | 2.4 GHz Point-to-Point Link | Decibel Result |
|---|---|---|---|
| Link Distance (d_km) | B2 | 5 km | 20*LOG10(5) = 13.98 dB |
| Carrier Frequency (f_MHz) | B3 | 2,400 MHz (2.4 GHz) | 20*LOG10(2400) = 67.60 dB |
| Tx Power & Gains (Pt, Gt, Gr) | B4:B6 | 20 dBm + 6 dBi + 6 dBi | 26 dBm EIRP; 32 dBm before path loss including Rx gain |
| FSPL & Friis Rx Power | LOG10 Formula | FSPL = 114.02 dB | Pr = -82.02 dBm | 10 km doubles distance -> 120.04 dB |
ITU Free-Space Path Loss FSPL(dB) for km and MHz
If distance is entered in meters and frequency in GHz, the constant is 32.44 - 60 + 60 = 32.44 (identical!).
=IF(OR(COUNT(B2:B3)<>2,B2<=0,B3<=0),"Invalid inputs",ROUND(20 * LOG10(B2) + 20 * LOG10(B3) + 32.44, 2))Friis Received Power Pr (dBm) = Pt + Gt + Gr - FSPL
Subtract receiver sensitivity from modeled received power for a nominal link margin. Real design also needs required reliability, receiver bandwidth/modulation and additional losses. Use distance in km and frequency in MHz for this worksheet.
=IF(OR(COUNT(B2:B6)<>5,B2<=0,B3<=0),"Invalid inputs",ROUND(B4 + B5 + B6 - (20 * LOG10(B2) + 20 * LOG10(B3) + 32.44), 2))Try the example
Use the original values or change them to test your understanding.