How to compute the RF link budget: derived from Friis formula by Harald Friis (Denmark-USA 1893-1976) Bell Telephone Laboratories Murray Hill NJ published 1946 "A Note on a Simple Transmission Formula" Proceedings IRE 34:254. Formula in dB: Pr = Pt + Gt + Gr - FSPL - L_extra, where Pr received power (dBm), Pt transmit power (dBm), Gt transmit antenna gain (dBi vs isotropic), Gr receive antenna gain (dBi), FSPL Free-Space Path Loss (dB), L_extra additional cable connector atmosphere losses (dB). FSPL complete formula: FSPL = 20*log10(4*pi*d/lambda) = 32.45 + 20*log10(f_MHz) + 20*log10(d_km) dB. EIRP=Pt+Gt Effective Isotropic Radiated Power. Examples: WiFi 2.4 GHz at 100 m FSPL=80 dB, GSM 900 MHz at 5 km FSPL=105 dB, GPS L1 1575 MHz from satellite 20200 km FSPL=182 dB. Essential tool for: cellular network design GSM 4G LTE 5G NR (Verizon AT&T T-Mobile USA leaders, Vodafone Orange Deutsche Telekom Europe), site planning antenna location coverage, satellite communication GEO 36000 km Inmarsat Iridium Starlink LEO, GPS GNSS positioning Trimble Garmin, drone UAV telemetry control 433/868 MHz Long Range, WiFi range planning IEEE 802.11 ax/be Wi-Fi 6/7, IoT LoRaWAN Sigfox NB-IoT, Starlink Lightspeed OneWeb LEO constellations 550-1200 km, deep space NASA Voyager Pioneer, automotive radar 24/77 GHz ADAS, military tactical radio AN/PRC-117G Harris L3.

Friis link budget formulas

Friis equation (1946): Pr/Pt = Gt*Gr*(lambda/(4*pi*d))^2 in linear power. In dB: Pr_dBm = Pt_dBm + Gt_dBi + Gr_dBi - FSPL_dB - L_extra_dB. Free-Space Path Loss: FSPL = 20*log10(4*pi*d/lambda) = 20*log10(d) + 20*log10(f) - 147.55 dB (d in m, f in Hz). Practical form: FSPL_dB = 32.45 + 20*log10(f_MHz) + 20*log10(d_km).

Unit conversions: dBm absolute power referenced to 1 mW: 0 dBm=1 mW, 30 dBm=1 W, 60 dBm=1 kW. Conversion W to dBm: dBm=10*log10(W*1000). dB ratio: dB=10*log10(P2/P1). Example: 100 mW=20 dBm, double power=+3 dB, 10x power=+10 dB.

Antenna gain dBi: dBi gain relative to isotropic antenna (perfect spherical, theoretical reference). Typical: dipole 2.15 dBi (0 dBd vs dipole), patch antenna PCB 6-8 dBi, Yagi-Uda 8-15 dBi directional, parabolic dish 30-50 dBi high directivity. EIRP = Pt + Gt isotropic equivalent power. Regulatory limits: WiFi 2.4 GHz EIRP <20 dBm EU FCC, GSM 900 EIRP <33 dBm, satellite uplink ITU regulated unlimited.

Wavelength lambda: lambda = c/f, c=3e8 m/s vacuum. WiFi 2.4 GHz lambda=12.5 cm. GSM 900 MHz lambda=33 cm. FM 100 MHz lambda=3 m. GPS L1 1575 MHz lambda=19 cm. 5G 28 GHz lambda=1.07 cm. Antenna size scaling: dipole half-wave lambda/2: WiFi 6.25 cm, GSM 17 cm, FM radio 1.5 m. Patch antenna ~lambda/2 dimensions polarized patch elements 5G mmWave smartphone arrays.

Fade margin and sensitivity: Fade margin = Pr - Sensitivity. Good link >10 dB recommended weather rain fade. Typical receiver sensitivity: WiFi -85 dBm, LTE -100 dBm, GPS -160 dBm (sky-derived reduced). Margin 20-30 dB for satellite professional links, 10-15 dB cellular outdoor, 5-10 dB indoor weak signal. Rain fade Ka-band 30 GHz: 5-15 dB heavy rain.

History and context

Harald Trap Friis (Denmark-USA 1893-1976) telecommunications engineer Bell Telephone Laboratories Murray Hill New Jersey USA from 1919, published 1946 "A Note on a Simple Transmission Formula" Proceedings IRE 34:254 deriving simple relationship between received power and system parameters (power, antenna gains, frequency, distance). His other contributions: 1946 antenna effective area Aeff = (lambda^2)*(G/(4*pi)), 1944 noise figure standard receivers. James Clerk Maxwell (Scotland 1831-1879) Cambridge electromagnetic unification 1865 propagation theory foundation. Heinrich Hertz (Germany 1857-1894) Karlsruhe University 1887-1888 experimentally verified Maxwell radio waves. Guglielmo Marconi (Italy 1874-1937) Bologna inventor wireless radio 1895 Pontecchio Marconi, Nobel Physics 1909, first transatlantic transmission Cornwall-Newfoundland 1901. Karl Jansky (USA 1905-1950) Bell Labs 1932 discovered radio astronomy Milky Way emissions. Edward Murrow Bowen (Australia 1911-1991) Telecommunications Research Establishment UK 1942 microwave 10 GHz radar development. John Howard Dellinger (USA 1886-1962) NIST Bureau Standards 1928 ionosphere radio propagation. Pioneer satellite: Sputnik USSR October 4 1957 first satellite, Telstar 1 AT&T NASA July 10 1962 first telecommunications satellite Andover ME. Marconi RCA 1965 Comsat Early Bird Intelsat I first geostationary commercial 36000 km altitude GEO orbit.

USA telecom: Verizon Communications New York NY 5G UWB mmWave 28 GHz major US cities, AT&T Dallas TX 5G+, T-Mobile US Bellevue WA 5G UC Ultra Capacity, Comcast Xfinity Philadelphia PA cable. Equipment: Cisco Systems San Jose CA leader switches routers, Juniper Networks Sunnyvale CA, Arista Networks Santa Clara CA, Nokia Espoo Finland 5G infrastructure, Ericsson Stockholm Sweden leader, Marvell Santa Clara CA, Qualcomm San Diego CA chipsets. Antenna manufacturers: Commscope Hickory NC USA leader, RFS Radio Frequency Systems Meriden CT USA Nokia subsidiary, Andrew Wireless Buffalo Grove IL Commscope acquisition 2007, Galtronics Tempe AZ. Satellite operators USA: Intelsat McLean VA leader globally (Telstar Galaxy fleet), SES Luxembourg, ViaSat Carlsbad CA, Inmarsat London UK maritime aviation, Iridium McLean VA LEO 66 satellites global, Starlink SpaceX Boca Chica Texas LEO 12000+ satellites Elon Musk, OneWeb London UK LEO constellation 648 satellites. GPS: USAF GPS Operations Center Schriever SFB CO USA constellation 31 satellites GPS Block IIIF newest. NASA Goddard Space Flight Center Greenbelt MD GPS missions. Drone industry: DJI Shenzhen China global leader Mavic Phantom (FAA registration USA, EU EASA C0-C6 categories), Parrot Paris France quadcopter, Skydio Redwood City CA autonomous drones, AeroVironment Arlington VA USA military Switchblade, Anduril Costa Mesa CA, Northrop Grumman Falls Church VA Global Hawk RQ-4.

NSF FCC Federal Communications Commission Washington DC USA spectrum management auctions, ITU-R Geneva Switzerland International Telecommunications Union international coordination. American Radio Relay League ARRL Newington CT USA radio amateur community 700000+ licensed. Universities: MIT 6.013 Electromagnetic Fields & Energy Cambridge MA, Stanford EE142 Optoelectronic Devices, Caltech EE150 Optoelectronics, UC Berkeley EE117 Antennas, Georgia Tech ECE Atlanta, University of Michigan EECS Ann Arbor radio astronomy. NASA JPL Pasadena CA Deep Space Network DSN 70 m antennas Goldstone CA Madrid Spain Canberra Australia.

FSPL frequency and distance table

• FSPL practical formula: 32.45 + 20*log10(f_MHz) + 20*log10(d_km) dB
• WiFi 2.4 GHz at 10 m: FSPL=60 dB
• WiFi 2.4 GHz at 100 m: FSPL=80 dB
• WiFi 2.4 GHz at 1 km: FSPL=100 dB
• WiFi 5 GHz at 100 m: FSPL=86 dB
• WiFi 6 GHz at 100 m: FSPL=88 dB
• GSM 900 MHz at 1 km: FSPL=92 dB
• GSM 1800 MHz at 1 km: FSPL=98 dB
• 5G NR 3.5 GHz at 1 km: FSPL=103 dB
• 5G mmWave 28 GHz at 100 m: FSPL=101 dB
• FM 100 MHz at 50 km: FSPL=106 dB
• GPS L1 1575 MHz from GEO 20200 km: FSPL=182 dB
• Iridium LEO 800 km at 1620 MHz: FSPL=155 dB
• Starlink LEO 550 km at 14 GHz Ku-band: FSPL=170 dB
• Inmarsat GEO 36000 km at 1.5 GHz: FSPL=187 dB
• Voyager 1 deep space 25 ly: FSPL=270+ dB
• Isotropic antenna gain: 0 dBi reference theoretical
• Half-wave dipole: 2.15 dBi
• PCB patch antenna: 6-8 dBi
• Yagi-Uda directional: 8-15 dBi
• Parabolic dish 1 m: 30-35 dBi @ 10 GHz
• Parabolic dish 70 m DSN NASA: 73 dBi @ X-band Goldstone Madrid Canberra
• WiFi sensitivity: -85 dBm (Pr minimum decoding)
• LTE sensitivity: -100 dBm
• GPS sensitivity: -160 dBm sky-derived
• Iridium handheld: -120 dBm
• Recommended fade margin: >10 dB outdoor, >20 dB satellite professional

Detailed numerical examples

Example 1 - WiFi 2.4 GHz at 100 m home router. Standard WiFi router Cisco Linksys: Pt=20 dBm (100 mW), Gt=3 dBi (omni antenna). Apple Galaxy smartphone Gr=3 dBi receiver. Frequency f=2.4 GHz, d=100 m=0.1 km. FSPL=32.45+20*log10(2400)+20*log10(0.1)=32.45+67.6+(-20)=80.05 dB. Pr=20+3+3-80.05=-54.05 dBm. WiFi sensitivity -85 dBm: fade margin=85-54=31 dB EXCELLENT (>20 dB). Practical test: bars restaurants airports public WiFi <100 m range USA Starbucks airports.

Example 2 - 5G NR 3.5 GHz cellular base station 1 km. Nokia Ericsson base station Pt=43 dBm (20 W) eNodeB, Gt=15 dBi MIMO 4x4 antenna array sector. Smartphone receiver Gr=0 dBi internal omni. f=3.5 GHz, d=1 km. FSPL=32.45+20*log10(3500)+20*log10(1)=32.45+70.9+0=103.4 dB. Pr=43+15+0-103.4=-45.4 dBm. LTE sensitivity -100 dBm: fade margin=100-45=55 dB GOOD. USA: Verizon NY 5G C-band 3.7-3.98 GHz mid-band rollout 2022+, AT&T 3.45-3.55 GHz, T-Mobile 2.5 GHz mid-band leader US.

Example 3 - GPS L1 1575 MHz from satellite 20200 km. GPS Block IIIF SVN 76 USAF satellite: Pt=50 W=47 dBm, Gt=13 dBi (earth coverage antenna pattern). Smartphone GPS receiver Gr=3 dBi (internal patch). f=1575 MHz, d=20200 km (semi-synchronous GPS orbit). FSPL=32.45+20*log10(1575)+20*log10(20200)=32.45+63.9+86.1=182.5 dB. Pr=47+13+3-182.5=-119.5 dBm. GPS receiver sensitivity -160 dBm sky-derived (extreme): fade margin 40 dB. USA: Trimble Sunnyvale CA, Garmin Olathe KS GPS receivers professional cm-level RTK.

Example 4 - DJI 433 MHz LR drone control 10 km. DJI Mavic 3 Long Range drone telemetry control: Pt=30 dBm (1 W) 433 MHz module, Gt=5 dBi remote controller. Drone receiver Gr=5 dBi. d=10 km. FSPL=32.45+20*log10(433)+20*log10(10)=32.45+52.7+20=105.2 dB. Pr=30+5+5-105.2=-65.2 dBm. Drone LR sensitivity -110 dBm: fade margin 45 dB. Application: drone delivery Amazon Prime Air, drones cinematographic Red Cinema, FAA rules USA Part 107 commercial 122 m max altitude, EU EASA categories C0-C6 2024.

Example 5 - Satcom uplink Ku-band 14 GHz GEO 36000 km. Eutelsat satellite GEO: Pt=50 dBm (100 W), Gt=40 dBi 1.2 m parabola uplink terminal. Satellite receiver Gr=35 dBi (HPA medium gain). f=14 GHz Ku-band uplink, d=36000 km GEO altitude. FSPL=32.45+20*log10(14000)+20*log10(36000)=32.45+82.9+91.1=206.5 dB. Pr=50+40+35-206.5=-81.5 dBm. Strong nominal signal. USA: Intelsat McLean VA leader globally, SES Luxembourg, ViaSat Carlsbad CA broadband, Hughes Network Systems Germantown MD. NASA Goldstone DSN 70 m antennas California 73 dBi gain.

Limits and considerations

1. Friis formula valid only for free-space line-of-sight (LOS) propagation. Indoor multi-path NLOS Non-Line-of-Sight requires Rayleigh fading models.
2. FSPL assumes isotropic radiation pattern: real antennas non-isotropic patterns, gain depends direction (azimuth elevation).
3. Atmospheric absorption: O2 60 GHz 16 dB/km, H2O 22 GHz 0.18 dB/km, rain 12 GHz 0.3-3 dB/km. Critical mmWave 5G satellite Ka-band.
4. Diffraction edge mountains buildings: Knife-edge diffraction model additional loss 6-30 dB.
5. Multipath fading Rayleigh Rician: deviation from Friis ±10-20 dB indoor outdoor low-elevation.
6. Polarization mismatch: cross-polarization 20-30 dB loss.
7. EIRP regulatory: WiFi 2.4 GHz EIRP <20 dBm EU FCC, GSM 900 limit, satellite uplink ITU regulated.
8. Doppler shift: fast moving (cars airplanes satellite LEO): frequency offset ±5-50 kHz.
9. Cochannel adjacent interference: thermal noise floor -174 dBm/Hz +NF receiver typical noise figure 5-10 dB.
10. Earth curvature radio horizon: d=4.12*sqrt(h_t)+4.12*sqrt(h_r) km. Limit terrestrial radio 30-50 km typical.

Common errors

1. Confusing dB with dBm: dBm absolute power (1 mW=0 dBm), dB dimensionless ratio.
2. Computing wrong FSPL formula: 32.45 + 20*log10(f_MHz) + 20*log10(d_km) standard practical.
3. Neglecting receiver sensitivity: link works only if Pr > Sensitivity with margin 10+ dB.
4. Confusing dBi with dBd antenna gain: dBi vs isotropic, dBd vs dipole, dBi=dBd+2.15.
5. Assuming Friis formula NLOS: Multipath Rayleigh fading deviates ±20 dB.
6. Neglecting rain fade Ka-band 30 GHz: 5-15 dB heavy rain.
7. Computing wrong lambda: lambda=c/f, c=3e8 m/s.
8. Assuming unlimited EIRP: WiFi 2.4 GHz <20 dBm EU FCC regulated.
9. Confusing transmit power Pt with EIRP=Pt+Gt: EIRP includes antenna gain.
10. Neglecting cable connector losses: typically 1-3 dB additive loss.

Numbered applications

1. 5G cellular networks USA: Verizon NY UWB mmWave, AT&T Dallas 5G+, T-Mobile Bellevue WA 5G UC, Comcast Xfinity.
2. WiFi planning: Cisco San Jose CA, Aruba HPE Santa Clara CA, Ruckus CommScope Sunnyvale, Ubiquiti New York NY UniFi.
3. GEO LEO satellites: Intelsat McLean VA, SES Luxembourg, ViaSat Carlsbad CA, Iridium McLean VA, Starlink SpaceX Boca Chica TX.
4. GPS GNSS: Trimble Sunnyvale CA, Garmin Olathe KS, USAF GPS Block IIIF Schriever SFB CO, Galileo ESA 30 satellites.
5. UAV drones: DJI Shenzhen leader, Skydio Redwood City CA autonomous, AeroVironment Arlington VA Switchblade military.
6. USA telecom infrastructure: Verizon Communications NY, AT&T Dallas, T-Mobile Bellevue WA, Comcast Philadelphia PA cable.
7. Antenna manufacturers: Commscope Hickory NC USA leader, RFS Nokia Meriden CT, Andrew Wireless Buffalo Grove IL.
8. Amateur radio: ARRL American Radio Relay League Newington CT USA 700000+ licensed, RSGB UK, IARU global.
9. Radio astronomy: NRAO National Radio Astronomy Observatory Charlottesville VA, JPL DSN Goldstone Madrid Canberra, MIT Haystack Observatory MA.
10. Educational teaching: MIT 6.013 EM Fields, Stanford EE142, Caltech EE150, UC Berkeley EE117, Georgia Tech ECE Atlanta.

Support

For technical questions or reports: info@calcoi.com. Educational tool for preliminary RF telecommunications. For professional engineering Friis HT 1946 'A Note on a Simple Transmission Formula' Proc IRE 34:254, Balanis CA 'Antenna Theory' 2016 Wiley, Pozar DM 'Microwave Engineering' 2011 Wiley, Rappaport TS 'Wireless Communications Principles and Practice' 2002 Prentice Hall, ITU-R P.525 free-space propagation recommendation.

Updated July 2026