Comment calculer le bilan de liaison RF formule Friis

Calculez bilan liaison RF formule Friis Pr=Pt+Gt+Gr-FSPL-L. Free-space path loss FSPL=32,45+20*log(f_MHz)+20*log(d_km). Harald Friis Bell Labs 1946. WiFi 2,4 GHz, GSM, GPS L1 1575, 5G mmWave 28 GHz Orange SFR France.

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Comment calculer le bilan de liaison RF: derive de la formule Friis par Harald Friis (Danemark-USA 1893-1976) Bell Telephone Laboratories Murray Hill NJ publiee 1946. Formule en dB: Pr = Pt + Gt + Gr - FSPL - L_extra, ou Pr puissance recue (dBm), Pt puissance transmission (dBm), Gt gain antenne emettrice (dBi vs isotropic), Gr gain antenne receptrice (dBi), FSPL Free-Space Path Loss (dB), L_extra pertes additionnelles cables connecteurs atmosphere (dB). FSPL formule complete: 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. Exemples: WiFi 2,4 GHz a 100 m FSPL=80 dB, GSM 900 MHz a 5 km FSPL=105 dB, GPS L1 1575 MHz depuis satellite 20200 km FSPL=182 dB. Outil essentiel pour: design reseaux cellulaires 5G (Orange Paris SFR Free Bouygues Telecom France), planification site cells antenne, communication satellite GEO 36000 km Eutelsat Inmarsat Iridium Starlink LEO, GPS GNSS, drones UAV telemetrie 433/868 MHz, WiFi range IEEE 802.11, IoT LoRaWAN Sigfox NB-IoT, deep space NASA Voyager, automotive radar 24/77 GHz ADAS.

Formules bilan liaison Friis

Équation Friis (1946): Pr/Pt = Gt*Gr*(lambda/(4*pi*d))^2 linéaire. dB: Pr_dBm = Pt_dBm + Gt_dBi + Gr_dBi - FSPL_dB - L_extra_dB. FSPL pratique: FSPL_dB = 32,45 + 20*log10(f_MHz) + 20*log10(d_km).

Conversions unités: dBm puissance absolue 1 mW: 0 dBm=1 mW, 30 dBm=1 W. Conversion W a dBm: dBm=10*log10(W*1000). dB ratio: dB=10*log10(P2/P1).

Gain antenne dBi: dBi gain par rapport antenne isotropic. Typiques: dipole 2,15 dBi, patch antenne PCB 6-8 dBi, Yagi-Uda 8-15 dBi directionnel, parabole dish 30-50 dBi haute directivite. EIRP = Pt + Gt.

Longueur onde lambda: lambda = c/f, c=3e8 m/s. WiFi 2,4 GHz lambda=12,5 cm. GPS L1 1575 MHz lambda=19 cm. 5G 28 GHz lambda=1,07 cm.

Fade margin sensibilite: Fade margin = Pr - Sensitivity. Bon link >10 dB recommande. Sensibilite recepteur: WiFi -85 dBm, LTE -100 dBm, GPS -160 dBm. Marge 20-30 dB satellite professional, 10-15 dB cellular outdoor.

Histoire et contexte

Harald Trap Friis (Danemark-USA 1893-1976) ingenieur telecommunications Bell Telephone Laboratories Murray Hill New Jersey USA depuis 1919, publia 1946 "A Note on a Simple Transmission Formula" Proc IRE 34:254. James Clerk Maxwell (Ecosse 1831-1879) Cambridge unification electromagnetique 1865. Heinrich Hertz (Allemagne 1857-1894) Karlsruhe 1887-1888. Guglielmo Marconi (Italie 1874-1937) Bologna inventeur radio wireless 1895, Nobel Physique 1909, première transmission transatlantique 1901. Pioneer satellite: Sputnik USSR 4 octobre 1957, Telstar 1 AT&T NASA 10 juillet 1962. Industrie globale telecom: Verizon NY USA 5G UWB, AT&T Dallas, T-Mobile Bellevue, Vodafone UK Newbury, Orange Paris-Issy France, Deutsche Telekom Bonn. France telecom: Orange Paris-Issy France Telecom historique operateur principal national, SFR Numericable Paris (Altice), Bouygues Telecom Velizy, Free Iliad Paris-Levallois disruptive low-cost. Industrie francaise: Alcatel-Lucent Paris-Boulogne-Billancourt (Nokia 2016 acquisition) infrastructure 5G, Thales Paris-La Defense electronique embarquee defense, Naval Group Lorient Cherbourg defense. Equipementiers RF: Cisco San Jose CA leader, Juniper Sunnyvale CA, Nokia Espoo, Ericsson Stockholm, Marvell Santa Clara CA, Qualcomm San Diego CA chipsets.

Operateurs satellite: Intelsat McLean VA leader globale, SES Luxembourg, Eutelsat Paris France leader Europe historique francais, ViaSat Carlsbad CA USA, Inmarsat London UK maritime, Iridium McLean VA LEO 66 satellites global, Starlink SpaceX Boca Chica Texas LEO 12000+ satellites Elon Musk. ESA-CNES Kourou Guyane Francaise base lancement Ariane 6 Vega-C 5°N latitude. CNES Centre National Etudes Spatiales Toulouse Paris-La Defense agence spatiale francaise. Galileo ESA Toulouse France 30 satellites European GNSS. ONERA Office National Etudes Recherches Aerospatiales Chatillon Toulouse Modane recherche soufflerie aerospace. Industrie drones UAV: DJI Shenzhen Cina leader globale, Parrot Paris France quadcopter (première marque francaise drones grand public). Universites: ENSL Lyon ecole normale superieure, Telecom Paris Palaiseau ingenieurs telecom, Ecole Polytechnique Palaiseau, INSA Lyon, Centrale Lyon ECL, ENSTA ParisTech Palaiseau. France radio: Radio France Paris RFI France Inter, Free RTL Europe 1 NRJ NRJ Group Paris.

Tableau FSPL fréquences distances

  • FSPL pratique: 32,45 + 20*log10(f_MHz) + 20*log10(d_km) dB
  • WiFi 2,4 GHz a 10 m: FSPL=60 dB
  • WiFi 2,4 GHz a 100 m: FSPL=80 dB
  • WiFi 5 GHz a 100 m: FSPL=86 dB
  • GSM 900 MHz a 1 km: FSPL=92 dB
  • 5G NR 3,5 GHz a 1 km: FSPL=103 dB
  • 5G mmWave 28 GHz a 100 m: FSPL=101 dB
  • GPS L1 1575 MHz depuis GEO 20200 km: FSPL=182 dB
  • Iridium LEO 800 km a 1620 MHz: FSPL=155 dB
  • Starlink LEO 550 km a 14 GHz Ku-band: FSPL=170 dB
  • Inmarsat GEO 36000 km a 1,5 GHz: FSPL=187 dB
  • Antenne isotropic: 0 dBi référence
  • Dipole lambda/2: 2,15 dBi
  • Patch antenne PCB: 6-8 dBi
  • Yagi-Uda directionnel: 8-15 dBi
  • Parabole dish 1 m: 30-35 dBi @ 10 GHz
  • WiFi sensibilite: -85 dBm
  • LTE sensibilite: -100 dBm
  • GPS sensibilite: -160 dBm
  • Fade margin recommande: >10 dB outdoor, >20 dB satellite

Exemples numériques detailles

Exemple 1 - WiFi 2,4 GHz a 100 m routeur maison. Pt=20 dBm, Gt=3 dBi, Gr=3 dBi. FSPL=80,05 dB. Pr=-54,05 dBm. Fade margin=31 dB EXCELLENT. Application: bars restaurants aeroports WiFi public Paris Lyon Marseille <100 m portee.

Exemple 2 - 5G NR 3,5 GHz cellular 1 km. Pt=43 dBm, Gt=15 dBi MIMO. Smartphone Gr=0 dBi. FSPL=103,4 dB. Pr=-45,4 dBm. Fade margin 55 dB. Application: Orange France 3,5 GHz 5G NR rollout 2020+, SFR Free Bouygues Telecom mid-band.

Exemple 3 - GPS L1 1575 MHz depuis satellite 20200 km. Pt=47 dBm, Gt=13 dBi. Smartphone Gr=3 dBi. FSPL=182,5 dB. Pr=-119,5 dBm. Application: Galileo ESA Toulouse 30 satellites European GNSS, Garmin Trimble importations France.

Exemple 4 - Drone DJI 433 MHz 10 km. Pt=30 dBm, Gt=5 dBi, Gr=5 dBi. FSPL=105,2 dB. Pr=-65,2 dBm. Fade margin 45 dB. Application: Parrot Paris France quadcopter première marque francaise, EU EASA categorie C0-C6 2024.

Exemple 5 - Satcom uplink Ku-band 14 GHz GEO 36000 km. Pt=50 dBm, Gt=40 dBi parabole 1,2 m. Satellite Gr=35 dBi. FSPL=206,5 dB. Pr=-81,5 dBm. Application: Eutelsat Paris France leader Europe historique satelite, CNES Toulouse agence spatiale francaise.

Limites et considerations

  1. Friis seulement free-space line-of-sight (LOS). Indoor multi-path NLOS Rayleigh.
  2. FSPL suppose isotropic radiation: réelles antennes non-isotropic.
  3. Atmospheric absorption: O2 60 GHz, H2O 22 GHz, pluie 12 GHz.
  4. Diffraction edge mountains buildings: Knife-edge model.
  5. Multipath fading Rayleigh Rician: deviation ±10-20 dB.
  6. Polarization mismatch: cross-polarization 20-30 dB loss.
  7. EIRP regulatoire: WiFi 2,4 GHz <20 dBm UE FCC.
  8. Doppler shift fast moving cars airplanes satellite.
  9. Cochannel interference thermal noise floor.
  10. Earth curvature radio horizon 30-50 km.

Erreurs courantes

  1. Confondre dB avec dBm.
  2. FSPL formule erronee.
  3. Negliger sensibilite recepteur.
  4. Confondre dBi avec dBd antenne gain.
  5. Pretendre Friis NLOS.
  6. Negliger rain fade Ka-band 30 GHz.
  7. lambda erronee: lambda=c/f.
  8. EIRP illimite: WiFi 2,4 GHz <20 dBm.
  9. Confondre Pt avec EIRP=Pt+Gt.
  10. Negliger cable connector losses 1-3 dB.

Applications numerotees

  1. Reseaux cellulaires 5G France: Orange Paris-Issy historique, SFR Numericable, Bouygues Telecom Velizy, Free Iliad disruptive.
  2. WiFi planning: Cisco USA, Aruba HPE, Ubiquiti UniFi importations France distribution.
  3. Satellite GEO LEO: Eutelsat Paris France leader Europe historique, Intelsat Iridium Starlink importations.
  4. GPS GNSS: Galileo ESA Toulouse 30 satellites European GNSS, Garmin Trimble importations France.
  5. Drones UAV: Parrot Paris France première marque francaise quadcopter, DJI Shenzhen importation France.
  6. France telecom infrastructure: Alcatel-Lucent Paris-Boulogne-Billancourt (Nokia 2016), Thales Paris-La Defense.
  7. Antenna manufacturers: Commscope USA leader, RFS Nokia Meriden CT, Andrew Wireless importations France.
  8. Radio amateur: REF Reseau Emetteurs Francais 11000+ licencies France, ARRL USA, RSGB UK communaute.
  9. Radioastronomie: Observatoire Nancay Cher 95 m antenna, IRAM Plateau Bure Hautes-Alpes 30 m, Effelsberg 100 m Allemagne.
  10. Educational: Telecom Paris Palaiseau, Centrale Lyon ECL, INSA Lyon, Polytechnique Palaiseau cours RF.

Support

Pour questions techniques: info@calcoi.com. Outil didactique telecommunications RF preliminaire. Pour ingenierie professionnelle Friis HT 1946, Balanis CA 'Antenna Theory' 2016 Wiley, Pozar DM 'Microwave Engineering' 2011, ITU-R P.525.

Mis à jour en juillet 2026

Questions fréquentes

Que mesure le bilan de liaison Friis?

Bilan de liaison RF (Harald Friis Bell Labs 1946) mesure puissance recue Pr fonction puissance Pt, antennes Gt Gr, distance d. Formule dB: Pr = Pt + Gt + Gr - FSPL - L_extra. FSPL Free-Space Path Loss = 32,45 + 20*log10(f_MHz) + 20*log10(d_km) dB. Exemples: WiFi 2,4 GHz a 100 m FSPL=80 dB, GSM 900 MHz a 5 km FSPL=105 dB, GPS satellite 20200 km FSPL=182 dB. Applications: design reseaux cellulaires 5G Orange Paris-Issy SFR Free Bouygues Telecom France, satellite Eutelsat Paris leader Europe, GPS Galileo ESA Toulouse, drones Parrot Paris France.

Qu'est-ce que dBm vs dB vs dBi?

dBm: puissance absolue 1 mW. 0 dBm=1 mW, 30 dBm=1 W. dB: ratio adimensionnel puissances. dB=10*log10(P2/P1). dBi: gain antenne référence antenne isotropic ideale. dBd: référence dipole lambda/2. dBi=dBd+2,15. Patch antenne 6-8 dBi typique. Parabole 30-50 dBi. EIRP=Pt+Gt.

Comment fonctionne FSPL?

FSPL = 20*log10(4*pi*d/lambda) dB ideal vide isotropic propagation. Pratique: FSPL = 32,45 + 20*log10(f_MHz) + 20*log10(d_km). Double distance -> +6 dB FSPL. Double fréquence -> +6 dB FSPL. Exemple: WiFi 5 GHz pire 6 dB vs 2,4 GHz. ITU-R P.525 standard international propagation free-space. NE inclut PAS atmospheric absorption, multipath, diffraction.

Comment calcule-t-on sensibilite recepteur?

Sensibilite Pr_min = -174 dBm/Hz (thermal noise floor 290 K) + 10*log10(BW_Hz) + NF_dB + SNR_min_dB. WiFi 802.11n 20 MHz: -81 dBm. LTE 20 MHz NF=8 SNR=-7: -100 dBm. GPS 2 MHz NF=2 SNR=-30: -139 dBm spec, -160 dBm sky-derived. Boltzmann thermal noise fondamental. France: LNE Laboratoire National Essais Paris référence calibration.

Que affecte fade margin?

Fade margin = Pr - Sensitivity. Bon link >10 dB outdoor, >20 dB satellite professional. Variables: 1) rain fade Ka-band 30 GHz 5-15 dB pluie heavy; 2) atmospheric absorption O2 60 GHz; 3) multipath fading Rayleigh ±20 dB; 4) Doppler shift LEO ±50 kHz; 5) cable connector losses 1-3 dB; 6) polarization mismatch 20-30 dB; 7) cochannel adjacent interference. France: Orange SFR Free Bouygues Telecom 5G design fade margin 15-20 dB.

Difference Friis cellular vs satellite?

Cellular terrestre: distances 0,1-30 km, fréquences 700 MHz-39 GHz, FSPL 60-130 dB. Multipath dominante NLOS urban suburban. Modèles Hata Cost-231 Okumura account building loss. Satellite: distances 500-36000 km LEO/MEO/GEO, fréquences 1-40 GHz, FSPL 150-220 dB enorme. Compenser high gain antennas 30-50 dBi parabolic dishes. France: Eutelsat Paris leader Europe satellite, ESA-CNES Kourou Guyane base lancement Ariane 6 Vega-C 5°N latitude optimum equatorial.

Limites regulatoires EIRP cellular WiFi?

WiFi 2,4 GHz EIRP <20 dBm UE FCC ETSI EN 300 328 (100 mW max). WiFi 5 GHz <23 dBm UE 5,15-5,35 GHz indoor, <30 dBm 5,47-5,725 outdoor. WiFi 6 GHz -1 dBm/MHz LPI. GSM 900 <58 dBm EIRP, GSM 1800 <55 dBm. 5G mmWave 28 GHz beam-formed EIRP <75 dBm. France: ARCEP Autorite Regulation Communications Electroniques Postes Paris regulation telecom, ANFR Agence Nationale Fréquences Maisons-Alfort attribution. ITU-R Geneva, ETSI Sophia Antipolis France standards.

Formule

Pr/Pt = Gt*Gr*(lambda/(4*pi*d))^2
Pr_dBm = Pt_dBm + Gt_dBi + Gr_dBi - FSPL_dB - L_extra_dB
FSPL_dB = 32.45 + 20*log10(f_MHz) + 20*log10(d_km)
FSPL_dB = 20*log10(4*pi*d/lambda)
EIRP_dBm = Pt_dBm + Gt_dBi - effective isotropic radiated power
Fade margin = Pr - Sensitivity; recommended >10 dB outdoor, >20 dB satellite
lambda = c/f; c=2.998e8 m/s
isotropic 0 dBi, dipole 2.15 dBi, patch 6-8 dBi, Yagi 8-15 dBi, dish 30-50 dBi
WiFi 2.4 GHz 100m=80dB, GSM 900 MHz 5km=105dB, GPS 1575 MHz 20200km=182dB, GEO 36000 km=187dB
WiFi 2.4 GHz EIRP <20 dBm EU FCC, GSM 900 base <58 dBm, 5G mmWave 28 GHz <75 dBm beam
Friis HT 1946 'A Note on a Simple Transmission Formula' Proceedings IRE 34:254; Balanis CA 2016 'Antenna Theory' 4th ed Wiley; Pozar DM 2011 'Microwave Engineering' 4th ed Wiley; Rappaport TS 2002 'Wireless Communications' 2nd ed Prentice Hall; ITU-R P.525 free-space propagation recommendation

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