Come calcolare il link budget RF: derivato dalla formula di Harald Friis (Danimarca-USA 1893-1976) Bell Telephone Laboratories Murray Hill NJ pubblicata 1946 "A Note on a Simple Transmission Formula" Proceedings IRE 34:254. Formula in dB: Pr = Pt + Gt + Gr - FSPL - L_extra, dove Pr potenza ricevuta (dBm), Pt potenza trasmissione (dBm), Gt guadagno antenna trasmittente (dBi rispetto isotropic), Gr guadagno antenna ricevente (dBi), FSPL Free-Space Path Loss (dB), L_extra perdite addizionali cavi connettori atmosfera (dB). FSPL formula completa: 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. Esempi: WiFi 2,4 GHz a 100 m FSPL=80 dB, GSM 900 MHz a 5 km FSPL=105 dB, GPS L1 1575 MHz da satellite 20200 km FSPL=182 dB. Strumento essenziale per: progettazione cellular networks GSM 4G LTE 5G NR (Verizon AT&T T-Mobile Vodafone TIM Orange Deutsche Telekom), pianificazione site cells antenna location coverage planning, satellite communication GEO 36000 km Inmarsat Iridium Starlink LEO, GPS GNSS positioning Trimble Garmin, droni 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, satellitare Starlink Lightspeed OneWeb LEO constellations 550-1200 km, deep space NASA Voyager Pioneer, automotive radar 24/77 GHz advanced driver assistance systems ADAS, military tactical radio AN/PRC-117G Harris L3.

Formule link budget Friis

Equazione Friis (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). Forma pratica: FSPL_dB = 32,45 + 20*log10(f_MHz) + 20*log10(d_km).

Conversioni unita: dBm potenza assoluta riferita 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). Esempio: 100 mW=20 dBm, doppio potenza=+3 dB, 10x potenza=+10 dB.

Antenna gain dBi: dBi guadagno rispetto antenna isotropic (sferica perfetta, theoretical reference). Tipici: dipolo 2,15 dBi (0 dBd vs dipolo), patch antenna PCB 6-8 dBi, Yagi-Uda 8-15 dBi direzionale, parabola dish 30-50 dBi alta direttivita. EIRP = Pt + Gt potenza isotropica equivalente. Limiti regolatori: WiFi 2,4 GHz EIRP <20 dBm EU FCC, GSM 900 EIRP <33 dBm, satellite uplink illimitato regolamentato ITU.

Lunghezza d'onda 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 per polarized patch elementi 5G mmWave smartphone.

Fade margin e sensibilità: Fade margin = Pr - Sensitivity. Buon link >10 dB raccomandato weather rain fade. Sensibilità ricevitore tipica: WiFi -85 dBm, LTE -100 dBm, GPS -160 dBm (sky-derived ridotta). Margine 20-30 dB per link satellitare professional, 10-15 dB cellular outdoor, 5-10 dB indoor weak signal. Rain fade Ka-band 30 GHz: 5-15 dB heavy rain.

Storia e contesto

Harald Trap Friis (Danimarca-USA 1893-1976) ingegnere telecomunicazioni Bell Telephone Laboratories Murray Hill New Jersey USA dal 1919, pubblico' 1946 "A Note on a Simple Transmission Formula" Proceedings IRE 34:254 derivando relazione semplice tra potenza ricevuta e parametri sistema (potenza, guadagni antenne, frequenza, distanza). Sue altre contribuzioni: 1946 antenna effective area Aeff = (lambda^2)*(G/(4*pi)), 1944 noise figure standard receivers. James Clerk Maxwell (Scozia 1831-1879) Cambridge unificazione elettromagnetica 1865 base teoria propagazione. Heinrich Hertz (Germania 1857-1894) Karlsruhe University 1887-1888 verifico sperimentalmente onde radio Maxwell. Guglielmo Marconi (Italia 1874-1937) Bologna inventore radio wireless 1895 Pontecchio Marconi, Nobel Fisica 1909, prima trasmissione transatlantica Cornwall-Newfoundland 1901. Karl Jansky (USA 1905-1950) Bell Labs 1932 scopri radio astronomy emissioni Via Lattea. Edward Murrow Bowen (Australia 1911-1991) Telecommunications Research Establishment UK 1942 sviluppo radar microwave 10 GHz. John Howard Dellinger (USA 1886-1962) NIST Bureau Standards 1928 ionosfera radio propagation. Pioneer satellite: Sputnik USSR 4 ottobre 1957 primo satellite, Telstar 1 AT&T NASA 10 luglio 1962 primo telecomunicazioni satellite Andover ME. Marconi RCA 1965 Comsat Early Bird Intelsat I primo geostationary commercial 36000 km altitude GEO orbit.

Industria globale 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, Vodafone Group Newbury UK Europe leader, Orange Paris-Issy France, Deutsche Telekom Bonn Germany, China Mobile Beijing leader globale subscribers. Italia: TIM Telecom Italia Roma operatore principale, Iliad Milano sfidante low-cost, Open Fiber Roma wholesale FTTH, Vodafone Italia Ivrea, WindTre Pomezia Roma. Equipaggiamento RF: Cisco Systems San Jose CA leader switches routers, Juniper Networks Sunnyvale CA, Arista Networks Santa Clara CA, Nokia Espoo Finlandia 5G infrastructure, Ericsson Stoccolma Svezia leader, Huawei Shenzhen Cina (USA sanctions 2019 disabilities), ZTE Shenzhen Cina. Antenna manufacturer: Commscope Hickory NC USA leader, Kathrein Stuttgart Germania historic (acquired Ericsson 2019), RFS Radio Frequency Systems Meriden CT USA filiale Nokia, Andrew Wireless Buffalo Grove IL (Commscope acquisition 2007). Satellite operators: Intelsat McLean VA USA leader globale (Telstar Galaxy fleet), SES Luxembourg, Eutelsat Paris France leader Europe, ViaSat Carlsbad CA USA, Inmarsat London UK maritime aviation, Iridium McLean VA USA LEO 66 satellites global, OneWeb London UK LEO constellation 648 satellites, Starlink SpaceX Boca Chica Texas LEO 12000+ satellites Elon Musk. GPS: USAF GPS Operations Center Schriever SFB CO USA constellation 31 satellites GPS Block IIIF newest.

Galileo ESA Toulouse France 30 satellites European GNSS. GLONASS Russian, BeiDou Chinese, QZSS Japanese regional. Industria droni UAV: DJI Shenzhen Cina leader globale 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. Italia ricerca telecom: Politecnico Milano DEIB DIEEE radio communications, Politecnico Torino DET, Sapienza Roma DIET, INFN Frascati Roma esperimenti acceleratori. INAF telescopi radioastronomici Sardinia Radio Telescope SRT Pranu Sanguni 64 m, Croce del Nord Medicina Bologna Northern Cross. ASI Agenzia Spaziale Italiana Roma collaborazioni ESA Vega Ariane satelliti. ESA Villafranca Madrid Spagna ESAC Centro Operazioni Europee. Universita: MIT 6.013 Electromagnetic Fields & Energy Cambridge MA, Stanford EE142 Optoelectronic Devices, Caltech EE150 Optoelectronics, UC Berkeley EE117 Antennas. Federal Communications Commission FCC Washington DC USA spectrum management, ITU-R Geneva Switzerland International Telecommunications Union international coordination.

Tabella FSPL frequenze e distanze tipiche

• FSPL formula pratica: 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 2,4 GHz a 1 km: FSPL=100 dB
• WiFi 5 GHz a 100 m: FSPL=86 dB
• WiFi 6 GHz a 100 m: FSPL=88 dB
• GSM 900 MHz a 1 km: FSPL=92 dB
• GSM 1800 MHz a 1 km: FSPL=98 dB
• 5G NR 3,5 GHz a 1 km: FSPL=103 dB
• 5G mmWave 28 GHz a 100 m: FSPL=101 dB
• FM 100 MHz a 50 km: FSPL=106 dB
• GPS L1 1575 MHz da 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
• Voyager 1 deep space 25 ly: FSPL=270+ dB
• Antenna isotropic gain: 0 dBi reference theoretical
• Dipolo lambda/2: 2,15 dBi
• Patch antenna PCB: 6-8 dBi
• Yagi-Uda direzionale: 8-15 dBi
• Parabola dish 1 m: 30-35 dBi @ 10 GHz
• Parabola dish 10 m DSN NASA: 60-65 dBi @ X-band
• WiFi sensibilità: -85 dBm (Pr minimo decoding)
• LTE sensibilità: -100 dBm
• GPS sensibilità: -160 dBm sky-derived
• Iridium handheld: -120 dBm
• Fade margin raccomandato: >10 dB outdoor, >20 dB satellite professional

Esempi numerici dettagliati

Esempio 1 - WiFi 2,4 GHz a 100 m router casa. Router WiFi standard Cisco Linksys: Pt=20 dBm (100 mW), Gt=3 dBi (antenna omni). Smartphone Apple Galaxy ricevitore Gr=3 dBi. Frequenza 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. Sensibilità WiFi -85 dBm: fade margin=85-54=31 dB ECCELLENTE (>20 dB). Test pratico: bar ristoranti aeroporti WiFi pubblico <100 m raggio.

Esempio 2 - 5G NR 3,5 GHz cellular base station 1 km. Base station Nokia Ericsson Pt=43 dBm (20 W) eNodeB, Gt=15 dBi MIMO 4x4 antenna array sector. Smartphone receiver Gr=0 dBi omni internal. 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. Sensibilità LTE -100 dBm: fade margin=100-45=55 dB BUONO. Italia: TIM Roma 3,5 GHz 5G NR rollout 2020+, Vodafone Italia Ivrea, WindTre Pomezia Roma.

Esempio 3 - GPS L1 1575 MHz da satellite 20200 km. GPS satellite Block IIIF SVN 76 USAF: Pt=50 W=47 dBm, Gt=13 dBi (antenna pattern earth coverage). GPS receiver smartphone Gr=3 dBi (patch internal). f=1575 MHz, d=20200 km (semi-sincrono 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. Sensibilità GPS receiver -160 dBm sky-derived (estremo): fade margin 40 dB. Trimble Sunnyvale CA, Garmin Olathe KS GPS receivers professional cmlevel.

Esempio 4 - Drone DJI 433 MHz LR controllo 10 km. Telemetria controllo drone DJI Mavic 3 Long Range: Pt=30 dBm (1 W) modulo 433 MHz, 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. Sensibilità drone LR -110 dBm: fade margin 45 dB. Applicazione: drone delivery Amazon Prime Air, droni cinematografici Red Cinema, Italia normative ENAC 120 m max altezza, EU EASA categorie C0-C6 2024.

Esempio 5 - Satcom uplink Ku-band 14 GHz GEO 36000 km. Satellite Eutelsat Hot Bird 13E GEO: Pt=50 dBm (100 W), Gt=40 dBi antenna parabola 1,2 m terminale uplink. Satellite receiver Gr=35 dBi (medio gain HPA). 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 signal nominal. Italia: Eutelsat 5 West A-B-C orbit 5°W broadcast Hot Bird tv satellitare, Inmarsat Roma maritime aviation. ESA Villafranca Spagna ESAC operations center coordinating European fleet.

Limiti e considerazioni

1. Friis formula valida solo per propagazione free-space line-of-sight (LOS). Indoor multi-path NLOS Non-Line-of-Sight richiede Rayleigh fading models.
2. FSPL assume isotropic radiation pattern: real antennas patterns non isotropic, gain dipende direzione (azimut 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 addittional loss 6-30 dB.
5. Multipath fading Rayleigh Rician: deviation Friis ±10-20 dB indoor outdoor low-elevation.
6. Polarization mismatch: cross-polarization 20-30 dB loss.
7. EIRP regolatorio: WiFi 2,4 GHz EIRP <20 dBm EU FCC, GSM 900 limite, satellite uplink ITU regolamentato.
8. Doppler shift: fast moving (cars, airplanes, satellite LEO): frequency offset ±5-50 kHz.
9. Interference cochannel adjacent: 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 tipico.

Errori comuni

1. Confondere dB con dBm: dBm potenza assoluta (1 mW=0 dBm), dB rapporto adimensionale.
2. Calcolare FSPL formula errata: 32,45 + 20*log10(f_MHz) + 20*log10(d_km) standard pratico.
3. Trascurare sensitivity ricevitore: link funziona solo se Pr > Sensitivity con margine 10+ dB.
4. Confondere dBi con dBd antenna gain: dBi vs isotropic, dBd vs dipolo, dBi=dBd+2,15.
5. Pretendere Friis formula NLOS: Multipath Rayleigh fading deviates ±20 dB.
6. Trascurare rain fade Ka-band 30 GHz: 5-15 dB heavy rain.
7. Calcolare lambda errato: lambda=c/f, c=3e8 m/s.
8. Pretendere EIRP illimitato: WiFi 2,4 GHz <20 dBm UE FCC regolamentato.
9. Confondere transmit power Pt con EIRP=Pt+Gt: EIRP includes antenna gain.
10. Trascurare cable losses connector: tipicamente 1-3 dB additivo loss.

Applicazioni numerate

1. Cellular networks 5G: TIM Roma operatore principale, Vodafone Ivrea, WindTre Pomezia, Iliad Milano sfidante.
2. WiFi planning: Cisco San Jose CA, Aruba HPE Santa Clara CA, Ruckus CommScope Sunnyvale, Ubiquiti New York NY UniFi.
3. Satellite GEO LEO: Intelsat McLean VA, SES Luxembourg, Eutelsat Paris, ViaSat Carlsbad CA, Starlink SpaceX, Iridium McLean.
4. GPS GNSS: Trimble Sunnyvale CA, Garmin Olathe KS, USAF GPS Block IIIF, Galileo ESA Toulouse France 30 satellites.
5. Droni UAV: DJI Shenzhen leader, Parrot Paris France, Skydio Redwood City CA, AeroVironment Arlington VA Switchblade military.
6. Italia telecom infrastruttura: Open Fiber Roma wholesale FTTH, Politecnico Milano DEIB, Politecnico Torino DET corsi RF.
7. Antenna manufacturers: Commscope Hickory NC USA leader, Kathrein Ericsson Stuttgart, RFS Nokia Meriden CT, Andrew Wireless.
8. Radio amatoriale ham: ARI Associazione Radioamatori Italiani 30000+ licenze, ARRL American Radio Relay League USA, RSGB UK.
9. Radioastronomia: Sardinia Radio Telescope SRT INAF 64 m Cagliari, Croce del Nord Medicina Bologna Northern Cross, Effelsberg 100 m Germania.
10. Educational didattica: MIT 6.013, Stanford EE142, Caltech EE150, UC Berkeley EE117, Politecnico Milano DEIB Torino DET corsi.

Per supporto

Per domande tecniche o segnalazioni: info@calcoi.com. Strumento didattico telecomunicazioni RF preliminare. Per progettazione professionale 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.

Aggiornato a luglio 2026