Comment calculer cascaded noise figure Friis chaine RF

Calcule cascaded noise figure NF chaine RF formule Friis 1944: F = F1+(F2-1)/G1+(F3-1)/(G1*G2). LNA front-end dominant. NF 0.6-1.2 dB satellite Ku; 2-3 dB cellulaire; 6-9 dB BT. CNRS LERMA Paris + IRAM 30 m + Telecom Paris.

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Comment calculer le cascaded noise figure chaine RF (LNA, mixer, amplificateur IF, filtres): formule Friis 1944 IRE 32:419 'Noise Figures of Radio Receivers' Harald T. Friis Bell Labs Holmdel NJ. F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2) + .... F facteur de bruit linéaire (F = 10^(NF_dB/10)) et G gain linéaire (G = 10^(G_dB/10)). NF_total dB = 10*log10(F_total). Insight: premier stage (LNA) domine NF total; etapes successives attenuees par gain cumulatif. T_e = (F-1)*T_0 avec T_0=290 K. Classification: NF10 dB lossy passive. France recherche radio + telecommunications: CNRS Centre National Recherche Scientifique 1939 fonde 32000 employees + LERMA Laboratoire Etudes Rayonnement Matière Astrophysique Observatoire Paris Meudon 200 + IRAM Institut Radioastronomie Millimetrique Grenoble FR-DE-ES 30 m Pico Veleta + NOEMA Plateau de Bure Alpes 12 antennes 15 m millimetrique submillimetric; Telecom Paris Telecom ParisTech 1878 1500 students grande ecole RF + reseaux; Telecom SudParis Evry 1979; CentraleSupelec Gif Saclay 1829 4500 students; Polytechnique Palaiseau 1794; Sorbonne Universite Paris 1257;

Universite Paris-Saclay 2020; INSA Lyon 1957; Telecom Bretagne IMT Atlantique Brest 1977; ENSEA Cergy 1941; EURECOM Sophia Antipolis 1991. France CNES Centre National Etudes Spatiales Toulouse + Paris 1961 2400 employees agence spatiale satellites; CNRS LATMOS Latmos Atmospheres Milieux Observations Spatiales Guyancourt + LATMOS Paris radar; France industrie RF satellite: Thales Group Paris La Defense 1968 81000 employees defense electronics + RF + radar + Thales Alenia Space 50% Italian Leonardo + Thales Defence Mission Systems Toulouse + Brest + Limours; Airbus Defence Space France Toulouse 35000 satellites + cohetes Ariane 6 + Eurofighter; ArianeGroup Paris Issy 2017 8500 lanceurs Ariane 5/6 + missiles M51; Eutelsat Communications Paris 1977 1100 satellite operator GEO Hot Bird Eutelsat 13 E + Eutelsat 9B; Orange SA Paris 1988 137000 telecom + Orange Espana + UK + Africa; Free Iliad Paris 1999 18000 disruptor low-cost mobile fixed; Bouygues Telecom Paris 1996 9000 mobile + fixed; SFR Numericable Paris 1987 16000 mobile + cable; SES Astra Luxembourg + France distribution. France operateurs telecom: Orange SA Paris 137000 dominant 35% mobile + 50% fixe FTTH; SFR Numericable 16000 25% mobile + 50% cable broadband;

Bouygues Telecom 9000 22% mobile; Free Iliad 18000 17% mobile + 25% fixe FTTH disruptor 2002 fondateur Xavier Niel. France 5G spectrum: ARCEP Autorite Regulation Communications Electroniques Postes Distribution Presse Paris 1996 200 employees regulator; ANFR Agence Nationale Fréquences Maisons Alfort 250 employees national frequency; CSA Conseil Supérieur Audiovisuel + Arcom 2022 fusion. 5G auctions: 700 MHz 2015 EUR 2.8 billion; 3.5 GHz 2020 EUR 2.8 billion; 26 GHz mmWave 2023 EUR 200 million 4 operators Orange Free SFR Bouygues. France microondes + radar: bandes RF L-band 1-2 GHz GPS Galileo + ECTS European Train Control System; S-band 2-4 GHz WiFi 2.4 GHz BT; C-band 4-8 GHz satellite SAR Sentinel-1 ESA Copernicus 5.4 GHz; X-band 8-12 GHz radar military Thales Group + Meteo France 32 radares meteorologiques + ATC controle traffic aerien DGAC; Ku-band 12-18 GHz Hot Bird Eutelsat 13 E + Astra 19.2 E TV digital; Ka-band 26-40 GHz Eutelsat KA-SAT + 5G mmWave; V-band 40-75 GHz emerging 6G CNRS LERMA + Telecom Paris research.

Formule cascaded noise figure

F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2) + ... Friis 1944 IRE 32:419. F linéaire F=10^(NF/10); G linéaire G=10^(G_dB/10); NF_dB=10*log10(F); T_e=(F-1)*290 K.

Histoire et contexte

Harald Trap Friis (Naestved Danemark 1893-1976) Bell Labs Holmdel NJ Long Lines Division Director Radio Research 1919-1958, Friis 1944 IRE 32:419 cascaded noise figure formula + Friis 1946 transmission équation IRE 34:254 link budget. France CNRS recherche: CNRS Centre National Recherche Scientifique Paris 1939 32000 employees + LERMA Laboratoire Etudes Rayonnement Matière Astrophysique Observatoire Paris Meudon 200 employees radio astronomy; IRAM Institut Radioastronomie Millimetrique Grenoble 1979 FR-DE-ES consortium MaxPlanck CNRS CSIC + 30 m parabolic Pico Veleta Sierra Nevada Granada + NOEMA Northern Extended Millimeter Array Plateau de Bure Hautes-Alpes 12 antennes 15 m millimetrique submillimetric high resolution VLBI; CNRS LATMOS Atmospheres Milieux Observations Spatiales Guyancourt + LATMOS Paris radar atmospheric remote sensing; Observatoire Paris-Meudon 1667 fonde Louis XIV oldest 200 employees astronomy + radio Stazione Radioastronomique Nancay Sologne Cher 1956 200 m radioheliograph + 'mille' antennes radioastronomy. France grandes ecoles: Telecom Paris Telecom ParisTech 1878 fondee 1500 students grande ecole RF microwave + reseaux + signal processing professeur Anne Ferreol antennes + Bernard Huyart microondas; CentraleSupelec Gif Saclay 1829 + 1894 fusion 4500 students; Polytechnique Palaiseau 1794 fondee Napoleon 2900 students; Sorbonne Universite Paris 1257 fondee oldest 50000 students;

Universite Paris-Saclay 2020 35000 students; Universite Pierre Marie Curie now Sorbonne; INSA Lyon 1957 institut national sciences appliquees 5500 students; Telecom Bretagne IMT Atlantique Brest 1977 800 students; ENSEA Cergy 1941 ecole nationale superieure electronique appliquees; EURECOM Sophia Antipolis 1991 800 students Telecom Paris + EPFL + Politecnico Torino consortium; Telecom SudParis Evry 1979 800 students. France CNES + ESA: CNES Centre National Etudes Spatiales Paris + Toulouse 1961 fondee 2400 employees agence spatiale francaise satellites + Ariane + Soyouz Kourou Guyane lanceur europeen + ESA participation 2 milliards EUR/anno; ArianeGroup Paris Issy 2017 fusion Airbus EADS Astrium + Safran 8500 employees lanceur Ariane 5/6 + missiles M51 nucleaires; Airbus Defence Space France Toulouse 35000 employees satellites + Eurofighter Typhoon + missiles + radars + ESA Ariane; Thales Alenia Space France Cannes 7800 employees joint venture Thales 67% Leonardo 33% satellite payloads + Sicral + Cosmo-SkyMed; Thales Group Paris La Defense 1968 fondee 81000 employees defense electronics + RF + radar + sonar + EW + cybersecurity; Eutelsat Communications Paris 1977 1100 employees satellite operator GEO 36 satellites Hot Bird Eutelsat 13 E + Eutelsat 9B + KA-SAT Ka-band; SES Astra Luxembourg + France distribution Astra 19.2 E satellite TV.

France operateurs telecom: Orange SA Paris 137000 employees telecom dominant 35% mobile share + 50% fixe FTTH + Orange Espana + UK + Africa multinational; SFR Numericable Paris 1987 16000 employees 25% mobile + 50% cable broadband Altice; Bouygues Telecom Paris 1996 9000 employees 22% mobile; Free Iliad Paris 1999 fondateur Xavier Niel 18000 employees disruptor low-cost 17% mobile + 25% fixe FTTH 2002 ADSL + 2012 mobile launch; SES Numericable + UPC + Numericable Completel; Salt Mobile Switzerland; Numericable cable. France 5G spectrum auctions: ARCEP Autorite Regulation Communications Electroniques Postes Paris 1996 200 employees regulator independent ARCOM 2022 fusion CSA Hadopi; ANFR Agence Nationale Fréquences Maisons Alfort 250 employees national frequency management; CNIL Commission Nationale Informatique Libertes Paris 1978 data protection. 5G spectrum: 700 MHz n28 2015 EUR 2.8 billion 4 operators; 3.5 GHz n78 2020 EUR 2.8 billion 4 operators 70 MHz each + 350 MHz total; 26 GHz mmWave 2023 EUR 200 million 4 operators Orange Free SFR Bouygues. France microondes + radar military: bandes RF L-band 1-2 GHz GPS Galileo + ECTS European Train Control System SNCF; S-band 2-4 GHz WiFi 2.4 GHz BT WLAN; C-band 4-8 GHz satellite SAR Sentinel-1 ESA Copernicus 5.4 GHz + WiFi 5 GHz; X-band 8-12 GHz radar military Thales Group Saint-Andre Eure + Meteo France 32 radares meteorologiques nationaux + DGAC Direction Générale Aviation Civile controle traffic aerien Toulouse;

Ku-band 12-18 GHz Hot Bird Eutelsat 13 E + Astra 19.2 E TV digital + DTH satellite broadcast; Ka-band 26-40 GHz Eutelsat KA-SAT 9 A high throughput + 5G mmWave emerging; V-band 40-75 GHz emerging 6G research CNRS LERMA + Telecom Paris + EURECOM Sophia.

Tableau cascaded NF

  • F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2) + ...
  • NF<1 dB: excellent LNA cryogenique HEMT InP 4 K
  • NF 1-3 dB: tres bas GaAs LNA satellite
  • NF 3-6 dB: bas consumer
  • NF 6-10 dB: modere mixer-first
  • NF>10 dB: eleve lossy passive
  • T_e=(F-1)*290 K: température ruido equivalente
  • Friis 1944 IRE 32:419: cascaded NF
  • France CNRS LERMA Paris: 200 radioastronomie
  • France IRAM 30 m + NOEMA Plateau Bure: 12 antennes 15 m
  • France Telecom Paris 1878: 1500 students RF
  • France CNES Toulouse 1961: 2400 spatial
  • France Thales 1968: 81000 defense electronics
  • France ArianeGroup 2017: 8500 lanceurs
  • France Airbus DS 35000: satellites Eurofighter
  • France Eutelsat 1977: 1100 GEO Ku Ka
  • France Orange SA 1988: 137000 35% mobile
  • France ARCEP 1996: 200 regulator
  • 5G auction 2020 3.5 GHz: EUR 2.8 mdi

Exemples numériques

Exemple 1 - LNA single-stage. NF1=0.8 dB G1=20 dB. NF_total=0.8 dB. T_e=58.6 K. France: Eutelsat ground stations Rambouillet teleport.

Exemple 2 - LNA + mixer. NF1=1.5 dB G1=15 dB; NF2=8 dB G2=-7 dB. NF_total=1.99 dB. France: Orange 137000 + SFR 16000 + Bouygues 9000 + Free 18000 5G.

Exemple 3 - Three stages. NF_total=1.10 dB. LNA dominant. France: Telecom Paris + CentraleSupelec research.

Exemple 4 - No LNA front. NF_total=9.20 dB high. Bad design.

Exemple 5 - Cryogenic LNA. NF=0.2 dB. T_e=13.6 K. France: IRAM 30 m Pico Veleta + NOEMA Plateau Bure 12 antennes + Nancay radioastronomie.

Limites

  1. Impedance matching 50 ohm.
  2. Bandwidth dependence.
  3. Stadi correlated.
  4. Compression P1dB IIP3.
  5. Lossy passive first.
  6. Image rejection mixer.
  7. Phase noise oscillator.
  8. Antenna temp T_ant.
  9. ADC quantization.
  10. Friis reciprocity.

Erreurs communes

F linéaire vs NF dB: F=10^(NF/10); NF=10*log10(F). Pas sumar dB directement.

Lossy passive front: switch filter cable losses ajoutent dB.

Mixer conversion loss: passive 6-8 dB; active 8-12 dB.

Image noise raddoppia: superhet sans filtre.

Y-factor calibration: NIST traceable.

Applications

  1. Radioastronomie LNA cryogenique: France IRAM 30 m Pico Veleta + NOEMA Plateau Bure 12 antennes + Nancay radioastronomie + Observatoire Paris-Meudon LERMA.
  2. Satellite ground: Eutelsat Paris 1100 + SES Astra distribution + Thales Alenia Space Cannes 7800.
  3. Cellulaire 5G: Orange 137000 + SFR 16000 + Bouygues 9000 + Free 18000 700 MHz + 3.5 GHz + 26 GHz mmWave.
  4. WiFi 6E + BLE IoT: 6 GHz NF 4-6 dB; BLE 2.4 GHz NF 6-9 dB.
  5. GPS Galileo L-band: 1.575 GHz LNA NF 1-2 dB CNES Toulouse + ESA Galileo Operations.
  6. SAR satelitale: Sentinel-1 ESA Copernicus C-band 5.4 GHz CNES + Airbus DS Toulouse.
  7. Radar military weather: Thales Group 81000 + Meteo France 32 radares + DGAC ATC.
  8. Microondes TV satellite: Hot Bird Eutelsat 13 E + Astra 19.2 E LNB consumer.
  9. Front-end RFIC GaN: Telecom Paris + CentraleSupelec + EURECOM mmWave 5G/6G.
  10. Deep space: ESA Estec + CNES Toulouse + Nancay 200 m DSN-equivalent BepiColombo.

Mis à jour en juillet 2026

Questions fréquentes

Comment calculer cascaded noise figure?

Procedure: (1) F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2) + ... Friis 1944; (2) F_i = 10^(NF_i/10); (3) G_i linéaire; (4) NF_total dB = 10*log10(F). Exemple LNA NF1=1 dB G1=20 dB + mixer NF2=8 dB G2=-7 dB: NF_total = 1.18 dB. France: CNRS LERMA + IRAM 30 m Pico Veleta + Telecom Paris 1500 + CNES Toulouse 2400.

Qu est-ce que la formule Friis?

Harald T. Friis Bell Labs Holmdel NJ 1944 IRE 32:419 cascaded noise figure F_total = F1 + (F2-1)/G1 + ... + Friis 1946 transmission équation link budget. Insight: premier LNA domine NF total. France: IRAM 30 m + NOEMA Plateau Bure + Eutelsat Paris satellite + Thales Group 81000.

Pourquoi LNA est critique?

Premier stage domine NF cascaded. G1=20 dB (100x linéaire) reduit NF mixer (8 dB) a ~0.07 dB total. LNA NF 0.5-2 dB GaAs HEMT pHEMT premier avant mixer assure NF dominant. France: cryogenique HEMT InP 4 K IRAM 30 m + NOEMA + Nancay radioastronomie.

Qu est-ce que noise température equivalente?

T_e = (F-1)*T_0 avec T_0=290 K. NF_dB = 10*log10(1+T_e/T_0). NF=0.5 dB → T_e=35 K cryogenique; NF=1 dB → T_e=75 K satellite Ku; NF=3 dB → T_e=290 K cellulaire. France: IRAM 30 m T_sys 30 K mmWave.

Quels valeurs NF typiques?

Cryogenique radioastronomie NF<1 dB IRAM + NOEMA; satellite Ku NF 0.6-1.2 dB Eutelsat ground; cellulaire 5G NF 2-3 dB Orange SFR Bouygues Free; WiFi 6E NF 4-6 dB; BLE NF 6-9 dB; direct conversion NF 6-10 dB.

Difference NF dB vs F linéaire?

F linéaire rapport SNR_in/SNR_out>=1 adimensionnel; NF dB=10*log10(F). F=2 → NF=3 dB; F=4 → NF=6 dB. Erreur: sumar NF dB directement. Correct: convertir F linéaire, appliquer Friis.

Applications cascaded NF?

Applications: radioastronomie France IRAM 30 m Pico Veleta + NOEMA Plateau Bure 12 antennes + Nancay; satellite ground Eutelsat 1100; cellulaire 5G Orange 137000 + SFR + Bouygues + Free; SAR Sentinel-1 CNES; radar Thales 81000 + Meteo France 32; GPS Galileo CNES Toulouse + ESA.

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