How to calculate VSWR reflection coefficient antenna RF

Calculate VSWR voltage standing wave ratio + reflection coefficient Gamma + return loss RF transmission line formula (1+|G|)/(1-|G|); G=(Zl-Z0)/(Zl+Z0). VSWR<1.5 acceptable cellular; 1.1-1.3 satellite. NIST + Caltech JPL DSN + MIT Lincoln + Bell Labs Smith.

Calculation parameters
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How to calculate VSWR (Voltage Standing Wave Ratio) and reflection coefficient Gamma on RF transmission line characterized by impedance Z0 (typically 50 Ohm radio frequency standard, 75 Ohm video broadcast CATV): formula VSWR = (1+|Gamma|)/(1-|Gamma|) with Gamma = (Zl - Z0) / (Zl + Z0) complex reflection coefficient. Zl load impedance (antenna, amplifier input, terminator) Ohm; Z0 transmission line characteristic impedance 50 Ohm RF / 75 Ohm video.

Return loss RL_dB = -20*log10(|Gamma|) measures reflected power relative to incident.

Mismatch loss ML_dB = -10*log10(1-|Gamma|^2). Power reflected = |Gamma|^2 * P_incident; power delivered = (1-|Gamma|^2) * P_incident.

VSWR classification: VSWR32 dB lab grade calibration network analyzer reference termination; VSWR 1.05-1.2 very good RL 20-32 dB satellite Ku-band ground; VSWR 1.2-1.5 good RL 14-20 dB cellular eNodeB acceptable; VSWR 1.5-2.0 acceptable RL 9.5-14 dB consumer WiFi; VSWR 2.0-3.0 marginal RL 6-9.5 dB needs tuning; VSWR>3 poor RL<6 dB severe mismatch.

VSWR=1 perfect match no reflection; VSWR=infinite open/short total reflection. Reflected power: VSWR=1 → 0%; VSWR=1.5 → 4%; VSWR=2 → 11.1%; VSWR=3 → 25%.

Heinrich Hertz (Germany 1857-1894) Karlsruhe 1888 electromagnetic waves experiments + standing wave demonstration metallic plate reflector + Lord Rayleigh Cambridge UK 1890s mathematical analysis + Heaviside transmission lines telegrapher equation 1885 + Lecher 1890 wires standing waves pattern.

Phillip Hagar Smith (USA 1905-1987) Bell Labs Murray Hill NJ 1939 paper Electronics 12:29 'Transmission Line Calculator' Smith chart graphical tool plot impedance + reflection coefficient on polar coordinate complex plane unit circle |Gamma|<=1; Mobius transformation maps Z half-plane to Gamma disk. Smith chart now standard textbook RF + microwave engineering Pozar 'Microwave Engineering' Wiley + Razavi 'RF Microelectronics' Prentice Hall + Lee 'CMOS Radio-Frequency Integrated Circuits' Cambridge + Rogers 'Radio Frequency Integrated Circuit Design' Artech House.

S-parameters scattering: Kurokawa 1965 IEEE Trans Microwave Theory and Techniques MTT-13:194 'Power Waves and the Scattering Matrix' generalize Gamma to multi-port. S11 input reflection = Gamma; S21 forward gain; S12 reverse isolation; S22 output reflection. Now standard RF + microwave network analyzer Keysight + Rohde Schwarz + Anritsu + Tektronix.

USA RF/microwave research: MIT Lincoln Laboratory Lexington MA 1951 4000 employees DOD FFRDC defense radar phased arrays AESA AN/FPS-115 PAVE PAWS; NASA JPL Caltech Pasadena CA 1936 6000 Deep Space Network DSN Goldstone Madrid Canberra 70 m parabolic antennas Voyager Cassini Mars rovers; Stanford SLAC Menlo Park CA 1962 1500 linear accelerator + LCLS X-ray free-electron laser; NIST Boulder CO 1901 3000 employees noise standards + traceable VSWR calibration Vector Network Analyzer SOLT Short-Open-Load-Through cal kits; NRAO National Radio Astronomy Observatory Charlottesville VA 1956 500 employees + VLA Socorro NM 27 antennas Y-shape 25 m parabolic 1980 + ALMA Atacama Chile 66 antennas 12 m + 7 m + GBT Green Bank WV 100 m parabolic 2002 largest fully-steerable; NASA Goddard Greenbelt MD 1959 10000 satellite communications; Caltech Pasadena CA 1891 Owens Valley Radio Observatory OVRO 40 m + 130 ft + CARMA combined array; UC Berkeley Hat Creek Radio Observatory CA Allen Telescope Array ATA SETI institute.

USA companies RF microwave: Analog Devices Norwood MA 1965 25000 ADI premier analog RF transceiver IC ADRV9009 ADRV9026 5G mmWave; Texas Instruments Dallas TX 1930 30000 RF analog AFE; Qualcomm San Diego CA 1985 50000 RF transceivers cellular modems Snapdragon X65 5G mmWave 26-39 GHz Sub-6 GHz; Broadcom San Jose CA 1991 20000 RF + WiFi 6/6E/7; Skyworks Solutions Irvine CA 2002 11000 RF front-end modules cellular eNodeB; Qorvo Greensboro NC 2015 8000 RF GaN HEMT power amplifiers + LNAs; MaxLinear Carlsbad CA 2003 RF receivers; Marvell Santa Clara CA 1995. Keysight Technologies Santa Rosa CA 2014 14000 employees + Agilent Technologies Santa Clara CA 1999 spinoff HP Hewlett-Packard 1939 + RF/microwave instruments Vector Network Analyzer PNA-X N5247B 110 GHz + spectrum analyzer + signal generator + oscilloscope DSAZ + UXR Oscilloscope 110 GHz; Anritsu Morgan Hill CA 1985 USA subsidiary Japanese parent network analyzer ShockLine MS46522B + spectrum analyzer; Tektronix Beaverton OR 1946 + Rohde Schwarz Munich Germany USA subsidiary Columbia MD; National Instruments Austin TX 1976 LabVIEW VXI + PXI modular instruments.

USA defense electronics radar: Raytheon Technologies Waltham MA 1922 180000 employees radar Patriot AEGIS AESA F-22 F-35 + AN/SPY-6 + AN/APG-77 F-22 + AN/APG-81 F-35; Lockheed Martin Bethesda MD 1995 116000 radar Aegis SPY-1 SPY-6; Northrop Grumman Falls Church VA 1994 95000 AN/APG-77 + AN/APG-81 + AN/SPS-67; L3Harris Melbourne FL 2019 50000 RF systems + GPS Block IIIF receiver; BAE Systems North America Arlington VA RF EW; General Dynamics Mission Systems Fairfax VA satellite ground; Leonardo DRS Arlington VA Italian Leonardo subsidiary.

USA satellite operators: SpaceX Hawthorne CA 2002 13000 Starlink LEO 5000+ satellites Ka-band 17.8-19.3 GHz / 27.5-30 GHz user terminals; Boeing El Segundo CA + Long Beach 142000 + 702 satellite bus geostationary GEO; Lockheed Martin Sunnyvale CA Space Systems satellites GPS Block IIIF + AEHF; Maxar Westminster CO commercial Earth Observation WorldView-3/4 30 cm; Iridium Communications McLean VA LEO 66 satellites L-band 1616-1626.5 MHz; Globalstar Covington LA LEO 48 satellites; Hughes Network Systems Germantown MD HughesNet GEO Ka-band 26.5-40 GHz; Viasat Carlsbad CA HTS Ka-band ViaSat-1/2/3 + Inmarsat 2023 acquisition; Telesat Ottawa Canada Lightspeed LEO Ka-band; Amazon Project Kuiper Bellevue WA LEO Ka-band 3236 satellites planned launch 2024.

VSWR formula

Gamma = (Zl - Z0) / (Zl + Z0) complex reflection coefficient. VSWR = (1+|Gamma|)/(1-|Gamma|) dimensionless ratio 1-infinite. RL_dB = -20*log10(|Gamma|) return loss. ML_dB = -10*log10(1-|Gamma|^2) mismatch loss. P_reflected = |Gamma|^2 * P_incident.

History and context

Standing waves discovered Heinrich Hertz Karlsruhe Germany 1888 electromagnetic waves experiments dipole spark + reflection metal plate. Lord Rayleigh Cambridge UK 1890s mathematical analysis. Heaviside 1885 transmission line telegrapher equation. Bell Labs Holmdel NJ 1930s-1940s formal definitions RF coaxial transmission lines + waveguides + Friis 1944 cascaded NF + Friis 1946 transmission equation. RCA Princeton NJ 1930s-1960s coaxial cables + connectors + television broadcast 75 Ohm.

Smith chart: Phillip Hagar Smith Bell Labs Murray Hill NJ 1939 paper Electronics 12:29 'Transmission Line Calculator' graphical tool plot impedance + reflection on polar coordinate complex plane unit circle. Mobius transformation (Zl-Z0)/(Zl+Z0) maps half-plane to disk. Smith chart utilized graphical matching network L stub + open-circuit + short-circuit + LC matching design.

S-parameters scattering: Kurokawa 1965 IEEE Trans MTT-13:194 'Power Waves and the Scattering Matrix' generalize Gamma to multi-port.

USA universities + national labs: MIT Lincoln Laboratory Lexington MA 1951 4000 employees DOD FFRDC defense radar phased arrays AESA AN/FPS-115 PAVE PAWS Cape Cod MA + Beale CA + Clear AK ICBM detection + AN/SPY-1 AEGIS shipboard; NASA JPL Caltech Pasadena CA 1936 6000 employees Deep Space Network DSN Goldstone CA + Madrid Spain + Canberra Australia 70 m parabolic antennas Voyager 1+2 Cassini Saturn Galileo Jupiter Mars rovers Curiosity Perseverance communications S/X/Ka-band; Stanford SLAC Menlo Park CA 1962 1500 linear accelerator electron-positron 50 GeV + LCLS X-ray free-electron laser; NIST Boulder CO 1901 3000 employees noise standards Y-factor calibration WR-15 WR-28 waveguides + Vector Network Analyzer SOLT Short-Open-Load-Through cal kits NIST traceable reference; NRAO National Radio Astronomy Observatory Charlottesville VA 1956 500 employees + VLA Very Large Array Socorro NM 27 antennas Y-shape 25 m parabolic 1980 + ALMA Atacama Chile 66 antennas 12 m + 7 m millimeter array 2013 + GBT Green Bank Telescope WV 100 m parabolic 2002 largest fully-steerable; Caltech Owens Valley Radio Observatory Bishop CA OVRO 40 m + 130 ft + CARMA combined array; UC Berkeley Hat Creek Radio Observatory CA Allen Telescope Array ATA SETI institute.

USA private sector RF microwave instruments: Keysight Technologies Santa Rosa CA 2014 14000 employees + Agilent Technologies Santa Clara CA 1999 spinoff HP Hewlett-Packard 1939 + RF/microwave instruments Vector Network Analyzer PNA-X N5247B 110 GHz + N5290A 110 GHz banded + spectrum analyzer N9020A MXA + N9030A PXA + signal generator E8267D + oscilloscope DSAZ + UXR Oscilloscope 110 GHz; Anritsu Morgan Hill CA 1985 USA subsidiary Japanese parent network analyzer ShockLine MS46522B + spectrum analyzer MS27201A; Tektronix Beaverton OR 1946 oscilloscope + spectrum analyzer; Rohde Schwarz Munich Germany USA subsidiary Columbia MD; National Instruments Austin TX 1976 LabVIEW VXI + PXI modular instruments PXIe-5645 vector signal transceiver.

USA RF semiconductor companies: Analog Devices Norwood MA 1965 25000 employees ADI premier analog mixed-signal RF transceiver ICs ADRV9009 ADRV9026 5G mmWave wideband; Texas Instruments Dallas TX 1930 30000 employees RF analog AFE; Qualcomm San Diego CA 1985 50000 RF transceivers cellular modems Snapdragon X65 5G mmWave 26-39 GHz Sub-6 GHz integrated; Broadcom San Jose CA 1991 20000 RF + WiFi 6/6E/7 chipsets; Skyworks Solutions Irvine CA 2002 11000 RF front-end modules FEMs cellular eNodeB + WiFi PA + LNA; Qorvo Greensboro NC 2015 8000 RF GaN HEMT power amplifiers + LNAs cellular base stations + radar military; MaxLinear Carlsbad CA 2003 RF receivers tuners cable broadband; Marvell Santa Clara CA 1995 networking SoC ARM cores.

USA defense electronics radar industry: Raytheon Technologies Waltham MA 1922 180000 employees AESA radar Patriot PAC-3 + AEGIS SPY-1 SPY-6 AN/SPQ-9 + AN/APG-79 F/A-18 + AN/APG-77 F-22 + AN/APG-81 F-35 AESA airborne; Lockheed Martin Bethesda MD 1995 116000 employees Aegis Combat System + COBRA Judy SPY-1; Northrop Grumman Falls Church VA 1994 95000 AN/APG-77 F-22 + AN/APG-81 F-35 + AN/SPS-67 + Joint STARS; L3Harris Melbourne FL 2019 50000 employees RF systems + GPS Block IIIF receiver.

USA satellite operators NewSpace: SpaceX Hawthorne CA 2002 13000 employees Starlink LEO Low Earth Orbit 5000+ satellites Ka-band 17.8-19.3 GHz / 27.5-30 GHz user terminals + Falcon 9 Falcon Heavy reusable launchers + Starship; Boeing El Segundo CA + Long Beach 142000 employees defense + 702 satellite bus GEO; Lockheed Martin Sunnyvale CA Space Systems satellites GPS Block IIIF + AEHF Advanced Extremely High Frequency; Maxar Westminster CO 2017 commercial Earth Observation WorldView-3/4 30 cm resolution + DigitalGlobe heritage; Iridium Communications McLean VA LEO 66 satellites L-band 1616-1626.5 MHz; Globalstar Covington LA LEO 48 satellites L-band + S-band; Hughes Network Systems Germantown MD HughesNet GEO Ka-band 26.5-40 GHz; Viasat Carlsbad CA HTS Ka-band ViaSat-1/2/3 + Inmarsat 2023 acquisition; Telesat Ottawa Canada Lightspeed LEO Ka-band; Amazon Project Kuiper Bellevue WA LEO Ka-band 3236 satellites planned launch 2024.

VSWR table

  • VSWR = (1+|Gamma|)/(1-|Gamma|)
  • Gamma = (Zl-Z0)/(Zl+Z0)
  • VSWR32 dB: excellent lab grade
  • VSWR 1.05-1.2 RL 20-32 dB: very good satellite Ku
  • VSWR 1.2-1.5 RL 14-20 dB: good cellular
  • VSWR 1.5-2 RL 9.5-14 dB: acceptable WiFi
  • VSWR 2-3 RL 6-9.5 dB: marginal needs tuning
  • VSWR>3 RL<6 dB: poor severe mismatch
  • VSWR=1: 0% reflected perfect
  • VSWR=1.5: 4% reflected ML=0.18 dB
  • VSWR=2: 11.1% reflected ML=0.51 dB
  • VSWR=3: 25% reflected ML=1.25 dB
  • VSWR=infinite: 100% reflected open/short
  • Z0 50 Ohm: RF radio standard
  • Z0 75 Ohm: video CATV broadcast
  • Smith 1939 Bell Labs: chart Electronics 12:29
  • Kurokawa 1965 MTT-13:194: S-parameters
  • USA MIT Lincoln Lab 1951: 4000 AESA radar
  • USA NASA JPL 1936: 6000 DSN 70 m
  • USA SLAC Stanford 1962: linac LCLS
  • USA NIST Boulder 1901: VSWR cal SOLT
  • USA NRAO 1956: VLA + ALMA + GBT
  • USA Caltech OVRO Bishop CA: 40 m
  • USA Keysight Santa Rosa 2014: 14000 PNA-X 110 GHz
  • USA Anritsu Morgan Hill: ShockLine VNA
  • USA ADI Norwood 1965: 25000 RF IC
  • USA Qualcomm 1985: 50000 5G modems
  • USA Skyworks 2002: 11000 RF FEMs
  • USA Raytheon 1922: 180000 AESA AEGIS
  • USA SpaceX 2002: 13000 Starlink Ka

Numerical examples detailed

Example 1 - Perfect match. Zl=50 Z0=50. Gamma=0. VSWR=1.0 perfect. RL=infinite. P_reflected=0%. USA: NIST Boulder calibration reference termination 50 Ohm + Keysight PNA-X SOLT cal.

Example 2 - Antenna 75 on Z0=50. Zl=75 Z0=50. Gamma=0.2. VSWR=1.5 acceptable. RL=14 dB. P_reflected=4%. USA: WiFi router consumer + cellular eNodeB acceptable Verizon AT&T T-Mobile.

Example 3 - Open circuit. Zl=infinite. Gamma=1. VSWR=infinite total reflection. RL=0 dB. USA: cable disconnected protezione transmitter tube damage.

Example 4 - Short circuit. Zl=0 Z0=50. Gamma=-1. VSWR=infinite. Phase=180°. USA: cable shorted ground critical protection.

Example 5 - Complex 40+j30. Zl=40+j30 Z0=50. |Gamma|=0.333. VSWR=2.0 marginal. RL=9.54 dB. USA: antenna design MIT Lincoln Lab + JPL DSN matching network.

Limits

  1. Frequency dependence VSWR varies with frequency.
  2. Connector mismatch SMA/N/BNC adds VSWR 1.05-1.15.
  3. Cable losses mask measured VSWR.
  4. Bandwidth narrow vs broadband matching.
  5. Calibration SOLT NIST traceable required.
  6. Power handling circulator + isolator high-power.
  7. TDR alternative time-domain reflectometry.
  8. S-parameters multi-port.
  9. Waveguide higher-order modes.
  10. Mismatch loss vs return loss different scales.

Common errors

VSWR vs RL: VSWR ratio 1-infinite; RL dB negative scale. Conversion table.

50 Ohm vs 75 Ohm: 50 RF / 75 video. Mismatch error.

Open vs short: Gamma=+1 vs -1. VSWR=infinite both.

Cable loss masking: long lossy cable hides actual mismatch.

Power handling: VSWR>1.5 protezione critical.

Practical applications

  1. Antenna design + matching: USA MIT Lincoln Lab Lexington 4000 + Caltech OVRO + Berkeley Hat Creek + Stanford SLAC.
  2. Cellular base station 5G: Verizon NYC + AT&T Dallas + T-Mobile Bellevue 600 MHz n71 + Sub-6 GHz n77/n78 + 24-39 GHz mmWave.
  3. Satellite ground station Ku-band: USA Hughes Germantown MD + Viasat Carlsbad CA + Intelsat McLean VA Ka-band 27-40 GHz.
  4. WiFi router consumer 6E: 6 GHz Cisco + Aruba VSWR 1.5-2 acceptable.
  5. RF amplifier output matching: USA Qorvo GaN HEMT + Skyworks + ADI ADRV9026.
  6. Network analyzer measurement: USA Keysight PNA-X 110 GHz + Anritsu ShockLine + Tektronix + R&S USA SOLT cal NIST traceable.
  7. RF connector + cable test: SMA + N + BNC + TNC chain VSWR 1.05-1.15 typical.
  8. Radar military weather: USA Raytheon AEGIS SPY-1 SPY-6 + Lockheed + Northrop F-22 F-35 X-band; NEXRAD WSR-88D weather S-band.
  9. Radio astronomy VLBI: USA NRAO VLA + GBT 100 m + ALMA Chile + JPL DSN 70 m + Caltech OVRO 40 m.
  10. Test mess RF lab: USA national labs MIT Lincoln + JPL + SLAC + NIST + universities Stanford + MIT + Caltech + Berkeley + Wharton.

Updated July 2026

Frequently Asked Questions

What is VSWR?

VSWR Voltage Standing Wave Ratio = (1+|Gamma|)/(1-|Gamma|) dimensionless ratio 1-infinite measures impedance match between load Zl and transmission line Z0 (50 Ohm RF / 75 Ohm video). VSWR=1 perfect match no reflection; VSWR=infinite open/short total reflection. Reflection coefficient Gamma=(Zl-Z0)/(Zl+Z0) complex. RL dB = -20*log10|Gamma|. USA: NIST Boulder VSWR calibration + MIT Lincoln Lab AESA radar + NASA JPL DSN 70 m parabolic.

How to calculate reflection coefficient?

Procedure: (1) Gamma = (Zl - Z0) / (Zl + Z0) complex; (2) |Gamma| magnitude 0-1; (3) VSWR = (1+|Gamma|)/(1-|Gamma|); (4) RL_dB = -20*log10|Gamma|. Example Zl=75 Z0=50: Gamma=25/125=0.2, VSWR=1.5, RL=14 dB acceptable cellular. USA: Keysight PNA-X 110 GHz Vector Network Analyzer + Anritsu ShockLine + R&S USA + Tektronix SOLT calibration NIST traceable.

Acceptable VSWR values?

VSWR32 dB excellent lab grade; VSWR 1.05-1.2 RL 20-32 dB very good satellite Ku ground; VSWR 1.2-1.5 RL 14-20 dB good cellular eNodeB acceptable; VSWR 1.5-2 RL 9.5-14 dB acceptable WiFi consumer; VSWR 2-3 RL 6-9.5 dB marginal needs matching tuning; VSWR>3 RL<6 dB poor severe mismatch protezione critical. USA: Verizon AT&T T-Mobile 5G eNodeB VSWR<1.5.

Difference Z0 50 Ohm and 75 Ohm?

Z0 50 Ohm RF radio standard amateur professional cellular satellite WiFi BT GPS Galileo SMA N BNC TNC connector. Z0 75 Ohm video broadcast CATV cable RG6 RG11 F-connector consumer composite video. Mixing impedance error -> wrong VSWR + power loss. USA: DirecTV Dish Network 75 Ohm cable; Verizon AT&T 5G + cellular 50 Ohm; NRAO radio astronomy 50 Ohm cryogenic LNA.

What is return loss RL?

Return loss RL_dB = -20*log10(|Gamma|) reflected power relative to incident dB scale. RL=0 total reflection; RL=10 dB 10% reflected; RL=20 dB 1%; RL=30 dB 0.1% lab grade. SMA connector typical RL 30 dB DC-18 GHz. Conversion: VSWR=1.5 → RL=14 dB; VSWR=2 → RL=9.54 dB; VSWR=3 → RL=6 dB. USA: Keysight PNA-X N5247B 110 GHz + NIST Boulder SOLT calibration.

What is Smith chart?

Phillip H. Smith (USA 1905-1987) Bell Labs Murray Hill NJ 1939 paper Electronics 12:29 'Transmission Line Calculator' graphical tool plot impedance + reflection coefficient on polar coordinate complex plane unit circle |Gamma|<=1. Mobius transformation (Zl-Z0)/(Zl+Z0) maps half-plane to disk. Permits graphical solution matching network L stub + LC matching design. Now standard textbook RF microwave engineering Pozar + Razavi + Lee + Rogers.

Applications of VSWR?

Applications: antenna design + matching USA MIT Lincoln Lab 4000 + Caltech OVRO + Stanford SLAC + Berkeley; cellular eNodeB 5G Verizon AT&T T-Mobile 600 MHz + Sub-6 GHz + 24-39 GHz mmWave; satellite Ku ground Hughes + Viasat + Intelsat; WiFi router 6E consumer Cisco Aruba; RF amplifier matching Qorvo GaN HEMT + Skyworks + ADI ADRV9026; radar military Raytheon AEGIS + Lockheed + Northrop F-22 F-35; radio astronomy VLBI NRAO VLA + GBT + ALMA + JPL DSN.

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