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Antenna

Parabolic Dish Antenna Calculator

Calculate parabolic dish gain, HPBW, effective aperture, and noise temperature. Design satellite and microwave dish antennas. Free, instant results.

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Formula

G=10⋅log10(4π⋅η⋅A/λ2);HPBW≈70λ/DG = 10·log₁₀(4π·η·A/λ²); HPBW ≈ 70λ/D
G— Antenna gain (dBi)
η— Aperture efficiency
D— Dish diameter (m)
λ— Wavelength (0.3/f_GHz) (m)
HPBW— Half-power beamwidth (degrees)

How It Works

Parabolic dish calculator computes gain, beamwidth, and aperture efficiency from diameter and frequency — satellite ground station engineers, radio astronomers, and microwave backhaul designers achieve the highest gains (30-60 dBi) through aperture antennas. Gain is G = eta * (pi*D/lambda)^2, where eta is aperture efficiency (typically 55-70%) and D is dish diameter, per Balanis's 'Antenna Theory' (4th ed.) and ITU-R S.465-6.

A 1-meter dish at 12 GHz (Ku-band satellite TV) achieves G = 0.6 * (pi*1/0.025)^2 = 37.7 dBi with 55% efficiency. Doubling diameter adds 6 dB gain; doubling frequency adds 6 dB gain for the same physical dish. The 3-dB beamwidth theta = 70*lambda/D narrows with increasing gain: a 3-meter dish at 12 GHz has 0.7-degree beamwidth, requiring precision pointing within 0.2 degrees.

Aperture efficiency is limited by: illumination taper (feed pattern doesn't uniformly illuminate aperture, typically 1-2 dB loss), spillover (feed radiation missing the reflector, 0.5-1 dB), surface accuracy (RMS error should be < lambda/16 for < 0.5 dB loss), blockage (feed and support structure shadow the aperture, 0.3-1 dB), and feed mismatch. Prime-focus feeds are simpler; Cassegrain and Gregorian configurations allow shorter focal length and easier feed access but add subreflector blockage.

Worked Example

Problem: Design a satellite earth station antenna for C-band (4 GHz receive, 6 GHz transmit) with G/T > 30 dB/K.

System analysis per ITU-R S.465:

  1. Operating frequencies: 3.7-4.2 GHz (receive), 5.925-6.425 GHz (transmit)
  2. Design frequency for sizing: 4.0 GHz (receive determines G/T)
  3. Wavelength: lambda = c/f = 3e8/4e9 = 75 mm = 0.075 m
G/T requirement breakdown:
  1. Target G/T = 30 dB/K = 10*log10(G_linear/T_sys)
  2. Assume system noise temperature T_sys = 100 K (25 K LNA + 75 K antenna temperature)
T_sys in dB: 10*log10(100) = 20 dBK
  1. Required gain: G = G/T + T_sys(dB) = 30 + 20 = 50 dBi
Dish diameter calculation:
  1. G = eta * (pi*D/lambda)^2
50 dBi = 100,000 linear eta = 0.6 (typical for well-designed prime-focus)
  1. D = lambda/pi sqrt(G/eta) = 0.075/pi sqrt(100000/0.6) = 9.75 m
  2. Use standard 10-meter dish for margin
Verify performance at 10 m:
  1. Gain at 4 GHz: G = 0.6 * (pi*10/0.075)^2 = 0.6 * 175,000 = 105,000 = 50.2 dBi
  2. Gain at 6 GHz: G = 0.6 * (pi*10/0.05)^2 = 0.6 * 395,000 = 55.7 dBi
  3. G/T = 50.2 - 20 = 30.2 dB/K (meets requirement)
  4. 3-dB beamwidth: theta = 70*0.075/10 = 0.53 degrees
  5. Pointing accuracy requirement: < 0.15 degrees (theta/3)
Surface accuracy requirement:
  1. For < 0.5 dB gain loss: RMS error < lambda/16 = 75/16 = 4.7 mm at 4 GHz
  2. At 6 GHz transmit: RMS < 50/16 = 3.1 mm — use this as specification
  3. Practical dish construction: 2-3 mm RMS achievable with solid aluminum panels

Practical Tips

  • ✓For fixed satellite reception, use offset-fed dishes — no feed blockage improves efficiency 5-10% and eliminates rain/snow accumulation in feed
  • ✓Specify surface accuracy as RMS error < lambda/20 for < 0.3 dB gain degradation; solid dishes achieve 1-2 mm, mesh dishes 5-10 mm, limiting mesh to frequencies below approximately 10 GHz
  • ✓For transportable stations, consider shaped reflector dishes (edge-tapered illumination) that maintain efficiency while reducing sidelobe levels for interference mitigation per ITU-R S.465

Common Mistakes

  • ✗Neglecting aperture efficiency — theoretical maximum gain assumes eta = 1; practical dishes achieve 55-70% efficiency; using G = (pi*D/lambda)^2 without eta factor overestimates gain by 1.5-2.5 dB
  • ✗Ignoring surface accuracy requirements — RMS surface error > lambda/16 causes significant gain loss; a 3-meter mesh dish suitable for C-band (lambda = 75 mm, needs 5 mm RMS) fails at Ku-band (lambda = 25 mm, needs 1.5 mm RMS)
  • ✗Underestimating pointing requirements — 1-degree pointing error on a 1-degree beamwidth antenna causes 3 dB gain loss; high-gain dishes require motorized tracking with 0.1-degree accuracy for satellite tracking
  • ✗Overlooking noise temperature contribution — antenna temperature from ground spillover and atmospheric absorption adds 20-100 K to system noise; G/T improvement requires both high gain AND low noise temperature

Frequently Asked Questions

Three factors per Balanis analysis: (1) Aperture area A = pi*(D/2)^2 — doubling diameter quadruples area and gain (+6 dB). (2) Wavelength lambda = c/f — halving wavelength (doubling frequency) quadruples electrical area and gain (+6 dB). (3) Aperture efficiency eta (55-70% typical) accounting for illumination taper, spillover, surface errors, and blockage. Combined: G = eta*(pi*D/lambda)^2. A 3 m dish at 12 GHz with 60% efficiency: G = 0.6*(pi*3/0.025)^2 = 85,000 = 49.3 dBi.
Parabolic curvature is essential — all rays parallel to axis reflect to focal point with equal path length, creating in-phase addition. Deviations from perfect parabola cause phase errors: RMS surface error sigma causes gain loss of exp(-(4*pi*sigma/lambda)^2). At sigma = lambda/16: loss = 0.5 dB. At sigma = lambda/8: loss = 2 dB. Practical implications: (1) Solid dishes achieve 1-3 mm RMS (usable to 30 GHz). (2) Mesh dishes achieve 5-10 mm RMS (usable to 10 GHz). (3) Inflatable dishes achieve 10-20 mm RMS (limited to low microwave). Surface accuracy is often the limiting factor for high-frequency performance.
Practical range: 1-100 GHz, with size-frequency tradeoffs: Below 1 GHz: Dishes become very large (10+ meters for useful gain); Yagis or arrays often preferred. 1-10 GHz (L/S/C-band): 2-10 m dishes for satellite earth stations, radio astronomy, radar. 10-30 GHz (Ku/Ka-band): 0.5-3 m dishes for satellite TV, VSAT, point-to-point links. 30-100 GHz (mm-wave): 0.2-1 m dishes for high-capacity backhaul, radio astronomy. Above 100 GHz: Surface accuracy requirements (< 0.1 mm RMS) make machined metal reflectors or holographic surfaces necessary.
Aperture efficiency eta = G_actual / G_ideal represents how effectively the physical aperture converts to gain. Components per Balanis: Illumination efficiency (80-90%): Feed doesn't uniformly illuminate aperture — edge taper reduces sidelobe but wastes outer aperture. Spillover efficiency (90-95%): Feed radiation missing reflector adds to noise. Surface efficiency (95-99%): Phase errors from surface inaccuracies. Blockage efficiency (95-99%): Feed and struts shadow aperture. Polarization efficiency (99%+): Cross-pol mismatch loss. Combined: eta = 0.85 * 0.92 * 0.97 * 0.97 * 0.99 = 0.72 typical. Offset-fed dishes eliminate blockage, achieving 75-80% efficiency.
Work backwards from link budget: (1) Determine required EIRP (transmit) or G/T (receive) from link margin analysis. (2) Assume system noise temperature T_sys (typically 50-150 K for cooled LNA). (3) Required gain G = G/T + 10*log10(T_sys) for receive; G = EIRP - P_transmitter for transmit. (4) Solve for diameter: D = (lambda/pi)*sqrt(G/(eta)). Example: G/T = 35 dB/K at 12 GHz, T_sys = 80 K. G = 35 + 19 = 54 dBi. D = (0.025/pi)*sqrt(250000/0.6) = 5.1 m. Standard dish sizes: 1.2, 1.8, 2.4, 3.0, 3.7, 4.5, 6.0, 7.3, 9.0 m — select next size up for margin.

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