How does beamwidth relate to antenna gain?

For antennas with a single main lobe and low sidelobes, the directivity can be approximated from the E-plane and H-plane half-power beamwidths: D approximately equals 41253 divided by the product of the E-plane and H-plane beamwidths in degrees (for a cosine-tapered aperture) or 32400 for a uniformly illuminated aperture. A 3-meter parabolic dish at 10 GHz has a beamwidth of about 0.7 degrees, giving approximately 41253 / (0.7 times 0.7) = 84,000 or about 49 dBi directivity. Gain equals directivity times the aperture efficiency (typically 55 to 70%).

Why do phased arrays have a beamwidth that changes with scan angle?

When a phased array scans off broadside, the projected aperture in the scan direction shrinks by the cosine of the scan angle. Since beamwidth is inversely proportional to aperture size, the beam broadens as 1/cos(theta). At 60 degrees scan, the beam is twice as wide as at broadside. Additionally, the element pattern (the individual antenna element's radiation pattern) rolls off at wide scan angles, reducing the peak gain. The combined effect is that a phased array at 60 degrees scan has a beam roughly 2 times wider and 3 to 4 dB less gain than at broadside.

What beamwidth do I need for my application?

For point-to-point microwave links, narrow beamwidth (0.5 to 2 degrees) concentrates energy on the far antenna and rejects multipath. For cellular base station sector antennas, 65 degrees horizontal and 7 to 15 degrees vertical covers one 120-degree sector. For satellite earth stations, the beamwidth must be narrow enough to avoid interference from adjacent satellites at 2-degree orbital spacing, requiring dishes 1.2 meters or larger at Ku-band. For radar search, wider beamwidth covers more sky per second but reduces detection range.

Antenna Technology

Beamwidth

Double the aperture size and the beam gets half as wide. That single relationship governs everything from the size of satellite dishes to the angular resolution of radar systems. Beamwidth, the angular spread of an antenna's main lobe, is inversely proportional to the aperture dimension measured in wavelengths. A 3-meter dish at 10 GHz produces a pencil beam just 0.7 degrees wide. The same dish at 1 GHz spreads to 7 degrees. This is why radar systems use the highest practical frequency for angular precision, and why 5G mmWave base stations need phased arrays with dozens of elements to steer a sufficiently narrow beam.

Category: Antenna Technology

Common Spec: HPBW (−3 dB beamwidth)

Formula: θ ≈ kλ/D

Narrower Beams from Larger Apertures

Half-power beamwidth for a uniformly illuminated circular aperture:
θ_3dB = 58.4° × λ/D (uniform)
θ_3dB = 70° × λ/D (tapered, typical parabolic dish)

Directivity from beamwidths:
D ≈ 41,253 / (θ_E × θ_H) (degrees)

Example: 1.2 m dish at 12 GHz (Ku-band, λ = 25 mm):
θ_3dB = 70 × 0.025 / 1.2 = 1.46°
D ≈ 41,253 / (1.46 × 1.46) = 19,350 = 42.9 dBi
Gain (at 60% efficiency) = 42.9 − 2.2 = 40.7 dBi

Beamwidth by Antenna Type

Antenna Type	Typical HPBW	Gain Range	Application
Dipole / monopole	78° (E-plane)	2 to 5 dBi	Omnidirectional coverage
Patch (single)	60 to 90°	5 to 8 dBi	WLAN, GPS, RFID
Sector (base station)	65°H, 7 to 15°V	15 to 18 dBi	Cellular sector coverage
Yagi-Uda	30 to 60°	8 to 15 dBi	Point-to-point, amateur
Horn (standard gain)	10 to 40°	10 to 25 dBi	Feed, measurement
Parabolic dish (1 m, 10 GHz)	2.1°	35 to 40 dBi	Microwave link, VSAT
Phased array (64 el, 28 GHz)	6 to 12°	25 to 30 dBi	5G mmWave base station

Common Questions

Frequently Asked Questions

How does beamwidth relate to gain?

D ≈ 41,253 / (θ_E × θ_H) in degrees. A 1.2 m Ku-band dish with 1.46° beamwidth has ~43 dBi directivity. Gain = directivity × aperture efficiency (typically 55 to 70%).

Why does phased array beamwidth change with scan?

Projected aperture shrinks by cos(θ), so beam broadens as 1/cos(θ). At 60° scan: 2× wider beam and 3 to 4 dB less gain than broadside. Element pattern rolloff adds additional loss.

What beamwidth for my application?

Point-to-point: 0.5 to 2°. Cellular sector: 65°H × 7 to 15°V. Satellite earth station: narrow enough for 2° orbital spacing (≥1.2 m at Ku). Radar search: wider = faster scan, narrower = longer range.

Related Terms

← Beam Squint Bessel Filter →

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