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What is antenna directivity?

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Directivity is the ratio of the radiation intensity in a given direction to the radiation intensity averaged over all directions, D = 4πU(θ,φ)/Prad; when no direction is specified, the maximum is implied.[1] It depends only on the shape of the pattern, not on losses, and is expressed in dBi relative to an isotropic radiator.[2]

How is directivity calculated?

With the normalized power pattern F(θ,φ), D0 = 4π/ΩA, where ΩA = ∬F(θ,φ) sinθ dθ dφ is the beam solid angle.[2] An isotropic antenna has ΩA = 4π sr and D = 1 (0 dBi); a Hertzian dipole has D = 1.5; a half-wave dipole 1.64 (2.15 dBi).

How can directivity be estimated from beamwidths?

For a single narrow main beam with half-power beamwidths θ1 and θ2 in degrees, Kraus’s approximation is D ≈ 41,253/(θ1θ2), and Tai and Pereira’s is D ≈ 72,815/(θ1²+θ2²).[3][2] Because practical antennas waste power in sidelobes, many engineers use about 26,000–32,000/(θ1θ2) as a realistic gain estimate.[4]

What are typical directivities?

AntennaDirectivity
Isotropic0 dBi
Hertzian / small loop1.76 dBi
Half-wave dipole2.15 dBi
λ/4 monopole on infinite ground5.16 dBi
Microstrip patch≈ 6–9 dBi
Standard gain horn10–25 dBi
1 m dish at 12 GHz≈ 40 dBi

Values from Balanis and Stutzman; patch and horn ranges depend on substrate and size.[2][4]

What limits directivity for a given size?

For a uniformly illuminated aperture of area A, Dmax = 4πA/λ². Higher “superdirective” values are possible in theory but require large, rapidly oscillating currents with extremely high Q and loss, so they are impractical.[5]

Frequently asked questions

Is directivity the same as gain?

No. Gain equals directivity multiplied by radiation efficiency.

What does dBi mean?

Decibels relative to an isotropic radiator.

Can directivity be less than 1?

Peak directivity cannot; directivity in a particular direction (e.g., a null) can be far below 1.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

  1. “IEEE Standard for Definitions of Terms for Antennas (IEEE Std 145-2013)”. IEEE Antennas and Propagation Society. 2014.
  2. “Antenna Theory: Analysis and Design, 4th ed.”. C. A. Balanis, Wiley. 2016.
  3. “Antennas for All Applications, 3rd ed.”. J. D. Kraus and R. J. Marhefka, McGraw-Hill. 2002.
  4. “Antenna Theory and Design, 3rd ed.”. W. L. Stutzman and G. A. Thiele, Wiley. 2012.
  5. “Electrically Small, Superdirective, and Superconducting Antennas”. R. C. Hansen, Wiley. 2006.
Categories: Fundamentals