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Antenna Parameters: Gain, Directivity and Efficiency

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Antenna parameters describe how an antenna radiates: directivity measures concentration of power in the best direction versus spreading it evenly, gain is directivity reduced by the antenna's own losses, and efficiency is the fraction of input power actually radiated. Together they answer: for one watt in, how much power heads toward the receiver?

Every link budget, coverage plan and regulatory limit uses them. Base stations are chosen by gain and beamwidth, dishes by gain, and regulators cap EIRP (effective isotropic radiated power), not raw transmitter power. Read gain, efficiency and pattern off a datasheet and you can predict real range.

Key Concepts

  • Radiation pattern: 3D plot of power vs direction, with main lobes, side lobes and nulls.
  • Isotropic radiator: hypothetical equal-in-all-directions antenna; the 0 dBi reference.
  • Directivity D: peak radiation intensity over the average; depends only on pattern shape.
  • Efficiency: radiated / input power; losses come from conductor resistance and dielectric heating.
  • Gain G: efficiency x directivity; the measured, datasheet-quoted number in dBi.
  • EIRP: transmit power x antenna gain; the power an isotropic antenna would need for the same peak intensity.
  • Half-power beamwidth: angular width where power halves (-3 dB); narrower beam means higher gain.

Formulas

  • Directivity: D = 4 x pi x U_max / P_rad (U_max = peak intensity in W/steradian, P_rad = total radiated power).
  • Gain: G = efficiency x D; G(dBi) = 10 log_10(G).
  • EIRP: EIRP = P_t x G_t; in dB: EIRP(dBm) = P_t(dBm) + G_t(dBi).
  • dBi vs dBd: G(dBi) = G(dBd) + 2.15 (dipole reference).
  • Assumptions: far field, matched polarization, gain in the peak direction at the operating frequency.

Worked Example

Wi-Fi access point: P_t = 1 W into a 10 dBi antenna. Find linear gain and EIRP:

  1. Linear gain = 10^(10/10) = 10.
  2. EIRP = 1 W x 10 = 10 W; in dB: 30 dBm + 10 dBi = 40 dBm.
  3. Check: 40 dBm = 10,000 mW = 10 W. In its beam peak this 1 W radio looks like a 10 W isotropic radiator, exactly what a 40 dBm EIRP limit permits.

Common Misconceptions

  • "High gain amplifies." Antennas are passive; gain concentrates the same power into a narrower beam, like a flashlight reflector. Power is redirected, never created.
  • "dBi equals dBd." They differ by 2.15 dB; always check the reference.
  • "Higher gain is always better." Higher gain means a narrower beam, bad for wide-area coverage or moving users; sector antennas trade gain for beamwidth deliberately.

Real-World Applications

  • Cellular sectors: ~15-18 dBi gain, 65-degree beamwidth covering hexagonal cells.
  • Satellite dishes: 30-50 dBi gains enabling intercontinental links.
  • Wi-Fi routers: 2-5 dBi omnidirectional antennas balancing range and room coverage.
  • Radar: very high gain narrow beams detecting distant targets.

Directivity describes pattern concentration, efficiency accounts for losses, and gain is their product: the number in every link budget. EIRP folds transmit power and gain into the quantity regulators limit. Choose gain for reach, beamwidth for coverage, and never mistake passive gain for amplification.

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