How do antenna gain, directivity and efficiency differ?
Directivity D is the ratio of radiation intensity in a direction to the average over all directions. Gain G = er·D includes radiation efficiency; realized gain also includes mismatch: Grealized = (1 − |Γ|²)·G. Effective isotropic radiated power is EIRP = Pt + Gt − Lfeed in dB units.[1][2]
How is directivity estimated from beamwidths?
For a single main lobe, D ≈ 41,253/(θE·θH) with half-power beamwidths in degrees (Kraus’s approximation); practical estimates often use ~32,000–41,000 depending on sidelobes. For an aperture of physical area A and aperture efficiency eap: G = eap·4πA/λ².[2]
What is the difference between EIRP and ERP?
EIRP references an isotropic radiator; ERP references a half-wave dipole, so ERP = EIRP − 2.15 dB. Regulations specify one or the other; FCC Part 15 rules frequently limit conducted power and antenna gain, or EIRP.[3]
What gains are typical?
| Antenna | Typical gain |
|---|---|
| Short dipole | 1.76 dBi (directivity 1.5) |
| Half-wave dipole | 2.15 dBi |
| Chip antenna on small PCB | often below 0 dBi |
| Microstrip patch | ~5–8 dBi |
| Horn | 10–25 dBi |
| 1 m dish at 12 GHz (55% efficiency) | ~39 dBi |
Frequently asked questions
Can gain exceed directivity?
No; for passive antennas G ≤ D because efficiency ≤ 1.
Is dBd larger than dBi?
A value in dBd is 2.15 dB smaller than the same gain in dBi.
What is realized gain?
Gain reduced by impedance mismatch loss.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “IEEE Standard for Definitions of Terms for Antennas (IEEE Std 145)”. IEEE. 2013 revision.
- “Antenna Theory: Analysis and Design, 4th ed.”. C. A. Balanis, Wiley. 2016.
- “47 CFR Part 15: Radio Frequency Devices”. U.S. Federal Communications Commission, via eCFR. current.