Fraunhofer far-field criterion: R_ff = 2D²/λ, where D is the largest antenna dimension and λ = c/f (c = 299,792,458 m/s). R_ff is the standard first-pass estimate for minimum measurement test distance.
All unit inputs (mm, cm, m, in, ft for D; MHz/GHz for f) are converted to SI (meters, Hz) before calculation.
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The far field (Fraunhofer region) is where the radiation pattern is independent of distance from the antenna. In this region the wavefront is approximately planar. The Fraunhofer criterion (R_ff = 2D²/λ) gives the minimum distance at which measurements are typically made, where D is the largest antenna dimension and λ is the wavelength. This is a standard first estimate — actual far-field boundaries depend on antenna type and measurement requirements.
The Fraunhofer criterion defines the far-field boundary as R_ff = 2D²/λ, where D is the largest physical dimension of the antenna and λ = c/f is the free-space wavelength. It is derived from the condition that the maximum phase error across the antenna aperture is less than π/8 radians (22.5°). It is the standard used in antenna measurements per IEEE Std 149 and similar standards.
3λ is a rule-of-thumb boundary between the reactive near field (very close to the antenna) and the radiating near field (Fresnel region). 10λ is sometimes cited as a transition reference. Neither is equivalent to the Fraunhofer criterion, which accounts for the antenna size D. For an electrically large antenna (D >> λ), R_ff >> 10λ. These values are shown as context only.
The Fraunhofer criterion (R_ff = 2D²/λ) assumes a large, planar aperture. For electrically small antennas (D << λ), the formula yields a very small R_ff and the reactive near-field extent (approximately λ/2π) may dominate. The criterion also does not account for multipath, ground reflections, or the specific beam pattern of the antenna. For precise EMC or antenna pattern measurements, consult antenna-specific standards such as IEEE 149, ANSI C63.4, or CISPR standards.
An antenna is electrically small when its largest dimension D is much smaller than the wavelength λ — typically D < λ/10. Electrically small antennas have different near-field characteristics than aperture antennas, and the Fraunhofer criterion may not give a meaningful result. A dipole at HF frequencies or a small loop antenna at VHF are common examples.