What are the three antenna field regions?

The electromagnetic field around an antenna is divided into three concentric regions. The reactive near field extends from the antenna surface to approximately lambda/(2*pi), or about 0.16 times lambda. In this region, the electric and magnetic fields are 90 degrees out of phase (reactive), energy oscillates back and forth between the field and antenna rather than radiating, and the field decreases rapidly (1/r^2 or 1/r^3). The radiating near field (Fresnel region) extends from the reactive boundary to 2*D^2/lambda. Here, the fields are radiating (real power flow), but the angular pattern depends on distance because different parts of the aperture contribute with varying phase relationships. The far field (Fraunhofer region) extends beyond 2*D^2/lambda to infinity. The pattern shape is fixed, E and H are orthogonal and transverse, and power density decreases as 1/r^2.

Why can't you measure antenna patterns in the near field directly?

In the near field, the angular field distribution changes with distance because different parts of the antenna aperture are at significantly different distances from the measurement point. The phase variation across the aperture means that the radiation contributions from different parts of the antenna interfere differently at each measurement distance, producing a pattern that depends on both angle and distance. However, near-field measurement techniques allow accurate far-field pattern determination by measuring the near field on a known surface (planar, cylindrical, or spherical) and computing the far field using a Fourier transform or spherical wave expansion. Planar near-field scanning at distance 3 to 10 lambda from the antenna can determine the far-field pattern with accuracy better than plus or minus 0.5 dB for the main beam and plus or minus 1 dB for sidelobes. This is essential for large antennas and phased arrays where far-field measurement would require impractically long ranges.

Antenna Radiation

Far Field

Q: What is the far-field distance formula?

The far-field distance (Fraunhofer distance) is d_ff = 2*D^2 / lambda, where D is the largest antenna dimension and lambda is the wavelength. This ensures the maximum phase error across the antenna aperture is less than pi/8 (22.5 degrees) when viewed from the measurement point. For a 1 meter dish antenna at 10 GHz (lambda = 3 cm): d_ff = 2 times 1^2 / 0.03 = 66.7 meters. For a 0.5 meter 5G NR antenna array at 28 GHz (lambda = 10.7 mm): d_ff = 2 times 0.5^2 / 0.0107 = 46.7 meters. For a mobile phone antenna (D = 0.15 m) at 2 GHz (lambda = 0.15 m): d_ff = 2 times 0.15^2 / 0.15 = 0.3 meters. This formula applies when D is much larger than lambda (D greater than 2.5 lambda). For electrically small antennas (D less than lambda), the minimum far-field distance is approximately 2 times lambda.

/fahr feeld/ — Fraunhofer Region

The radiation region where the angular field distribution is distance-independent. Far-field boundary: d_ff = 2D²/λ. Beyond this distance: E and H orthogonal, power density ∝ 1/r², antenna gain and pattern are well-defined. Three regions: reactive near field (<λ/2π), radiating near field (Fresnel, <2D²/λ), far field (>2D²/λ). Near-field scanning + Fourier transform enables far-field pattern computation from compact ranges.

Boundary: 2D²/λ

Power: ∝ 1/r²

Phase err: <π/8

Understanding the Far Field

The concept of far field is essential to antenna engineering because it defines the conditions under which antenna performance specifications (gain, pattern, polarization, efficiency) are valid and measurable. All antenna datasheets specify these parameters for far-field conditions. If you measure an antenna in the near field and interpret the results as far-field data, the gain, beamwidth, and sidelobe levels will all be wrong.

The far-field distance increases with both antenna size and frequency. A 1-meter satellite dish at 10 GHz requires 67 meters of clear range. A 5G mmWave antenna array at 28 GHz with 0.5 m aperture needs 47 meters. These distances create practical challenges: outdoor far-field ranges are expensive, weather-dependent, and subject to ground reflections. Compact antenna test ranges (CATR) use a parabolic reflector to create a plane wave in a shorter distance, and near-field scanning chambers measure the complete near field and compute the far-field pattern mathematically.

Far-Field Equations

Far-field distance:
d_ff = 2D²/λ (meters)
Phase error < π/8 across aperture

Example calculations:
1 m dish @ 10 GHz (λ=3 cm):
d_ff = 2×1/0.03 = 66.7 m
0.5 m array @ 28 GHz (λ=10.7 mm):
d_ff = 2×0.25/0.0107 = 46.7 m

Field region boundaries:
Reactive: r < λ/(2π) ≈ 0.16λ
Fresnel: 0.62√(D³/λ) < r < 2D²/λ
Far field: r > 2D²/λ

Power density (far field):
S = P_tG_t/(4πr²) W/m²
Decreases as 1/r² (inverse square)

Antenna Field Region Examples

Antenna	D	Frequency	Reactive NF	Far Field
Cell phone	0.15 m	2 GHz	0.024 m	0.3 m
BTS panel	1.3 m	1.8 GHz	0.027 m	20.3 m
Satellite dish	1.0 m	12 GHz	0.004 m	80 m
5G mmWave	0.1 m	28 GHz	0.0017 m	1.87 m
Radar array	3.0 m	10 GHz	0.005 m	600 m

Common Questions

Frequently Asked Questions

What is the far-field distance formula?

d_ff = 2D²/λ. Ensures <π/8 phase error across aperture. 1 m dish at 10 GHz: 67 m. 0.5 m array at 28 GHz: 47 m. Phone antenna at 2 GHz: 0.3 m. For D<λ: minimum d_ff ≈ 2λ. Larger aperture or higher frequency = longer far-field distance.

What are the three field regions?

Reactive near field: r < λ/2π (≈0.16λ). E, H 90° out of phase, energy oscillates, fields decrease as 1/r² or 1/r³. Fresnel (radiating near field): fields radiate but pattern depends on distance. Far field (Fraunhofer): pattern fixed, E⊥H, S ∝ 1/r², gain/pattern measurable.

Why not measure patterns in near field?

Near-field pattern changes with distance (aperture phase variation). But near-field scanning + Fourier transform computes far-field pattern from compact measurements. Planar NF scanning at 3-10λ: accuracy ±0.5 dB main beam, ±1 dB sidelobes. Essential for large antennas where far-field range is impractically long (radar: 600 m).

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