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Antenna Far-Field Boundary Checker

Calculate the Fraunhofer distance from frequency and antenna size, then check measurement-distance margin.

FORMULAv1.0.0
INPUT PARAMETERS

Check the Fraunhofer far-field boundary

Calculate 2D²/λ from antenna dimension D and frequency, then check the current measurement distance.

CALCULATION RESULT

Calculation result

Calculated locally
∿

Enter the parameters and run the calculation to see results and model assumptions here.

FORMULA & TRACEABILITY

Formulas and applicability

Formulas, variables, and model boundaries are published. References last reviewed on 2026-08-30.

3 formulas · 2 references
CORE EQUATIONS

Core equations

These equations directly produce the primary results and define the tool’s core model.

1
F02

Fraunhofer far-field boundary

rFF = 2D² / λ

Common far-field starting distance; the center-to-edge spherical-wavefront phase difference is about π/8 at this distance.

rFF
Fraunhofer distancem
D
Maximum dimension enclosing the radiating structurem
Applicability
  • D is the maximum aperture or maximum dimension enclosing the radiating structure
  • Precision measurements may require a distance greater than 2D²/λ
DERIVED & CONVERSION

Derived and conversion equations

Derive units, levels, and supporting engineering quantities from the core values.

1
F01

Free-space wavelength

λ = c / f

Calculate free-space wavelength from frequency as the basis of the far-field boundary.

λ
Free-space wavelengthm
c
Speed of light in vacuumm/s
f
FrequencyHz
Applicability
  • Free-space or air approximation
BOUNDARIES & RULES

Boundary and rule equations

Check model applicability, measurement conditions, and regulatory rules.

1
F03

Measurement-distance margin

M = rmeasurement / rFF

M ≥ 1 reaches the geometric 2D²/λ boundary, but does not automatically prove all test requirements are met.

M
Far-field distance ratio1
Applicability
  • Also check site effects, reflections, dynamic range, and the standard method
REFERENCES

References

01NIST · NIST Technical Note 2159Laboratory Method for Recording AWS-3 LTE Waveforms2021 · The appendix uses d = 2D²/λ to assess the Fraunhofer far-field condition for antenna measurements.
02NIST · Modern Antenna Handbook, Chapter 19Near-Field Scanning Measurements: Theory and Practice2008 · Explains far-field division using nD²/λ, typically n = 2, with larger values possible for precision measurement.
Engineering use notice

Results use the models and assumptions shown on this page for design estimates and pre-compliance risk review. Complex structures, dispersion, near-field coupling, and test setup can cause significant deviation.

FAQ

Frequently asked questions

What is the far-field (Fraunhofer) boundary formula?

d_F = 2D² / λ, where D is the maximum radiating dimension. Engineering practice also adds d ≫ D and d ≫ λ, taking the largest of the three as the far-field start.

When does a 3 m chamber violate the far field?

For a 1 m EUT at 1 GHz, 2D²/λ ≈ 6.7 m > 3 m, so a 3 m measurement is inside the radiating near field—distance normalization and antenna-factor validity degrade.

What does an unmet far-field condition mean?

Antenna-factor calibration conditions and inverse-distance normalization no longer strictly apply, and measurement uncertainty grows. Precision work may require nD²/λ (n > 2) or a larger distance.

PRE-COMPLIANCE SUPPORT

Need accredited testing or pre-compliance support?

These tools support design-stage estimates. For accredited EMC testing, compliance decisions, and troubleshooting, contact us.

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