Rectangular aperture antenna far-field calculation
A uniformly illuminated rectangular aperture produces a directional far-field pattern governed by sinc factors in its principal dimensions. The field also scales with aperture area and decreases inversely with observation distance.
This calculator evaluates a simplified magnitude model and checks the common Fraunhofer far-field boundary. It is useful for study and preliminary comparison, not a replacement for full-wave simulation or calibrated measurements.
How to use the aperture antenna calculator
- Enter aperture conditions: Provide peak aperture field, width, height, and wavelength in metres.
- Set the observation point: Enter distance and angular direction θ and φ.
- Calculate the field: Generate the far-field magnitude and review any boundary warning.
- Check model suitability: Use a full electromagnetic model when illumination, polarization, or near-field effects matter.
Formula and variables
The simplified far-field magnitude uses X = (πa/λ)sinθ cosφ and Y = (πb/λ)sinθ sinφ, with sinc(u) = sin(u)/u.
|E| = E₀ab/(λr) · |sinc(X)sinc(Y)|- E₀ — Peak aperture field
- Uniform electric-field magnitude across the aperture (V/m)
- a, b — Aperture dimensions
- Rectangular width and height (m)
- λ — Wavelength
- Free-space wavelength (m)
- r — Distance
- Distance from aperture to observation point (m)
- θ, φ — Observation angles
- Spherical direction angles (degrees)
Rectangular aperture example
A 0.10 m by 0.05 m aperture with E₀ = 10 V/m radiates at λ = 0.03 m. Find the field 100 m away at θ = 30° and φ = 0°.
- E₀
- 10 V/m
- Dimensions
- 0.10 m × 0.05 m
- λ and r
- 0.03 m and 100 m
- X = (π × 0.10 / 0.03)sin30° = 5.236
- Y = 0 when φ = 0°
- |E| ≈ 2.75665 × 10⁻³ V/m
Result: The estimated field magnitude is approximately 0.00275665 V/m.
The off-axis sinc factor reduces the field relative to the aperture boresight direction.
Understanding your results
Pattern and distance
Nulls and sidelobes occur where the sinc factors change magnitude. Field magnitude decreases approximately as 1/r in the far field.
- A boundary warning means the far-field approximation may be unreliable.
- The displayed value is magnitude and does not preserve phase or polarization.
Assumptions
- Uniform aperture illumination and a rectangular planar aperture.
- Free-space propagation and a far-field observation point.
- The simplified scalar magnitude model is adequate.
Limitations
- Does not include aperture efficiency, phase taper, polarization mismatch, losses, reflections, or mutual coupling.
- Near-field points require a more complete field integral.
Common mistakes
- Entering frequency instead of wavelength.
- Using centimetres where metres are expected.
- Treating the model as valid inside the Fraunhofer boundary.
- Mixing angle conventions.
Practical use cases
Preliminary antenna analysis
Compare aperture dimensions, wavelength, direction, and distance before detailed simulation.
Engineering education
Explore how sinc-pattern nulls arise from a rectangular aperture.
Frequently asked questions
What far-field distance does the calculator check?
It uses the common estimate r ≥ 2D²/λ, where D is the larger aperture dimension.
Why does the field decrease with distance?
In the radiation zone, field amplitude falls approximately as 1/r while power density falls approximately as 1/r².
Does this calculate received power?
No. Received power also requires receiving-antenna gain or effective area, polarization, impedance, and system losses.
Sources and review
- Antenna Theory: Analysis and Design — Wiley. Accessed 2026-07-13.
- IEEE Standard for Definitions of Terms for Antennas — IEEE Standards Association. Accessed 2026-07-13.
Reviewed 2026-07-13.