Uniform Linear Antenna Array Calculator
Estimate core design values for a uniformly excited linear antenna array: wavelength, physical length, beamwidth, steering phase shift, and grating-lobe risk.
What this antenna array calculator does
This calculator is built for fast, practical sizing of a uniform linear antenna array (ULA). If you are designing beamforming systems for wireless links, radar prototypes, Wi-Fi experiments, satellite terminals, or phased-array education projects, it helps you get the first-order numbers immediately.
Instead of manually working through wavelength, phase progression, and beamwidth equations every time you change frequency or spacing, you can adjust a few inputs and instantly compare designs.
Inputs and outputs explained
Inputs
- Operating Frequency: Sets wavelength and therefore all geometry scaling.
- Number of Elements (N): More elements usually mean higher directivity and a narrower beam.
- Element Spacing: Enter in either wavelengths or meters.
- Steering Angle: Beam steering angle measured from broadside (0° = broadside).
- Observation Angle: Used to evaluate normalized array factor at one direction.
Main outputs
- Wavelength in meters
- Actual spacing in meters and wavelengths
- Total array length
- Progressive phase shift between elements
- Approximate HPBW and FNBW
- Rough directivity estimate
- Grating-lobe warning based on scan angle and spacing
Core formulas used
The calculator uses standard first-order ULA relations:
- Wavelength: λ = c / f
- Array length: L = (N − 1)d
- Progressive phase shift: β = −360° · (d/λ) · sin(θscan)
- Approx. HPBW (broadside reference): 50.8 / (N·d/λ) degrees
- Approx. FNBW: 114.6 / (N·d/λ) degrees
- Normalized array factor: |sin(Nψ/2)/(N sin(ψ/2))| with ψ = 2π(d/λ)(sinθ − sinθscan)
These are excellent for quick trade studies. For production arrays, include element pattern, mutual coupling, finite ground effects, losses, and true taper weights.
Design guidance for better arrays
1) Keep spacing around 0.5λ when possible
A spacing near half-wavelength is a common sweet spot. It gives good aperture growth while reducing grating-lobe risk across moderate scan angles.
2) Watch scan-angle limits
As you steer farther off broadside, the main beam broadens and sidelobe behavior changes. If spacing is large, steering can create strong grating lobes that compete with your intended beam.
3) Use tapering when sidelobes matter
Uniform excitation is simple and efficient but tends to produce higher sidelobes. If interference rejection is important, amplitude tapers (Taylor, Chebyshev, etc.) can help at the expense of wider beamwidth.
Quick worked example
Suppose you choose 2.4 GHz, 8 elements, and 0.5λ spacing. You will get:
- λ ≈ 0.125 m
- d ≈ 0.0625 m
- Total length ≈ 0.4375 m
- Narrower beam than a 4-element version at the same spacing
If you then scan to 30°, the required inter-element phase shift increases in magnitude and grating-lobe margin tightens, especially if spacing is pushed above 0.5λ.
Limitations to remember
This tool is intended for fast calculation and learning. It does not replace full-wave electromagnetic simulation, measured calibration, or complete phased-array link-budget analysis. Still, for architecture decisions and sanity checks, it is highly effective.