array factor calculator - Aaron Graves, PhDude Replica

Uniform Linear Array Factor Calculator

Compute and visualize the normalized array factor for a uniformly excited linear antenna array.

Number of elements (N)

Element spacing (d/λ)

Progressive phase shift β (degrees)

Evaluation angle θ (degrees, 0 to 180)

Model assumes isotropic elements and uniform amplitude weighting.

Enter parameters and click Calculate Pattern.

What this array factor calculator does

This tool computes the normalized array factor of a uniform linear array (ULA). In practical terms, it helps you see how antenna elements combine to form a directional radiation pattern, and how that pattern changes with element count, spacing, and progressive phase shift.

If you work with phased arrays, beam steering, radar, wireless links, or signal processing, this gives a fast way to estimate where the main lobe points and how the sidelobes behave.

Formula used

For a uniform linear array of N elements with spacing d and progressive phase β:

ψ(θ) = 2π(d/λ)cos(θ) + β
AF(θ) = | sin(Nψ/2) / (N sin(ψ/2)) |

The calculator sweeps θ from 0° to 180°, normalizes by the maximum value, and then reports:

Array factor magnitude at your selected evaluation angle
Value in dB relative to the pattern maximum
Estimated main-beam direction
Approximate half-power beamwidth (HPBW)
Approximate peak sidelobe level outside the main lobe region

How to use the inputs

1) Number of elements (N)

Higher N usually means a narrower main beam and better angular resolution. But it also increases system complexity and feed network demands.

2) Element spacing (d/λ)

A common starting point is d = 0.5λ. Larger spacing can produce grating lobes, especially when scanning. Smaller spacing reduces grating lobe risk but can increase coupling and bandwidth constraints in real hardware.

3) Progressive phase shift (β)

This is the phase increment from one element to the next. Adjusting β steers the beam. A zero phase shift often yields broadside behavior in this coordinate convention.

4) Evaluation angle (θ)

Choose any angle from 0° to 180° to read the normalized field and dB level at that specific direction.

Interpreting the plot

Main lobe: strongest radiation direction.
Sidelobes: unwanted secondary peaks that can cause interference sensitivity.
Nulls: directions where the array response drops very low.
dB scale: 0 dB is the pattern maximum; negative values show attenuation from that peak.

Design tips for practical arrays

Start with N = 8 to 16 and d = 0.5λ for a balanced baseline.
Avoid aggressive spacing if you need wide-angle scanning.
Use tapering (Taylor, Chebyshev, etc.) if sidelobe suppression matters more than narrowest beamwidth.
Remember this calculator is the array factor only; real element patterns and coupling will modify results.

Assumptions and limitations

This page models ideal isotropic elements with uniform amplitude and no mutual coupling. In real antenna engineering, total pattern = element pattern × array factor, and feed errors can shift sidelobe levels. Use this as an excellent first-pass estimate, then validate with full-wave simulation or measurements.