Phased Array Antenna Simulator: Beam Steering & Radiation Patterns

simulator advanced ~12 min
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θ₃dB ≈ 6.3° — 16-element uniform array at broadside

A 16-element array with half-wavelength spacing at broadside produces a 6.3° beamwidth with -13.3 dB first sidelobes. Steering to 30° broadens the beam to 7.3° and shifts the pattern accordingly.

Formula

AF(θ) = Σ aₙ·exp(j·n·2π·d/λ·(sin(θ) - sin(θ₀)))
θ₃dB ≈ 0.886·λ / (N·d·cos(θ₀))
sin(θ_grating) = sin(θ₀) ± m·λ/d

Electronic Beam Steering

Phased array antennas revolutionized radar by replacing mechanical dish rotation with electronic beam steering. By controlling the phase of each radiating element, the combined beam can be pointed in any direction within microseconds — thousands of times faster than a rotating antenna. This enables modern radars to track hundreds of targets simultaneously, interleave search and track modes, and rapidly adapt to changing threats.

Array Factor and Pattern Synthesis

The radiation pattern of a phased array is the product of the individual element pattern and the array factor — a function determined by the number of elements, their spacing, and their excitation weights. For a uniform linear array, the array factor produces a sinc-like pattern with a main beam whose width scales inversely with the array length (Nd). Side lobes at -13.3 dB for uniform weighting can be suppressed using amplitude tapering at the cost of slightly broader beamwidth.

Grating Lobes and Element Spacing

The most critical design parameter is element spacing relative to wavelength. When d > λ/2, the array factor has additional maxima (grating lobes) at angles where the path difference between elements is a full wavelength. These spurious beams waste power and create ghost targets. The constraint d ≤ λ/(1 + |sin(θ_max)|) ensures no grating lobes within the scan volume, effectively requiring d ≤ λ/2 for ±90° scanning.

Modern Phased Array Systems

Today's active electronically scanned arrays (AESAs) integrate a transmit/receive module at each element, enabling per-element amplitude and phase control, waveform diversity, and graceful degradation if modules fail. Systems like the AN/SPY-6, AN/APG-81, and Patriot radar use thousands of elements to achieve simultaneous multi-function operation — tracking, searching, missile guidance, and electronic warfare — all from a single aperture.

FAQ

What is a phased array antenna?

A phased array is an antenna composed of multiple radiating elements whose signals are combined with electronically controlled phase shifts. By adjusting the phase of each element, the beam can be steered without physically moving the antenna. This enables rapid beam scanning (microseconds vs seconds for mechanical systems), multiple simultaneous beams, and adaptive nulling of interference.

How does beam steering work?

Each element's phase is set so that signals arriving from the desired direction add constructively (in phase). For a linear array with spacing d, steering to angle θ₀ requires a progressive phase shift of Δφ = 2π·d·sin(θ₀)/λ between adjacent elements. The combined array factor produces a narrow beam in the desired direction.

What are grating lobes?

Grating lobes are additional main beams that appear when element spacing exceeds λ/2. They occur at angles where the path difference between adjacent elements equals an integer number of wavelengths. Grating lobes waste transmit power and create ambiguous target angles, so most arrays maintain d ≤ λ/2.

How does tapering reduce sidelobes?

Amplitude tapering applies a window function (like Hamming, Taylor, or Chebyshev) across the array, reducing the amplitude of edge elements relative to the center. This reduces sidelobes at the cost of broader main beam and lower gain. A 25 dB Taylor taper, for example, achieves -25 dB sidelobes with only ~12% beam broadening.

Sources

Embed

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