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PolskiPhased Array Antenna: Beam Steering & Grating Lobes (2D)
2D phased-array antenna lab: set element count, spacing and per-element phase to steer a real array-factor radiation beam, watch its interference wavefield, and see grating lobes appear past λ/2 spacing.
This 2D companion computes the real array-factor mathematics behind a phased array — N point sources on a line, each fed with a progressive phase offset — instead of a decorative dashboard: drag the element count, spacing and steering-angle sliders and watch the interference wavefield tilt its main lobe electronically, the polar radiation pattern update from the exact |AF(θ)| formula, and grating lobes appear the moment spacing pushes past half a wavelength, exactly as it happens in real radar and 5G beamforming arrays.
2D phased-array antenna lab computing the exact array-factor AF(θ) = Σ w[n]·exp(j·n·2π·(d/λ)·(sinθ−sinθ₀)) for N synchronized point sources, rendering both the near-field interference wavefield and the far-field polar radiation pattern live as element count, spacing and steering angle change.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install
Each element radiates the same signal but with a slightly different phase. Off the array's broadside, the extra path length one element's wave travels compared to its neighbor is compensated by that phase offset, so all N wavefronts arrive in-phase at the new steering angle — the constructive-interference direction moves electronically, with no moving parts.
When element spacing exceeds about half a wavelength, the array-factor equation has more than one angle where all elements line up in phase — a second, equally strong beam appears (a grating lobe). In radar or wireless systems this wastes transmitted power and creates ambiguous or interfering directions, so real arrays are usually built with d ≤ λ/2 when wide steering range is required.
Feeding the edge elements less strongly than the center ones (here a raised-cosine/Hann taper) suppresses the sidelobes of the radiation pattern at the cost of a wider main beam — the same tradeoff used to design low-sidelobe radar and communication antennas.