Guide✕ Getting started in 30 seconds Pick a scenario at the top right, or set the number of elements and the array spacing. Click in the u-v map to steer the active beam. Add more beams with “+ Add a beam”: they are transmitted simultaneously. Tune the patch (frequency, substrate, dimensions, feed) and watch the impedance, S₁₁ and gain. Watch the wave propagate in the vertical cut; hover over it to probe E, H and the power density. Reading the views 3D patternRadius and colour give the level in dB in every direction of the half-space above the array. u-v spaceThe pattern seen from above: u = sinθ·cosφ, v = sinθ·sinφ. The centre is the array normal (θ = 0), the rim is the horizon (θ = 90°). ExcitationEach patch drawn to scale. Hue encodes the feed phase, opacity the amplitude. Vertical cutCoherent sum of the waves emitted by every element. E(t) and H(t) are animated; in the far zone H = E / 377 Ω and is perpendicular to E. Pattern cutLevel versus θ in the vertical plane containing the active beam. Physical model PatchWidth W = c / (2f) · √(2 / (εr + 1)), effective permittivity εeff, fringing extension ΔL (Hammerstad), length L = c / (2f·√εeff) − 2ΔL. ImpedanceRedge = 1 / (2·(G₁ + G₁₂)), then Rin = Redge·cos²(π·y₀ / L) for a feed inset at y₀. Around resonance: parallel RLC resonator whose Q is derived from the bandwidth. Element|E|² ∝ sinc²(k·W·v / 2) · cos²(k·Leff·u / 2) · (1 − v²). Arraywmn = am·an · Σb Ab·exp(−j·k·(xm·ub + yn·vb)): each beam contributes its own phase gradient, and the weight sets add up. DirectivityD = 4π·Pmax / ∬ P·sinθ dθ dφ, integrated numerically. Realized gain = D · (1 − |S₁₁|²). Limitations to keep in mind No mutual coupling between patches, no surface waves, infinite ground plane. Dielectric and conductor losses are ignored: “realized gain” only accounts for mismatch. The probe's E / H / S values are calibrated on the far field; very close to the array they are indicative only.