Phased array gain & scanning
A phased array forms a beam by combining many small radiating elements with controlled
phase. Adding elements raises the gain by 10·log₁₀(N), and steering the beam off broadside is
done electronically (no moving parts) by progressively phasing the elements.
Formulas used
Broadside gain: G₀ = G_element(dBi) + 10·log₁₀(N) − L_taper, N = N_x·N_y
Scan loss: ΔG = 10·log₁₀(cos θ_scan) (projected-aperture model; real arrays lose a little more from the element pattern)
Beamwidth: HPBW ≈ 0.886·λ / (N·d) at broadside, broadening as 1/cos θ when scanned
Grating lobes stay out of the visible region while sin θ_scan ≤ λ/d − 1;
with 0.5 λ spacing you can scan to the horizon without grating lobes.
This is a first-order model (uniform amplitude, ideal elements). All computation runs locally in your browser.