Phased Array Scanning Angle Calculator
Computes the steering phases βx and βy, beam deviation, and grating-lobe-safe scan range for a rectangular planar array.
Inputs
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Scan Diagram & Theory
Planar Array with Scan Direction
Key Equations
Wavelength: λ = c / f
Progressive phase shifts:
βx = −k·dx·sinθ₀·cosφ₀
βy = −k·dy·sinθ₀·sinφ₀
k = 2π/λ
Phase per element:
ϕ(m,n) = m·βx + n·βy
Grating-lobe-safe scan:
dx ≤ λ / (1 + |sinθ₀ cosφ₀|)
dy ≤ λ / (1 + |sinθ₀ sinφ₀|)
Beam Deviation Error (BDE): BDE ≈ sinθ − sinθ₀ (from projection effects)
Glossary
- βx, βy – required progressive phase shifts (rad)
- θ₀, φ₀ – desired steering angles
- k – wavenumber 2π/λ
- ϕ(m,n) – phase applied to each element