Phased Array: The Physics of "Electronic Steering"
How changing Time (Phase) changes Direction (Angle).
The Visual Derivation
1. Path Difference (Extra distance traveled):
δ = d · sin(θ)
2. Phase to Distance Ratio:
Δφ / 2π = δ / λ
3. Solve for Steering Angle (θ):
θ = arcsin( λ·Î”φ / 2Ï€d )
Intuition: If you increase the Phase Delay (Δφ), the wave from the next antenna starts "late," which tilts the whole wavefront.