Many Elements, One Beam
A single antenna element has limited directivity. By arranging many elements in a regular array and controlling their relative phases, engineers create antenna systems with extraordinary capabilities: narrow beams, high gain, and the ability to steer and reshape the beam electronically in microseconds. Phased arrays have revolutionized radar, communications, and radio astronomy since their development during World War II.
The Array Factor
The beauty of array theory lies in pattern multiplication: the total radiation pattern equals the element pattern times the array factor. The array factor depends only on geometry (number of elements, spacing) and excitation (amplitude and phase weights). For a uniform linear array with progressive phase shift β, the array factor has a characteristic sinc-like shape with a main beam and sidelobes, whose positions are entirely determined by the spacing-to-wavelength ratio and β.
Beam Steering Without Motion
By applying a linear phase gradient across the array elements, the direction of constructive interference tilts away from broadside. A positive phase gradient steers the beam one way; a negative gradient steers it the other. Modern arrays use digital phase shifters with sub-degree resolution, enabling precise beam pointing. 5G base stations steer hundreds of beams simultaneously to serve individual users — a technique called massive MIMO.
Grating Lobes & Design Limits
If element spacing exceeds one wavelength, additional directions of constructive interference appear — grating lobes that waste power and cause interference. The maximum scan angle without grating lobes constrains the spacing to d < λ/(1+sinθ_max). This tradeoff between scan range and element density determines the number of elements (and cost) required for a given performance specification, making array design a fascinating optimization challenge.