Explain the design principles of a phased array antenna system.

Phased array antennas electronically steer beams by controlling phase (and amplitude) of individual elements. Design principles: Element spacing typically λ/2 to avoid grating lobes; closer spacing for wider scan angles. Phase shift per element: Δφ = (2π/λ) × d × sin(θ), where d is spacing and θ is scan angle. Array factor multiplies element pattern for overall pattern; narrow beam with N elements has beamwidth ≈ λ/(Nd). Implementation uses: phase shifters (3-6 bit resolution for <1 dB loss), variable gain amplifiers, and calibration for manufacturing variations. Analog beamforming is lower cost; digital gives full flexibility; hybrid combines both. Challenges include beam squint with wideband signals, mutual coupling between elements, and scan blindness at certain angles.