How do I calculate the scan loss of a phased array as the beam is steered off boresight?
Scan Loss Analysis
The projected aperture effect is geometric: when viewed from the scanned beam direction, the array appears foreshortened by the factor cosθ₀. A 1m × 1m array scanned to 60° presents only a 0.5m × 1m effective aperture in the beam direction, reducing the gain by 3 dB (one dimension foreshortened). This effect is unavoidable for any planar array.
The element pattern factor further reduces the gain at wide scan angles. An ideal isotropic element would contribute no additional loss, but real elements have directional patterns that fall off at wide angles. A patch element pattern typically follows cos(θ) to cos^1.2(θ), adding 3 to 4 dB loss at 60° on top of the projected aperture loss.
For a well-designed phased array with moderate element directivity: total scan loss ≈ 10·log10(cos^n(θ₀)), where n = 1.3 to 1.8. Military radar specifications typically require the array to maintain acceptable performance to ±60°, accepting 4-6 dB scan loss. The system design must budget for this loss in the link equation.
Frequently Asked Questions
Can I compensate for scan loss?
Partially. Increase the transmitted power at wide scan angles (if the T/R modules have sufficient power margin). Use amplitude taper adjustment to optimize gain at the scanned angle. For receive: reduce the noise figure at wide scan angles (lower temperature LNA). None of these compensate for the fundamental projected aperture reduction.
Does scan loss affect beamwidth?
Yes. The beamwidth broadens as 1/cosθ₀ in the scan plane. At 60° scan: the beamwidth is approximately twice the broadside value. In the orthogonal plane, the beamwidth is unchanged. This beam broadening reduces the angular resolution at wide scan angles.
What about conformal arrays?
Conformal arrays wrapped around a curved surface can partially mitigate scan loss by selecting active elements on the side of the surface facing the desired beam direction. A cylindrical array providing 360° azimuthal coverage does not suffer from the progressive scan loss because different elements are activated for different beam directions.