Directivity vs. Gain
Directivity compares radiation intensity in the strongest direction with an isotropic radiator. Gain reduces directivity by antenna efficiency.
G = ηD
G(dBi) = D(dBi) + 10 log10(η)
A 12 dBi directivity with 70% efficiency produces about 10.45 dBi gain.
Beamwidth Approximation
A common estimate uses horizontal and vertical half-power beamwidths in degrees.
D ≈ 41,253 ÷ (HPBWaz × HPBWel)
This cannot describe sidelobes, backlobes, nulls, asymmetry, or pattern distortion. Full directivity requires integration of the three-dimensional pattern.
Array Factor
For an ideal uniform linear array, phase differences determine whether fields reinforce or cancel at an observation angle. The array factor excludes the pattern of each element and practical coupling effects.
Spacing larger than 0.5 wavelength can produce visible grating lobes for some steering conditions. Wide scanning may require smaller spacing.
Use simulated or measured element and array patterns for coverage, compliance, or hardware decisions.