Transient Behavior of Aperture Antennas

The transient behavior of aperture antennas is analyzed. For an antenna which is illuminated by a field of uniform phase and either uniform or cosine tapered amplitude, it is shown that the steady-state main lobe is established within (τ/,sub>2+R/c) seconds after the aperture is energized. τ is the period of the carrier frequency, R is the distance from the center of the aperture to the point where the field is evaluated, and c is the velocity of light. The time required for the establishment of the steady-state pattern at all angles between 0° and 90° is (τ/2θ
₀
+R/c) where 2θ
₀
radians is the beamwidth between first nulls of the steady-state pattern (θ
₀
<
_l
). An antenna may be useful, however, before (τ/2θ
₀
+R/c) seconds, because the maxima of the transient sidelobes are not higher than the maxima of the steady-state sidelobes. The requirement that the steady-state pattern be established at all angles between 0° and 90° leads to a limitation on range discrimination ΔR and angular discrimination Δθ for a pulse radar ΔRΔθ=λ, where λ is the wavelength of the carrier frequency. For a scanning antenna employing linear phase variation over the aperture, it is shown that the main lobe, located at an angle θ
_max
, is established within a time (τ/
₂
+ R/c + a sin θ
_max
/
₂
c) measured from the instant at which one edge of the aperture is first energized. The quantity a is the dimension of the aperture in the plane in which the field is evaluated.