Page 47 - Fundamentals of Radar Signal Processing

= sinθ can only range from –1 to +1. Because of this, is zero outside of this
range on s.
Equation (1.5) is a somewhat simplified expression that neglects a range-
dependent overall phase factor and a slight amplitude dependence on range
(Balanis, 2005). This Fourier transform property of antenna patterns will, in

Chap. 2, allow the use of linear system concepts to understand the effects of the
antenna on cross-range resolution and the pulse repetition frequencies needed to
avoid spatial aliasing.
An important special case of Eq. (1.5) occurs when the aperture current
illumination is a constant, A(y) = A . The normalized far-field voltage pattern is
0
then the familiar sinc function,

(1.8)

If the aperture current illumination is separable, then the far-field is the product
of two Fourier transforms, one in azimuth (θ) and one in elevation (ϕ).
The magnitude of E(θ) is illustrated in Fig. 1.6, along with the definitions
for two important figures of merit of an antenna pattern. The angular resolution

of the antenna is determined by the width of its mainlobe, and is conventionally
expressed in terms of the 3-dB beamwidth. This can be found by setting
and solving for the argument α = π(D /λ) sinθ. The answer can be
y
found numerically to be α = 1.4, which gives the value of θ at the –3-dB point
as θ = 0.445λ/D . The 3-dB beamwidth extends from –θ to +θ and is therefore
0
0
0
y