Introduction to Radar Basics - MATLAB Simulations for Radar Systems Design - page 14

increase the power density in a certain direction. Directional antennas are usu-
ally characterized by the antenna gain and the antenna effective aperture . G A e

They are related by

4π A e
λ 2

G = ------------

(1.40)

where is the wavelength. The relationship between the antennaÓs effective λ

aperture and the physical aperture is A e A

A e ρ A
0 ρ 1

= (1.41)

≤≤

is referred to as the aperture efficiency, and good antennas require . In
this topic we will assume, unless otherwise noted, that and are the same.
We will also assume that antennas have the same gain in the transmitting and
receiving modes. In practice,

ρ ρ → 1

A A e

is widely accepted. ρ = 0.7

The gain is also related to the antennaÓs azimuth and elevation beamwidths by

Gk 4π
θ e θ a

-----------

= (1.42)

where and depends on the physical aperture shape; the angles and

k ≤ 1 θ e θ a

are the antennaÓs elevation and azimuth beamwidths, respectively, in radians.
An excellent approximation of Eq. (1.42) introduced by Stutzman and reported
by Skolnik is

26000
θ e θ a

G ≈ --------------- (1.43)

where in this case the azimuth and elevation beamwidths are given in degrees.

The power density at a distance away from a radar using a directive

R

antenna of gain is then given by

G

P t G
4π R 2

P D = -------------

(1.44)

When the radar radiated energy impinges on a target, the induced surface cur-
rents on that target radiate electromagnetic energy in all directions. The amount
of the radiated energy is proportional to the target size, orientation, physical
shape, and material, which are all lumped together in one target-specific
parameter called the Radar Cross Section (RCS) denoted by

. σ

The radar cross section is defined as the ratio of the power reflected back to
the radar to the power density incident on the target,