Phased Arrays - MATLAB Simulations for Radar Systems Design - page 314

Phased Arrays

Chapter 8

8.1. Directivity, Power Gain, and Effective Aperture
Radar antennas can be characterized by the directive gain , power gain
, and effective aperture . Antenna gain is a term used to describe the abil-
ity of an antenna to concentrate the transmitted energy in a certain direction.
Directive gain, or simply directivity, is more representative of the antenna radi-
ation pattern, while power gain is normally used in the radar equation. Plots of
the power gain and directivity, when normalized to unity, are called antenna
radiation pattern . The directivity of a transmitting antenna can be defined by

G D

G A e

maximum radiation intensity
average radiation intensity

G D = ---------------------------------------------------------------------------------

(8.1)

The radiation intensity is the power per unit solid angle in the direction
and denoted by ( θφ , ) P θφ ( , ) . The average radiation intensity over 4π radi-

ans (solid angle) is the total power divided by 4π . Hence, Eq. (8.1) can be

written as

4π maximum radiated power ( ⁄ unit solid angle )

G D = -------------------------------------------------------------------------------------------------------------------------------------

(8.2)

total radiated power

It follows that

P θφ ( , ) max

----------------------------------------

G D = 4π (8.3)

2π
∫

π
∫

P θφ ( , ) d d φ

0 0

As an approximation, it is customary to rewrite Eq. (8.3) as

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