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224 ANTENNA BASICS

2

= (5.53)
4
Meanwhile, the directional antenna receives or transmits directivity-times more power than the
ideal isotropic radiator. Therefore, for any antenna, the effective aperture can be given as

2
= (5.54)
4
The equity (5.54) is interpreted in antenna theory as the critical definition independent of black
body physics and is written in the form

4
= (5.55)
2
This equity is another way to define the antenna directivity and extensively used in antenna
analysis, therefore, a remarkable fact that the effective antenna aperture can be established
by simple physical reasoning without complicated mathematical transformations like (5.47). As
an example, let us calculate the directivity of a parabolic dish antenna of 11 m diameter at the
frequency 11 GHz. Figure 5.2.13 illustrates the operational principle of a parabolic antenna as
the optic parabolic mirror with the point-size source of EM waves from the feed sited in focus
(point O). The 3D dish surface is formed by the rotation of the parabolic curve = around
2
the longitudinal z-axis. The idealized pattern of the point-size feed is close to isotropic and
shown in as the red circle. The parabolic reflector, as it is well-known from optics, has a
remarkable property: all waves radiated by the focal feed reach the dish aperture (the black
dotted line) at the same moment of time. Therefore, the dish front aperture shown on the left in
light blue can be considered as the
equivalent radiator with aperture
2
of = ⁄ 4. Unfortunately, this
ideal case doesn't happen in practice.
As demonstrated in 5.2.13 the
isotropic radiator is not the best feed
O
because a lot of energy radiated by it
Spillover slip the reflector (shown by
Loss shadowed grey area and yellow rays
in 5.2.13) and is lost. Evidently, the
feed like the one-directional
Figure 5.2.13 Geometry of parabolic dish antenna Huygens’ radiator shown in Figure
with focal feed 4.3.9 of Chapter 4 can diminish
energy waist called spillover loss but
not completely. There are many other factors (i.e. small deviations in the reflector shape and
many other irregularity in the production, slight variations in the field magnitude and phase
along the aperture, etc.) that degrade the dish antenna performance by reducing its gain. The
easiest way to account for all of these irregularities is to assume that the effective dish aperture
is less than its geometrical one by introducing the aperture efficiency factor

2

= =
4 � (5.56)
2

= � �