Page 168 - Satellite Communications, Fourth Edition

148 Chapter Six

From the definition of directivity d, the maximum radiation intensity is

(6.8)
U max dU i
The beam solid angle, A , for an actual antenna is defined as the
solid angle through which all the power would flow to produce a constant
radiation intensity equal to the maximum value. Thus

P rad
U max A (6.9)

Combining Eqs. (6.7), (6.8), and (6.9) yields the important result

4p (6.10)
d 5
A
This is important because for narrow-beam antennas such as used in
many satellite communications systems, a good approximation to the
solid angle is

> HPBW HPBW H (6.11)
E
A
is the half-power beamwidth in the E plane and HPBW
where HPBW E H
is the half-power beamwidth in the H plane, as shown in Fig. 6.6. This
equation requires the half-power beamwidths to be expressed in radi-
ans, and the resulting solid angle is in steradians.
The usefulness of this relationship is that the half-power beamwidths
can be measured, and hence the directivity can be found. When the
half-power beamwidths are expressed in degrees, the equation for the
directivity becomes

41253
d 5 (6.12)
HPBW8 3 HPBW8 H
E
6.9 Effective Aperture
So far, the properties of antennas have been described in terms of their
radiation characteristics. A receiving antenna has directional properties
also described by the radiation pattern, but in this case it refers to the
ratio of received power normalized to the maximum value.
An important concept used to describe the reception properties of an
antenna is that of effective aperture. Consider a TEM wave of a given
power density at the receiving antenna. Let the load at the antenna
terminals be a complex conjugate match so that maximum power trans-
fer occurs and power P rec is delivered to the load. Note that the power
delivered to the actual receiver may be less than this as a result of