0195136047.pdf

680 COMMUNICATION SYSTEMS

EXAMPLE 15.1.5

(a) Some antennas have a physical aperture areaAthat can be identified and is related to

the effective areaAebyAe=ρaA, whereρais known as theaperture efficiency.For a

circular-aperture antenna with a diameter of 2 m and an aperture efficiency of 0.5 at 4

GHz, calculate the power gain.

(b) Referring to Figure 15.1.5, let two such antennas be used for transmitting and receiving,

while the two stations are separated by 50 km. Let the total loss over the link be 9 dB,

while the transmitter generates 0.5 W. Find the available received power.

Solution

(a)λ=

c

f

=

3 × 108

4 × 109

= 0 .075 m. From Equation (15.1.17),

G=

4 πAe

λ^2

=

4 πρaA

λ^2

=

4 π× 0. 5 ×π

0. 0752

= 3509

(b)G=Gt=Gr= 3509 ;LdB=10 logL,orL= 7 .94. From Equation (15.1.24),

Sr=

0. 5 × 35092 × 0. 0752

( 4 π)^2 × 502 × 106 × 7. 94

∼= 1. 1 × 10 −^8 W

The variety and number of antennas are almost endless. However, for our introductory

purposes, they may be divided into the following types:

• Wire antennas,such as half-wavelength dipole, folded half-wave dipole, and helical antenna


• Array antennas,such as YAGI-UDA array


• Aperture antennas,such as pyramidal horn, conical horn, paraboloidal antenna, and Casse-
  grain antenna


• Lens-type antennasin radar and other applications.
  Some of their geometries are illustrated in Figure 15.1.7.
  Theradiation-intensity patterndescribing the power intensity in any spatial direction is
  an important antenna characteristic, since the antenna does not radiate power equally in all
  directions in space. Such patterns are three-dimensional in nature. One normally chooses spherical
  coordinates centered on the antenna atA, and represents the power-intensity functionP(θ,φ)at
  any distant pointRas a magnitudePfromA, which appears as a surface with a largemain lobe
  and severalside lobes(minor lobes), as shown in Figure 15.1.8.
  Generally speaking, in most of the communication systems the transmitting and receiving
  antennas (reciprocal elements) face each other directly such that their large main lobes point
  toward each other, and the received-power output will be maximum. When scaled such that
  the maximum intensity is unity, the radiation-intensity pattern is commonly called theradiation
  pattern. In many problems in practice, the radiation pattern occurs with one dominant main
  lobe, and as such, instead of considering the full three-dimensional picture, the behavior may
  adequately and conveniently be described in two orthogonal planes containing the maximum of
  the main lobe. These are known asprincipal-plane patternsin terms of anglesθandφ. Figure
  15.1.9 illustrates one such pattern in polar and linear angle plots as a function ofθ. The angular
  separation between points on the radiation pattern that are 3 dB down from the maximum is called