Page 549 - Engineering Electromagnetics, 8th Edition

CHAPTER 14 ELECTROMAGNETIC RADIATION AND ANTENNAS 531

In the half-wave dipole, the standing wave current amplitude maximizes at the
feed point, and the antenna is said to be operated on resonance.Asa result, the driving
point impedance, one-quarter wavelength in front of the open ends, would in principle
4
be purely real and equal to the 73-
radiation resistance, assuming that the antenna
is otherwise lossless. This is the primary motivation for using half-wave dipoles, in
that they provide a fairly close impedance match to conventional transmission lines
(whose characteristic impedances are on the same order).
Actually, because the antenna is essentially an unfolded transmission line, the
half-wave dipole does not behave as an ideal quarter-wave transmission line section, as
we might suspect considering the discussions in Section 14.1. An appreciable reactive
part of the input impedance will likely be present, but the half-wavelength dimension
is very close to the length at which the reactance goes to zero. Methods of evaluating
the reactance are beyond the scope of our treatment, but are considered in detail in
Ref. 1. For a thin lossless dipole of length exactly λ/2, the input impedance would be
Z in = 73 + jX, where X is in the vicinity of 40
. The input reactance is extremely
sensitive to the antenna length and can be reduced to zero by a very slight reduction
in the overall length below λ/2, leaving the real part essentially unaffected. Similar
behavior is seen in dipoles having lengths that are integer multiples of λ/2, but in
these, radiation resistances are considerably higher, thus yielding a poorer impedance
match. At dipole lengths between half-wavelength multiples, input reactances can
be much higher (in the vicinity of j600
) and can become sensitive to the wire
thickness, in addition to the length. In practice, when connecting a transmission line
feed, the input reactance can be zeroed by length reduction or by using matching
techniques such as those discussed in Chapter 10.
Plots of directivity and radiation resistance as functions of antenna length are
shown in Figure 14.9. Directivity increases modestly with length, whereas radiation
resistancereachesalocalmaximumatalengthbetween3λ/4andλ.Atgreaterlengths,
additional peaks in R rad occur at higher levels, but performance is compromised by
the presence of sidelobes. Again, half-wave dipoles are typically used because single-
lobe behavior is assured over a broad spectral bandwidth, whereas radiation resistance
(73
)is close to the impedance of standard transmission lines that are used to feed
the antenna.
As a final exercise in wire antennas, we consider the operation of a monopole
antenna. This is one-half a dipole plus a perfectly conducting plane, as shown in Figure
14.10a. The image principle discussed in Section 5.5 provides the image shown in
Figure 14.10b,so that the monopole and its image form a dipole. Therefore, all field
equationsthatpertaintothedipoleapplydirectlytotheupperhalf-space.ThePoynting
vector is therefore also the same above the plane, but the integration to find the total
power radiated is performed only through the hemisphere that surrounds the upper
half-space. So the radiated power and the radiation resistance for the monopole are
half the corresponding values for the dipole. As an example, a quarter-wave monopole

4 Think of a half-rotation (λ/4) around the Smith chart from the open circuit point, toward the
generator, where, with loss present, the end position would be somewhere on the negative real axis.